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xfQxK+q7a}nQLf7;*yoRz9L@i=sr4T^Wy7A@wFCPVI$e*fCrleLzf!Ye^FKWBIj#Tz literal 0 HcmV?d00001 diff --git a/_sources/api/bilevel/external-solvers/MibS.rst.txt b/_sources/api/bilevel/external-solvers/MibS.rst.txt new file mode 100644 index 000000000..64ba6044a --- /dev/null +++ b/_sources/api/bilevel/external-solvers/MibS.rst.txt @@ -0,0 +1,7 @@ +Bilevel::MibS +============= + +Doxygen +------- + +.. doxygenclass:: idol::Bilevel::MibS diff --git a/_sources/api/bilevel/external-solvers/Optimizers_MibS.rst.txt b/_sources/api/bilevel/external-solvers/Optimizers_MibS.rst.txt new file mode 100644 index 000000000..7850d3ba3 --- /dev/null +++ b/_sources/api/bilevel/external-solvers/Optimizers_MibS.rst.txt @@ -0,0 +1,7 @@ +Optimizers::Bilevel::MibS +========================= + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::Bilevel::MibS diff --git a/_sources/api/bilevel/index.rst.txt b/_sources/api/bilevel/index.rst.txt new file mode 100644 index 000000000..476f15970 --- /dev/null +++ b/_sources/api/bilevel/index.rst.txt @@ -0,0 +1,29 @@ +Bilevel Optimization +==================== + +Modeling +^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + modeling/* + +External Solvers +^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + external-solvers/* + +Single-level Reformulations +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + single-level/* diff --git a/_sources/api/bilevel/modeling/Description.rst.txt b/_sources/api/bilevel/modeling/Description.rst.txt new file mode 100644 index 000000000..dcae7b4e8 --- /dev/null +++ b/_sources/api/bilevel/modeling/Description.rst.txt @@ -0,0 +1,7 @@ +Bilevel::Description +==================== + +Doxygen +------- + +.. doxygenclass:: idol::Bilevel::Description diff --git a/_sources/api/bilevel/single-level/KKT.rst.txt b/_sources/api/bilevel/single-level/KKT.rst.txt new file mode 100644 index 000000000..d6c9b29a3 --- /dev/null +++ b/_sources/api/bilevel/single-level/KKT.rst.txt @@ -0,0 +1,7 @@ +Bilevel::KKT +============ + +Doxygen +------- + +.. doxygenclass:: idol::Bilevel::KKT diff --git a/_sources/api/bilevel/single-level/Optimizers_KKT.rst.txt b/_sources/api/bilevel/single-level/Optimizers_KKT.rst.txt new file mode 100644 index 000000000..c54671562 --- /dev/null +++ b/_sources/api/bilevel/single-level/Optimizers_KKT.rst.txt @@ -0,0 +1,7 @@ +Optimizers::Bilevel::KKT +======================== + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::Bilevel::KKT diff --git a/_sources/api/bilevel/single-level/Optimizers_StrongDuality.rst.txt b/_sources/api/bilevel/single-level/Optimizers_StrongDuality.rst.txt new file mode 100644 index 000000000..1b454d906 --- /dev/null +++ b/_sources/api/bilevel/single-level/Optimizers_StrongDuality.rst.txt @@ -0,0 +1,7 @@ +Optimizers::Bilevel::StrongDuality +================================== + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::Bilevel::StrongDuality diff --git a/_sources/api/bilevel/single-level/StrongDuality.rst.txt b/_sources/api/bilevel/single-level/StrongDuality.rst.txt new file mode 100644 index 000000000..b77e55744 --- /dev/null +++ b/_sources/api/bilevel/single-level/StrongDuality.rst.txt @@ -0,0 +1,7 @@ +Bilevel::StrongDuality +============ + +Doxygen +------- + +.. doxygenclass:: idol::Bilevel::StrongDuality diff --git a/_sources/api/classes/external-bilevel/MibS.rst.txt b/_sources/api/classes/external-bilevel/MibS.rst.txt new file mode 100644 index 000000000..8e17661db --- /dev/null +++ b/_sources/api/classes/external-bilevel/MibS.rst.txt @@ -0,0 +1,4 @@ +Bilevel::Mibs +============= + +.. doxygenclass:: idol::Bilevel::MibS diff --git a/_sources/api/classes/external-bilevel/Optimizers_MibS.rst.txt b/_sources/api/classes/external-bilevel/Optimizers_MibS.rst.txt new file mode 100644 index 000000000..0a1017ce3 --- /dev/null +++ b/_sources/api/classes/external-bilevel/Optimizers_MibS.rst.txt @@ -0,0 +1,4 @@ +Optimizers::Bilevel::MibS +========================= + +.. doxygenclass:: idol::Optimizers::Bilevel::MibS diff --git a/_sources/api/classes/external-bilevel/index.rst.txt b/_sources/api/classes/external-bilevel/index.rst.txt new file mode 100644 index 000000000..b2e2114fd --- /dev/null +++ b/_sources/api/classes/external-bilevel/index.rst.txt @@ -0,0 +1,8 @@ +External Bilevel Solvers +======================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/api/classes/index.rst.txt b/_sources/api/classes/index.rst.txt new file mode 100644 index 000000000..45ca55f1d --- /dev/null +++ b/_sources/api/classes/index.rst.txt @@ -0,0 +1,36 @@ +.. _classes: + +Class List +========== + +Mixed-Integer Programming +^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 2 + :glob: + + common/index + external-mip/index + universal-callbacks/index + branch-and-bound/index + column-generation/index + +Bilevel Optimization +^^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 2 + :glob: + + external-bilevel/index + +Robust Optimization +^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 2 + :glob: + + column-and-constraint-generation/index + diff --git a/_sources/api/classes/universal-callbacks/Callback.rst.txt b/_sources/api/classes/universal-callbacks/Callback.rst.txt new file mode 100644 index 000000000..c25b37cef --- /dev/null +++ b/_sources/api/classes/universal-callbacks/Callback.rst.txt @@ -0,0 +1,85 @@ +.. _api_Callback: + +Callback +======== + +Callbacks are user-defined functions which are invoked during the execution of branch-and-bound algorithms at certain +key steps of the procedure. These key m_n_points_bound are called :ref:`events ` in idol. +Callback functions can be used to monitor the algorithm's progress, control its behavior, or perform additional processing. + +UserCutCallback and LazyCutCallback +----------------------------------- + +A common use of callbacks is to implement custom cut generation procedures at each node of the branch-and-bound tree. Note that +idol offers out-of-the-box callback routines for cut separation. Namely, :ref:`UserCutCallback ` +and :ref:`LazyCutCallback `. Yet, it is totally possible to define your own cut generation procedure +by using the ``Callback::add_user_cut`` and ``Callback::add_lazy_cut`` methods inside your callback. + +In a nutshell, :ref:`UserCutCallback ` (or, similarly, ``Callback::add_user_cut``) are intended for +cuts which have a potential to improve the quality of the relaxation but whose presence in the model is not necessary for the +branch-and-bound to converge to an optimal solution. :ref:`UserCutCallback ` callbacks are called when +a non-valid solution has been found. + +:ref:`LazyCutCallback ` (or, similarly, ``Callback::add_lazy_cut``), +instead, are intended to generate constraints which should be part of the model but which were omitted in the model for some reason. +A typical reason for omitting constraints in a model's definition is the large number of such constraints. +:ref:`LazyCutCallback ` callbacks are called when a valid solution has been found. + +Creating your own callback +-------------------------- + +If you want to create your own callback, you should first create a new class which inherits the ``Callback`` class and +overrides the ``operator()(CallbackEvent)`` method. + +Note that callbacks cannot be given "as-is" to an optimizer but must be passed through a ``CallbackFactory``. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the ``CallbackFactory`` class. + +.. admonition:: Example + + We now give an example of callback which prints out every valid solution found. + + .. code-block:: + + class MyCallback : public CallbackFactory { + public: + + class Strategy { // Real callback implementation + protected: + void operator()(CallbackEvent t_event) { + + if (t_event != IncumbentSolution) { + return; + } + + std::cout << primal_solution() << std::endl; + } + } + + Callback* operator()() { // Creates a new callback object + return new Strategy(); + } + + CallbackFactory* clone() const { // Creates a copy of the callback factory + return new MyCallback(*this); + } + + } + + Later, it is then possible to use this callback in compliant optimizers like :ref:`Gurobi ` or :ref:`BranchAndBound `. + + .. code-block:: + + model.use( + Gurobi().with_callback(MyCallback(); + ); + + model.optimize(); + +.. hint:: + + Note that there also exists more advanced callbacks which are specific to idol's branch-and-bound implementation. + For these advanced feature, see :ref:`BranchAndBoundCallback `. + +.. doxygenclass:: idol::Callback + :protected-members: diff --git a/_sources/api/classes/universal-callbacks/CallbackFactory.rst.txt b/_sources/api/classes/universal-callbacks/CallbackFactory.rst.txt new file mode 100644 index 000000000..e795fb1dd --- /dev/null +++ b/_sources/api/classes/universal-callbacks/CallbackFactory.rst.txt @@ -0,0 +1,7 @@ +.. _api_CallbackFactory: + +CallbackFactory +=============== + +.. doxygenclass:: idol::CallbackFactory + :protected-members: diff --git a/_sources/api/classes/universal-callbacks/LazyCutCallback.rst.txt b/_sources/api/classes/universal-callbacks/LazyCutCallback.rst.txt new file mode 100644 index 000000000..ab4842756 --- /dev/null +++ b/_sources/api/classes/universal-callbacks/LazyCutCallback.rst.txt @@ -0,0 +1,60 @@ +.. _api_LazyCutCallback: + +LazyCutCallback +=============== + +Lazy cuts are essentially constraints which are part of an optimization model but which have been omitted in the current +definition of the model. Lazy cuts typically arise in models with a large number of constraints. Instead of enumerating +then all, it may be judicious to omit some of them to get a smaller optimization model. Then, the returned solution is +checked for feasibility against the whole set of constraints. If a violated constraint is identified, we add the +constraint to the model and resolve. If not, then all the constraints are satisfied and the solution is optimal for the +original model in which all constraints materializes. + +The LazyCutCallback can be used to implement lazy cut constraint generation on the fly, during the optimization process. + +Consider the following optimization problem: + +.. math:: + + \begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X, \\ + & \xi^\top x \le \xi_0 \quad (\xi_0,\xi) \in \Xi, + \end{align} + +in which assume that :math:`|\Xi|` is large (potentially infinite). The idea is to start by solving the following +relaxed master problem in which constraints associated to :math:`(\xi_0,\xi)` have been omitted. + +.. math:: + + \begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X. + \end{align} + +If we assume that this problem is feasible and bounded, we can denote by :math:`x^*` a solution of this problem. Then, +we search for a violated constraint ":math:`\xi^\top x \le \xi_0`" for some :math:`(\xi_0,\xi)\in\Xi`. Observe that +a constraint is violated if, and only if, the following holds: + +.. math:: + + \left(\exists(\xi_0,\xi)\in\Xi, \ \xi^\top x^* > \xi_0\right) + \Leftrightarrow + \left(\max_{(\xi_0,\xi)\in\Xi} \xi_0 - \xi^\top x^* < 0\right). + +Thus, the LazyCutCallback automatically solve the optimization problem on the right handside and checks for its value. +A new constraint is added if, and only if, + +.. math:: + \max_{\xi\in\Xi} \xi_0 - \xi^\top x^* < -\varepsilon, + +with :math:`\varepsilon` a given tolerance (by default, :code:`Tolerance::Feasibility`). + + +.. hint:: + + You may also be interested by a tutorial showing how you can implement a simple Benders Decomposition using lazy + cuts. :ref:`See Benders Decomposition tutorial `. + + +.. doxygenclass:: idol::LazyCutCallback \ No newline at end of file diff --git a/_sources/api/classes/universal-callbacks/UserCutCallback.rst.txt b/_sources/api/classes/universal-callbacks/UserCutCallback.rst.txt new file mode 100644 index 000000000..cf10e6e11 --- /dev/null +++ b/_sources/api/classes/universal-callbacks/UserCutCallback.rst.txt @@ -0,0 +1,6 @@ +.. _api_UserCutCallback: + +UserCutCallback +=============== + +.. doxygenclass:: idol::UserCutCallback \ No newline at end of file diff --git a/_sources/api/classes/universal-callbacks/index.rst.txt b/_sources/api/classes/universal-callbacks/index.rst.txt new file mode 100644 index 000000000..e97ddd7ed --- /dev/null +++ b/_sources/api/classes/universal-callbacks/index.rst.txt @@ -0,0 +1,8 @@ +Universal Callbacks +=================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/api/index.rst.txt b/_sources/api/index.rst.txt new file mode 100644 index 000000000..e4e958365 --- /dev/null +++ b/_sources/api/index.rst.txt @@ -0,0 +1,31 @@ +.. _api: + +API +=== + +Mixed-Integer Optimization +-------------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + + mixed-integer/index + +Bilevel Optimization +-------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + + bilevel/index + +Robust Optimization +------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + + robust/index diff --git a/_sources/api/mixed-integer/branch-and-bound/BranchAndBound.rst.txt b/_sources/api/mixed-integer/branch-and-bound/BranchAndBound.rst.txt new file mode 100644 index 000000000..8bb0a6d5e --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/BranchAndBound.rst.txt @@ -0,0 +1,34 @@ +.. _api_BranchAndBound: + +BranchAndBound +============== + +This class is an optimizer factory which creates a new branch-and-bound algorithm. +It can be used to create customized branch-and-bound algorithms with a large degree of freedom. + +.. seealso:: + + If you are not familiar with optimizers and optimizer factories, please refer to :ref:`this page `. + +.. admonition:: Example + + Here, we create a simple branch-and-bound algorithm where branching is done on integer variables which are being + relaxed. Each node is solved by the external solver GLPK. Nodes are selected according to the "best-bound" + rule while variables are selected according to the "most-infeasible" branching rule. + + The created algorithm also incorporates sub-tree exploration of maximum depth 2. + + .. code-block:: + + model.use( + BranchAndBound() + .with_node_optimizer( GLPK::ContinuousRelaxation() ) + .with_branching_rule( MostInfeasible() ) + .with_node_selection_rule( BestBound() ) + .with_subtree_depth(2) + ); + +Doxygen +------- + +.. doxygenclass:: idol::BranchAndBound diff --git a/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.rst.txt b/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.rst.txt new file mode 100644 index 000000000..d1681de2b --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.rst.txt @@ -0,0 +1,77 @@ +.. _api_BranchAndBoundCallback: + +BranchAndBoundCallback +====================== + +This class can be used to create callbacks to run on idol's :ref:`branch-and-bound implementation `. + +.. warning:: + + BranchAndBoundCallback-s is an *advanced* feature. + + Please, make sure that what you are trying do cannot be done with + a :ref:`solver-independent callback ` first, or with pre-existing callbacks, e.g., + :ref:`UserCutCallback ` or :ref:`LazyCutCallback `. + + The advantage of using a :ref:`BranchAndBoundCallback ` instead of a standard + solver-independent :ref:`Callback ` lies in the possibility to access specific information regarding + the execution of the branch-and-bound algorithm. For instance, accessing a node's information, or the current + relaxation model being solved. + +.. admonition:: Example + + Here is an example of callback which prints out the event triggering it and, when the event corresponds to `NodeLoaded`, + prints the node's model to be solved. + + .. code-block:: + + class MyCallback : public BranchAndBoundCallbackFactory { + public: + class Strategy : public BranchAndBoundCallback { + protected: + void operator()(CallbackEvent t_event) override { + + std::cout << "MyCallback is called for " << t_event << std::endl; + + if (t_event != NodeLoaded) { + return; + } + + std::cout << "The problem being solve at node " << node().id() << std::endl; + std::cout << relaxation() << std::endl; + + } + }; + + BranchAndBoundCallback *operator()() override { + return new Strategy(); + } + + [[nodiscard]] BranchAndBoundCallbackFactory *clone() const override { + return new MyCallback(*this); + } + }; + + Then, this callback can be used as follows. + + .. code-block:: + + model.use( + BranchAndBound() + .with_node_optimizer(GLPK::ContinuousRelaxation()) + .with_branching_rule(MostInfeasible()) + .with_node_selection_rule(DepthFirst()) + .with_callback(MyCallback()); + ); + +.. hint:: + + By default, most of the objects returned by BranchAndBoundCallback methods are const. If you wish to access non-const + versions (e.g., if you want to perform non-standard updates to the relaxed model or want to change the node's current + information manually), you should use the advanced interface obtained by calling ``BranchAndBoundCallback::advanced_interface``. + +Doxygen +------- + +.. doxygenclass:: idol::BranchAndBoundCallback + :protected-members: diff --git a/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.rst.txt b/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.rst.txt new file mode 100644 index 000000000..e103318ee --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.rst.txt @@ -0,0 +1,8 @@ +BranchAndBoundCallbackFactory +============================= + +Doxygen +------- + +.. doxygenclass:: idol::BranchAndBoundCallbackFactory + :protected-members: diff --git a/_sources/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.rst.txt b/_sources/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.rst.txt new file mode 100644 index 000000000..37c445a63 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.rst.txt @@ -0,0 +1,7 @@ +Cuts::KnapsackCover +=================== + +Doxygen +------- + +.. doxygenclass:: idol::Cuts::KnapsackCover diff --git a/_sources/api/mixed-integer/branch-and-bound/cuts/index.rst.txt b/_sources/api/mixed-integer/branch-and-bound/cuts/index.rst.txt new file mode 100644 index 000000000..8b8d02276 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/cuts/index.rst.txt @@ -0,0 +1,10 @@ +More on Cutting Planes... +========================= + +.. toctree:: + :maxdepth: 1 + :glob: + + * + + diff --git a/_sources/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.rst.txt b/_sources/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.rst.txt new file mode 100644 index 000000000..a4eae3aa2 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.rst.txt @@ -0,0 +1,7 @@ +Heuristics::LocalBranching +========================== + +Doxygen +------- + +.. doxygenclass:: idol::Heuristics::LocalBranching diff --git a/_sources/api/mixed-integer/branch-and-bound/heuristics/RENS.rst.txt b/_sources/api/mixed-integer/branch-and-bound/heuristics/RENS.rst.txt new file mode 100644 index 000000000..95663f024 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/heuristics/RENS.rst.txt @@ -0,0 +1,7 @@ +Heuristics::RENS +================ + +Doxygen +------- + +.. doxygenclass:: idol::Heuristics::RENS diff --git a/_sources/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.rst.txt b/_sources/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.rst.txt new file mode 100644 index 000000000..15707b903 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.rst.txt @@ -0,0 +1,7 @@ +Heuristics::SimpleRounding +========================== + +Doxygen +------- + +.. doxygenclass:: idol::Heuristics::SimpleRounding diff --git a/_sources/api/mixed-integer/branch-and-bound/heuristics/index.rst.txt b/_sources/api/mixed-integer/branch-and-bound/heuristics/index.rst.txt new file mode 100644 index 000000000..8fa6d695b --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/heuristics/index.rst.txt @@ -0,0 +1,10 @@ +More on Heuristics... +===================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * + + diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/BestBound.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/BestBound.rst.txt new file mode 100644 index 000000000..3f55812a9 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/BestBound.rst.txt @@ -0,0 +1,7 @@ +BestBound +========= + +Doxygen +------- + +.. doxygenclass:: idol::BestBound diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.rst.txt new file mode 100644 index 000000000..343f55803 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.rst.txt @@ -0,0 +1,9 @@ +BestEstimate +============ + +The "best estimate" node selection rule was introduced in *J. J. H. Forrest, J. P. H. Hirst, J. A. Tomlin, (1974) Practical Solution of Large Mixed Integer Programming Problems with Umpire. Management Science 20(5):736-773*. + +Doxygen +------- + +.. doxygenclass:: idol::BestEstimate diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.rst.txt new file mode 100644 index 000000000..a9bf2e7c0 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.rst.txt @@ -0,0 +1,7 @@ +BreadthFirst +============ + +Doxygen +------- + +.. doxygenclass:: idol::BreadthFirst diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.rst.txt new file mode 100644 index 000000000..d7245e902 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.rst.txt @@ -0,0 +1,7 @@ +DepthFirst +========== + +Doxygen +------- + +.. doxygenclass:: idol::DepthFirst diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/WorstBound.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/WorstBound.rst.txt new file mode 100644 index 000000000..c70a55e5f --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/WorstBound.rst.txt @@ -0,0 +1,7 @@ +WorstBound +========== + +Doxygen +------- + +.. doxygenclass:: idol::WorstBound diff --git a/_sources/api/mixed-integer/branch-and-bound/node-selection/index.rst.txt b/_sources/api/mixed-integer/branch-and-bound/node-selection/index.rst.txt new file mode 100644 index 000000000..a167dcd80 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/node-selection/index.rst.txt @@ -0,0 +1,10 @@ +More on Node Selection Rules... +=============================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * + + diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.rst.txt new file mode 100644 index 000000000..bb0a56053 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.rst.txt @@ -0,0 +1,7 @@ +FirstInfeasibleFound +==================== + +Doxygen +------- + +.. doxygenclass:: idol::FirstInfeasibleFound diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.rst.txt new file mode 100644 index 000000000..daa2410d6 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.rst.txt @@ -0,0 +1,7 @@ +LeastInfeasible +=============== + +Doxygen +------- + +.. doxygenclass:: idol::LeastInfeasible diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.rst.txt new file mode 100644 index 000000000..45a18ebdf --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.rst.txt @@ -0,0 +1,7 @@ +MostInfeasible +============== + +Doxygen +------- + +.. doxygenclass:: idol::MostInfeasible diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.rst.txt new file mode 100644 index 000000000..0b3b06970 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.rst.txt @@ -0,0 +1,7 @@ +PseudoCost +========== + +Doxygen +------- + +.. doxygenclass:: idol::PseudoCost diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.rst.txt new file mode 100644 index 000000000..6fdcdc1bb --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.rst.txt @@ -0,0 +1,7 @@ +StrongBranching +=============== + +Doxygen +------- + +.. doxygenclass:: idol::StrongBranching diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.rst.txt new file mode 100644 index 000000000..3cb5d3fd7 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.rst.txt @@ -0,0 +1,7 @@ +UniformlyRandom +=============== + +Doxygen +------- + +.. doxygenclass:: idol::UniformlyRandom diff --git a/_sources/api/mixed-integer/branch-and-bound/variable-selection/index.rst.txt b/_sources/api/mixed-integer/branch-and-bound/variable-selection/index.rst.txt new file mode 100644 index 000000000..837c226a5 --- /dev/null +++ b/_sources/api/mixed-integer/branch-and-bound/variable-selection/index.rst.txt @@ -0,0 +1,10 @@ +More on Branching Rules... +========================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * + + diff --git a/_sources/api/mixed-integer/column-generation/ArtificialCosts.rst.txt b/_sources/api/mixed-integer/column-generation/ArtificialCosts.rst.txt new file mode 100644 index 000000000..a4e84bc7a --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/ArtificialCosts.rst.txt @@ -0,0 +1,7 @@ +DantzigWolfe::ArtificialCosts +============================= + +Doxygen +------- + +.. doxygenclass:: idol::DantzigWolfe::ArtificialCosts diff --git a/_sources/api/mixed-integer/column-generation/DantzigWolfeDecomposition.rst.txt b/_sources/api/mixed-integer/column-generation/DantzigWolfeDecomposition.rst.txt new file mode 100644 index 000000000..4391c9085 --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/DantzigWolfeDecomposition.rst.txt @@ -0,0 +1,12 @@ +DantzigWolfeDecomposition +========================= + +.. hint:: + + This page documents on the `DantzigWolfeDecomposition` optimizer factory. Note that there are also + :ref:`Dantzig-Wolfe Decomposition tutorials `. + +Doxygen +------- + +.. doxygenclass:: idol::DantzigWolfeDecomposition diff --git a/_sources/api/mixed-integer/column-generation/FarkasPricing.rst.txt b/_sources/api/mixed-integer/column-generation/FarkasPricing.rst.txt new file mode 100644 index 000000000..e4df87e79 --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/FarkasPricing.rst.txt @@ -0,0 +1,7 @@ +DantzigWolfe::FarkasPricing +=========================== + +Doxygen +------- + +.. doxygenclass:: idol::DantzigWolfe::FarkasPricing diff --git a/_sources/api/mixed-integer/column-generation/IntegerMaster.rst.txt b/_sources/api/mixed-integer/column-generation/IntegerMaster.rst.txt new file mode 100644 index 000000000..963dfb760 --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/IntegerMaster.rst.txt @@ -0,0 +1,12 @@ +Heuristics::IntegerMaster +========================= + +.. warning:: + + This heuristic can only be used with a :code:`BranchAndBound` optimizer in which nodes are solved by + :code:`DantzigWolfeDecomposition`. + +Doxygen +------- + +.. doxygenclass:: idol::Heuristics::IntegerMaster diff --git a/_sources/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.rst.txt b/_sources/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.rst.txt new file mode 100644 index 000000000..bbeb2cabc --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.rst.txt @@ -0,0 +1,7 @@ +Optimizers::DantzigWolfeDecomposition +===================================== + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::DantzigWolfeDecomposition diff --git a/_sources/api/mixed-integer/column-generation/stabilization/Neame.rst.txt b/_sources/api/mixed-integer/column-generation/stabilization/Neame.rst.txt new file mode 100644 index 000000000..7bc717ccd --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/stabilization/Neame.rst.txt @@ -0,0 +1,7 @@ +DantzigWolfe::Neame +=================== + +Doxygen +------- + +.. doxygenclass:: idol::DantzigWolfe::Neame diff --git a/_sources/api/mixed-integer/column-generation/stabilization/Wentges.rst.txt b/_sources/api/mixed-integer/column-generation/stabilization/Wentges.rst.txt new file mode 100644 index 000000000..ce08f5a4e --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/stabilization/Wentges.rst.txt @@ -0,0 +1,7 @@ +DantzigWolfe::Wentges +===================== + +Doxygen +------- + +.. doxygenclass:: idol::DantzigWolfe::Wentges diff --git a/_sources/api/mixed-integer/column-generation/stabilization/index.rst.txt b/_sources/api/mixed-integer/column-generation/stabilization/index.rst.txt new file mode 100644 index 000000000..623ba3536 --- /dev/null +++ b/_sources/api/mixed-integer/column-generation/stabilization/index.rst.txt @@ -0,0 +1,8 @@ +More on Stabilization... +======================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/api/mixed-integer/external-solvers/GLPK.rst.txt b/_sources/api/mixed-integer/external-solvers/GLPK.rst.txt new file mode 100644 index 000000000..292cddc18 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/GLPK.rst.txt @@ -0,0 +1,9 @@ +.. _api_GLPK: + +GLPK +==== + +Doxygen +------- + +.. doxygenclass:: idol::GLPK diff --git a/_sources/api/mixed-integer/external-solvers/Gurobi.rst.txt b/_sources/api/mixed-integer/external-solvers/Gurobi.rst.txt new file mode 100644 index 000000000..08da5ca28 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Gurobi.rst.txt @@ -0,0 +1,9 @@ +.. _api_Gurobi: + +Gurobi +====== + +Doxygen +------- + +.. doxygenclass:: idol::Gurobi diff --git a/_sources/api/mixed-integer/external-solvers/HiGHS.rst.txt b/_sources/api/mixed-integer/external-solvers/HiGHS.rst.txt new file mode 100644 index 000000000..29a1db733 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/HiGHS.rst.txt @@ -0,0 +1,7 @@ +HiGHS +===== + +Doxygen +------- + +.. doxygenclass:: idol::HiGHS diff --git a/_sources/api/mixed-integer/external-solvers/Mosek.rst.txt b/_sources/api/mixed-integer/external-solvers/Mosek.rst.txt new file mode 100644 index 000000000..67c74ca45 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Mosek.rst.txt @@ -0,0 +1,7 @@ +Mosek +===== + +Doxygen +------- + +.. doxygenclass:: idol::Mosek diff --git a/_sources/api/mixed-integer/external-solvers/Optimizers_GLPK.rst.txt b/_sources/api/mixed-integer/external-solvers/Optimizers_GLPK.rst.txt new file mode 100644 index 000000000..bafb40213 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Optimizers_GLPK.rst.txt @@ -0,0 +1,9 @@ +.. _api_Optimizers_GLPK: + +Optimizers::GLPK +================ + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::GLPK diff --git a/_sources/api/mixed-integer/external-solvers/Optimizers_Gurobi.rst.txt b/_sources/api/mixed-integer/external-solvers/Optimizers_Gurobi.rst.txt new file mode 100644 index 000000000..cbd72d1c6 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Optimizers_Gurobi.rst.txt @@ -0,0 +1,7 @@ +Optimizers::Gurobi +================== + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::Gurobi diff --git a/_sources/api/mixed-integer/external-solvers/Optimizers_HiGHS.rst.txt b/_sources/api/mixed-integer/external-solvers/Optimizers_HiGHS.rst.txt new file mode 100644 index 000000000..450932770 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Optimizers_HiGHS.rst.txt @@ -0,0 +1,7 @@ +Optimizers::HiGHS +================= + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::HiGHS diff --git a/_sources/api/mixed-integer/external-solvers/Optimizers_Mosek.rst.txt b/_sources/api/mixed-integer/external-solvers/Optimizers_Mosek.rst.txt new file mode 100644 index 000000000..a9fa22b54 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Optimizers_Mosek.rst.txt @@ -0,0 +1,7 @@ +Optimizers::Mosek +================= + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::Mosek diff --git a/_sources/api/mixed-integer/external-solvers/Osi.rst.txt b/_sources/api/mixed-integer/external-solvers/Osi.rst.txt new file mode 100644 index 000000000..b46006e02 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Osi.rst.txt @@ -0,0 +1,40 @@ +More on coin-or/Osi (Cplex, Xpress, Cbc, ...)... +================================================ + +Idol can be linked with the `coin-or/Osi `_ library (*Open Solver Interface*) to use any solver having an osi interface. + +.. hint:: + + At the moment, only Cplex has been properly tested and can be used as follows. + + .. code-block:: + + model.use(OsiCplex()); + +.. hint:: + + Note that Osi can also be used with *any* Osi object by directly passing the interface as an argument. + + .. code-block:: + + model.use(Osi(OsiCpxSolverInterface())); // same as: model.use(OsiCplex()); + +.. warning:: + + Though idol has dedicated optimizers for Symphony, Cbc and Clp, it seems that the osi interface for these solvers do not + fully fulfill the interface requirement to have a stable usage. + +Related Classes +--------------- + +.. toctree:: + :maxdepth: 1 + :glob: + + Osi/* + +Doxygen +------- + +.. doxygenclass:: idol::Osi + diff --git a/_sources/api/mixed-integer/external-solvers/Osi/OsiCbc.rst.txt b/_sources/api/mixed-integer/external-solvers/Osi/OsiCbc.rst.txt new file mode 100644 index 000000000..294265d15 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Osi/OsiCbc.rst.txt @@ -0,0 +1,7 @@ +OsiCbc +====== + +Doxygen +------- + +.. doxygenclass:: idol::OsiCbc diff --git a/_sources/api/mixed-integer/external-solvers/Osi/OsiClp.rst.txt b/_sources/api/mixed-integer/external-solvers/Osi/OsiClp.rst.txt new file mode 100644 index 000000000..c16077c24 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Osi/OsiClp.rst.txt @@ -0,0 +1,7 @@ +OsiClp +====== + +Doxygen +------- + +.. doxygenclass:: idol::OsiClp diff --git a/_sources/api/mixed-integer/external-solvers/Osi/OsiCplex.rst.txt b/_sources/api/mixed-integer/external-solvers/Osi/OsiCplex.rst.txt new file mode 100644 index 000000000..8e35077b8 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Osi/OsiCplex.rst.txt @@ -0,0 +1,7 @@ +OsiCplex +======== + +Doxygen +------- + +.. doxygenclass:: idol::OsiCplex diff --git a/_sources/api/mixed-integer/external-solvers/Osi/OsiSymphony.rst.txt b/_sources/api/mixed-integer/external-solvers/Osi/OsiSymphony.rst.txt new file mode 100644 index 000000000..7c92f8d35 --- /dev/null +++ b/_sources/api/mixed-integer/external-solvers/Osi/OsiSymphony.rst.txt @@ -0,0 +1,7 @@ +OsiSymphony +=========== + +Doxygen +------- + +.. doxygenclass:: idol::OsiSymphony diff --git a/_sources/api/mixed-integer/index.rst.txt b/_sources/api/mixed-integer/index.rst.txt new file mode 100644 index 000000000..d40ce1a90 --- /dev/null +++ b/_sources/api/mixed-integer/index.rst.txt @@ -0,0 +1,64 @@ +.. _classes: + +Mixed-integer Optimization +========================== + +Modeling +^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + modeling/* + +External Solvers +^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + external-solvers/* + +Branch-and-Bound +^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + branch-and-bound/* + branch-and-bound/variable-selection/index + branch-and-bound/node-selection/index + branch-and-bound/heuristics/index + branch-and-bound/cuts/index + +Branch-and-Price +^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + column-generation/* + column-generation/stabilization/index + +Penalty Alternating Direction Method +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + padm/* + +Miscellaneous +^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + misc/* + diff --git a/_sources/api/mixed-integer/misc/CtrType.rst.txt b/_sources/api/mixed-integer/misc/CtrType.rst.txt new file mode 100644 index 000000000..ab331e899 --- /dev/null +++ b/_sources/api/mixed-integer/misc/CtrType.rst.txt @@ -0,0 +1,6 @@ +.. _api_CtrType: + +CtrType +======= + +.. doxygenenum:: idol::CtrType diff --git a/_sources/api/mixed-integer/misc/VarType.rst.txt b/_sources/api/mixed-integer/misc/VarType.rst.txt new file mode 100644 index 000000000..75c7d75e8 --- /dev/null +++ b/_sources/api/mixed-integer/misc/VarType.rst.txt @@ -0,0 +1,6 @@ +.. _api_variables_VarType: + +VarType +======= + +.. doxygenenum:: idol::VarType diff --git a/_sources/api/mixed-integer/misc/tolerances.rst.txt b/_sources/api/mixed-integer/misc/tolerances.rst.txt new file mode 100644 index 000000000..ae604d5a3 --- /dev/null +++ b/_sources/api/mixed-integer/misc/tolerances.rst.txt @@ -0,0 +1,6 @@ +.. _api_tolerances: + +Tolerances +========== + +.. doxygenfile:: numericals.h \ No newline at end of file diff --git a/_sources/api/mixed-integer/modeling/Annotation.rst.txt b/_sources/api/mixed-integer/modeling/Annotation.rst.txt new file mode 100644 index 000000000..3eccbd59b --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Annotation.rst.txt @@ -0,0 +1,30 @@ +Annotation +========== + +Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +The Annotation class takes one template arguments which is the value type. For instance, we +can create an annotation of type :code:`unsigned int` as follows. + +.. code:: cpp + + Env env; + + const unsigned int default_value = 0; + + Annotation annotation(env, "my_annotation", default_value); + +Annotations are global, i.e., they do not relate to a given optimization model and can, therefore, be accessed +anywhere in the code. Thus, given a constraint called :code:`constraint`, the value of the annotation can be accessed +by calling the :code:`Ctr::get` method. + +.. code:: cpp + + std::cout << "My annotation is " << constraint.get(annotation) << std::endl; // "0", i.e., the default_value value + +Annotations are, in particular, used to give decomposition instructions to idol when designing a Branch-and-Price algorithm. +To learn more, check our `Branch-and-Price tutorials `_. + +Doxygen +------- + +.. doxygenclass:: idol::Annotation diff --git a/_sources/api/mixed-integer/modeling/Ctr.rst.txt b/_sources/api/mixed-integer/modeling/Ctr.rst.txt new file mode 100644 index 000000000..92aacde21 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Ctr.rst.txt @@ -0,0 +1,9 @@ +.. _api_Ctr: + +Ctr +=== + +Doxygen +------- + +.. doxygenclass:: idol::Ctr diff --git a/_sources/api/mixed-integer/modeling/Dim.rst.txt b/_sources/api/mixed-integer/modeling/Dim.rst.txt new file mode 100644 index 000000000..cf6c45f8d --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Dim.rst.txt @@ -0,0 +1,9 @@ +.. _api_Dim: + +Dim +=== + +Doxygen +------- + +.. doxygenclass:: idol::Dim diff --git a/_sources/api/mixed-integer/modeling/Env.rst.txt b/_sources/api/mixed-integer/modeling/Env.rst.txt new file mode 100644 index 000000000..ff6860cee --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Env.rst.txt @@ -0,0 +1,9 @@ +.. _api_Env: + +Env +=== + +Doxygen +------- + +.. doxygenclass:: idol::Env diff --git a/_sources/api/mixed-integer/modeling/Expr.rst.txt b/_sources/api/mixed-integer/modeling/Expr.rst.txt new file mode 100644 index 000000000..1761afc42 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Expr.rst.txt @@ -0,0 +1,9 @@ +.. _api_Expr: + +AffExpr +======= + +Doxygen +------- + +.. doxygenclass:: idol::AffExpr diff --git a/_sources/api/mixed-integer/modeling/LinExpr.rst.txt b/_sources/api/mixed-integer/modeling/LinExpr.rst.txt new file mode 100644 index 000000000..305434c44 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/LinExpr.rst.txt @@ -0,0 +1,27 @@ +.. _api_LinExpr: + +LinExpr +======= + +This class is used to represent linear expressions in the modeling interface of idol. + +It consists in a set of linear terms which represent products of keys (typically, variables) and scalars. + +.. admonition:: Example + + In this example, we create a linear expression representing the following linear expression. + + .. math:: + + 3 x_0 + 2 x_1 + + .. code-block:: cpp + + auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x"); + + LinExpr lin_expr = 3 * x[0] + 2 * x[1]; + +Doxygen +------- + +.. doxygenclass:: idol::LinExpr diff --git a/_sources/api/mixed-integer/modeling/Model.rst.txt b/_sources/api/mixed-integer/modeling/Model.rst.txt new file mode 100644 index 000000000..f165bfdce --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Model.rst.txt @@ -0,0 +1,9 @@ +.. _api_Model: + +Model +===== + +Doxygen +------- + +.. doxygenclass:: idol::Model diff --git a/_sources/api/mixed-integer/modeling/Point.rst.txt b/_sources/api/mixed-integer/modeling/Point.rst.txt new file mode 100644 index 000000000..9856d9ac3 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Point.rst.txt @@ -0,0 +1,6 @@ +.. _api_Point: + +Point +===== + +.. doxygenclass:: idol::Point diff --git a/_sources/api/mixed-integer/modeling/QCtr.rst.txt b/_sources/api/mixed-integer/modeling/QCtr.rst.txt new file mode 100644 index 000000000..94c6c8de4 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/QCtr.rst.txt @@ -0,0 +1,9 @@ +.. _api_QCtr: + +QCtr +==== + +Doxygen +------- + +.. doxygenclass:: idol::QCtr diff --git a/_sources/api/mixed-integer/modeling/QuadExpr.rst.txt b/_sources/api/mixed-integer/modeling/QuadExpr.rst.txt new file mode 100644 index 000000000..fa0818bb4 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/QuadExpr.rst.txt @@ -0,0 +1,9 @@ +.. _api_QuadExpr: + +QuadExpr +======== + +Doxygen +------- + +.. doxygenclass:: idol::QuadExpr diff --git a/_sources/api/mixed-integer/modeling/TempCtr.rst.txt b/_sources/api/mixed-integer/modeling/TempCtr.rst.txt new file mode 100644 index 000000000..c895ea82e --- /dev/null +++ b/_sources/api/mixed-integer/modeling/TempCtr.rst.txt @@ -0,0 +1,9 @@ +.. _api_TempCtr: + +TempCtr +======= + +Doxygen +------- + +.. doxygenclass:: idol::TempCtr diff --git a/_sources/api/mixed-integer/modeling/TempQCtr.rst.txt b/_sources/api/mixed-integer/modeling/TempQCtr.rst.txt new file mode 100644 index 000000000..4501b7342 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/TempQCtr.rst.txt @@ -0,0 +1,9 @@ +.. _api_TempCtr: + +TempQCtr +======== + +Doxygen +------- + +.. doxygenclass:: idol::TempQCtr diff --git a/_sources/api/mixed-integer/modeling/TempVar.rst.txt b/_sources/api/mixed-integer/modeling/TempVar.rst.txt new file mode 100644 index 000000000..05310beb7 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/TempVar.rst.txt @@ -0,0 +1,9 @@ +.. _api_mip_variables_TempVar: + +TempVar +======= + +Doxygen +------- + +.. doxygenclass:: idol::TempVar diff --git a/_sources/api/mixed-integer/modeling/Var.rst.txt b/_sources/api/mixed-integer/modeling/Var.rst.txt new file mode 100644 index 000000000..e5e0fa7b0 --- /dev/null +++ b/_sources/api/mixed-integer/modeling/Var.rst.txt @@ -0,0 +1,9 @@ +.. _api_Var: + +Var +=== + +Doxygen +------- + +.. doxygenclass:: idol::Var diff --git a/_sources/api/mixed-integer/padm/Optimizers_PADM.rst.txt b/_sources/api/mixed-integer/padm/Optimizers_PADM.rst.txt new file mode 100644 index 000000000..cd9653869 --- /dev/null +++ b/_sources/api/mixed-integer/padm/Optimizers_PADM.rst.txt @@ -0,0 +1,9 @@ +.. _api_Optimizers_PADM: + +Optimizers::PADM +================ + +Doxygen +------- + +.. doxygenclass:: idol::Optimizers::PADM diff --git a/_sources/api/mixed-integer/padm/PADM.rst.txt b/_sources/api/mixed-integer/padm/PADM.rst.txt new file mode 100644 index 000000000..dea027a77 --- /dev/null +++ b/_sources/api/mixed-integer/padm/PADM.rst.txt @@ -0,0 +1,9 @@ +.. _api_PADM: + +PADM +==== + +Doxygen +------- + +.. doxygenclass:: idol::PADM diff --git a/_sources/api/robust/index.rst.txt b/_sources/api/robust/index.rst.txt new file mode 100644 index 000000000..e75f38004 --- /dev/null +++ b/_sources/api/robust/index.rst.txt @@ -0,0 +1,11 @@ +Robust Optimization +=================== + +Modeling +^^^^^^^^ + +.. toctree:: + :maxdepth: 1 + :glob: + + modeling/* diff --git a/_sources/api/robust/modeling/Description.rst.txt b/_sources/api/robust/modeling/Description.rst.txt new file mode 100644 index 000000000..832fd192e --- /dev/null +++ b/_sources/api/robust/modeling/Description.rst.txt @@ -0,0 +1,7 @@ +Robust::Description +=================== + +Doxygen +------- + +.. doxygenclass:: idol::Robust::Description diff --git a/_sources/api/types/index.rst.txt b/_sources/api/types/index.rst.txt new file mode 100644 index 000000000..64cc0da19 --- /dev/null +++ b/_sources/api/types/index.rst.txt @@ -0,0 +1,16 @@ +.. _types: + +Type List +========= + +Mixed-Integer Programming +^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. toctree:: + :maxdepth: 2 + :glob: + + common/index + universal-callbacks/index + + diff --git a/_sources/api/types/universal-callbacks/CallbackEvent.rst.txt b/_sources/api/types/universal-callbacks/CallbackEvent.rst.txt new file mode 100644 index 000000000..823233be2 --- /dev/null +++ b/_sources/api/types/universal-callbacks/CallbackEvent.rst.txt @@ -0,0 +1,6 @@ +.. _api_CallbackEvent: + +Events +====== + +.. doxygenenum:: idol::CallbackEvent \ No newline at end of file diff --git a/_sources/api/types/universal-callbacks/index.rst.txt b/_sources/api/types/universal-callbacks/index.rst.txt new file mode 100644 index 000000000..f04d73b46 --- /dev/null +++ b/_sources/api/types/universal-callbacks/index.rst.txt @@ -0,0 +1,9 @@ +Universal Callbacks +=================== + +.. toctree:: + :maxdepth: 1 + :glob: + + * + diff --git a/_sources/benchmark/index.rst.txt b/_sources/benchmark/index.rst.txt new file mode 100644 index 000000000..8dddf3132 --- /dev/null +++ b/_sources/benchmark/index.rst.txt @@ -0,0 +1,14 @@ +.. _benchmark: + +Benchmark +========= + +.. warning:: + + This page is under construction. + +Branch-and-Price for the Generalized Assignment Problem +------------------------------------------------------- + +.. image:: ../_static/ecdf-gap.png + diff --git a/_sources/developer_guide/build-the-doc.rst.txt b/_sources/developer_guide/build-the-doc.rst.txt new file mode 100644 index 000000000..6a425388d --- /dev/null +++ b/_sources/developer_guide/build-the-doc.rst.txt @@ -0,0 +1,61 @@ +.. highlight:: sh +.. _dev_build_the_doc: + +Build the Documentation +======================== + +This page explains how to build the documentation on a local machine. + +Dependencies +------------ + +Description +^^^^^^^^^^^ + +The documentation is built using `doxygen`_ and a bunch of other tools, in particular: + +* `doxygen`_ the C++ documentation generator; +* `Sphinx`_ the python documentation generator; +* `sphinx-rtd-theme `_ a Sphinx theme used to render the + HTML version of the documentation; +* `sphinx-sitemap `_ a Sphinx extension + to generate multi-version and multi-language sitemaps.org compliant sitemaps for the HTML version + of a Sphinx documentation; +* `sphinx-copybutton `_ a Sphinx extension which + automatically adds buttons on code-blocks environments to copy its content; +* `Breathe`_ the Sphinx plugin for integrating doxygen outputs into Sphinx. + +For a detailed description on how these tools interact, please refer to `this article `_. + +Installation guide (Ubuntu) +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +:: + + sudo apt-get install doxygen # installs the last version of doxygen + + sudo apt-get install python3-sphinx # installs the last version of Sphinx + + sudo apt-get install python3-breathe # installs the last version of Breathe + + pip3 install sphinx-sitemap sphinx-rtd-theme sphinx-copybutton # installs theme and extensions + +Build instructions +------------------ + +By default, CMake automatically creates a ``doc`` target. All you have to do to build the documentation website +is to build this target. For instance, inside a ``build`` directory, the following command can be used. + +:: + + cmake .. && make doc + +Note that you do not need to use ``make`` and use the following generic command. + +:: + + cmake --build . --target doc + +.. _doxygen: https://doxygen.nl/ +.. _Sphinx: https://www.sphinx-doc.org/en/master/ +.. _Breathe: https://github.com/breathe-doc/breathe \ No newline at end of file diff --git a/_sources/developer_guide/index.rst.txt b/_sources/developer_guide/index.rst.txt new file mode 100644 index 000000000..02af0cc17 --- /dev/null +++ b/_sources/developer_guide/index.rst.txt @@ -0,0 +1,33 @@ +.. _dev: + +Developers +========== + +Unit Tests and Integration +-------------------------- + +idol is tested using :code:`Catch2`. Currently, the level of testing is not sufficient, but we are working on it. + +Here is a grid plot of the code coverage: + +.. image:: https://codecov.io/gh/hlefebvr/idol/graphs/tree.svg?token=BWMH5522QP + :align: center + +*Each block represents a single file in the project. The size and color of each block is represented by the number of statements and the coverage, respectively.* (`see codecov `_) + +For more information on how to run the tests, please refer to the :ref:`tests` page. + +Building the Documentation +-------------------------- + +The documentation is built using `doxygen `_ and a bunch of other tools. For more information, please refer to the :ref:`dev_build_the_doc` page. + +Related Pages +------------- + +.. toctree:: + :maxdepth: 2 + :glob: + + build-the-doc + tests \ No newline at end of file diff --git a/_sources/developer_guide/tests.rst.txt b/_sources/developer_guide/tests.rst.txt new file mode 100644 index 000000000..aed0c370f --- /dev/null +++ b/_sources/developer_guide/tests.rst.txt @@ -0,0 +1,91 @@ +.. _tests: + +Unit and Integration Tests +========================== + +This page explains how to build the unit and integration tests on a local machine. + +Dependencies +------------ + +Tests are managed by the C++ unit testing framework `Catch2 `_. + +When CMake is told to create test targets, it will automatically look for an installation of Catch2 on your +machine. If it cannot be found, CMake will attempt to download Catch2 from its GitHub repository. + + +Installation guide (Ubuntu) +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code-block:: shell + + git clone https://github.com/catchorg/Catch2.git # Clone Catch2 repository + + cd Catch2 # go inside the new directory + + cmake -Bbuild -H. -DBUILD_TESTING=OFF # Create install target + + sudo cmake --build build/ --target install # Build and install + + +Build instructions +------------------ + +By default, CMake will not create test targets nor look for Catch2. To tell CMake to generate them, you +need to set the CMake option ``BUILD_TESTS`` to ``YES``. + + +.. admonition:: Example + + The following will tell CMake to create targets for tests. + + .. code-block:: + + cmake -DBUILD_TESTS=YES .. + + For instance, we can now build all the existing tests + + .. code-block:: + + make tests + + and run them. + + .. code-block:: + + ./tests/tests + +Code coverage options +--------------------- + +Code coverage is done via ``gcov``. + +If you want to active code coverage options, you shall set the CMake option ``WITH_TEST_COVERAGE`` to ``YES``. +Note that this only has an effect when ``BUILD_TESTS`` is also set to ``YES``. + +.. admonition:: Example + + The following command will tell CMake to generate targets for tests with code coverage options. + + .. code-block:: + + cmake -DBUILD_TESTS=YES -DWITH_CODE_COVERAGE=YES .. + + Then, you should build and run the tests. + + .. code-block:: + + make tests && ./tests/tests + + Once you are there, you may generate a report to a file called ``coverage.info`` by using ``gcov``. + + .. code-block:: + + lcov --directory . --capture --output-file coverage.info + +Also note that this forces ``g++`` to be used for compiling. + +.. tip:: + + Code coverage reports are also automatically generated at every push action on idol's GitHub repository and + are available on `codecov `_. diff --git a/_sources/examples/bilevel-kkt.rst.txt b/_sources/examples/bilevel-kkt.rst.txt new file mode 100644 index 000000000..8404fe2df --- /dev/null +++ b/_sources/examples/bilevel-kkt.rst.txt @@ -0,0 +1,37 @@ +.. _example_bilevel_kkt: + +Solving an optimistic LP-LP bilevel problem with KKT reformulation +================================================================== + +Problem Definition +------------------ + +This example is taken from :cite:`Kleinert2021` and is an LP-LP bilevel problem. + +The problem is formulated as follows: + +.. math:: + + \begin{align} + \min_{x, y} \quad & x + 6 y \\ + \text{s.t.} \quad & -x + 5y \le 12.5, \\ + & x \ge 0, \\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & -y \\ + \text{s.t.} \quad & 2 x - y \ge 0, \\ + & -x - y \ge -6, \\ + & -x + 6 y \ge -3, \\ + & x + 3 y \ge 3. + \end{array} + \end{align} + +In this example, we will reformulate the bilevel problem as a single-level problem using the KKT conditions. +The resulting problem will be solved by Gurobi as an NLP. Note that it is also possible to provide valid big-Ms to +reformulate this problem as an MILP. Check out our tutorials to learn more. + +Implementation +-------------- + +.. literalinclude:: ../../examples/bilevel/kkt.example.cpp + :language: cpp diff --git a/_sources/examples/bilevel-mibs.rst.txt b/_sources/examples/bilevel-mibs.rst.txt new file mode 100644 index 000000000..cdec56c34 --- /dev/null +++ b/_sources/examples/bilevel-mibs.rst.txt @@ -0,0 +1,34 @@ +.. _example_mibs: + +Solving an optimistic MILP-MILP bilevel problem with coin-or/MibS +================================================================= + +Problem Definition +------------------ + +This example is taken from :cite:`Moore1990` and is a bilevel problem where the upper level is a mixed-integer linear program (MILP) and the lower level is a mixed-integer linear program (MILP). + +The problem is formulated as follows: + +.. math:: + + \begin{align} + \min_{x, y} \quad & -x + -10 y \\ + \text{s.t.} \quad & x \in \mathbb Z_{\ge 0 },\\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & y \\ + \text{s.t.} \quad & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_{\ge 0}. + \end{array} + \end{align} + +Implementation +-------------- + +.. literalinclude:: ../../examples/bilevel/mibs.example.cpp + :language: cpp diff --git a/_sources/examples/bilevel-pessimistic.rst.txt b/_sources/examples/bilevel-pessimistic.rst.txt new file mode 100644 index 000000000..840cd2eb1 --- /dev/null +++ b/_sources/examples/bilevel-pessimistic.rst.txt @@ -0,0 +1,67 @@ +.. _example_bilevel_pessimistic: + +Solving a pessimistic bilevel problem using an optimistic reformulation +======================================================================= + +Problem Definition +------------------ + +This example is taken from :cite:`Zeng2020` (example 1) and is an LP-LP bilevel problem. + +.. math:: + + \begin{align} + \min_{x} \quad & -8 x_1 - 6x_2 + \max_{ y\in S(x) } - 25 y_1 - 30 y_2 + 2 y_3 + 16 y_4 \\ + \text{s.t.} \quad & x_1 + x_2 \le 10, \\ + & x_1, x_2 \ge 0, + \end{align} + +where :math:`S(x)` is defined as + +.. math:: + \begin{align} + S(x) := \underset{y}{\text{arg min}} \ & -10 y_1 - 10 y_2 - 10 y_3 - 10 y_4 \\ + \text{s.t.} \ & y_1 + y_2 + y_3 + y_4 \le 10 - x_1 - x_2, \\ + & -y_1 + y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & y_2 + y_4 \le 4 x_2, \\ + & y_1, y_2, y_3, y_4 \ge 0. + \end{align} + + +In this example, we will reformulate this pessimistic bilevel problem as an optimistic one. Then, we will solve it +using its KKT reformulation. The resulting problem will be solved by Gurobi as an MILP. + +.. hint:: + + Here, the optimistic reformulation reads as follows. + + .. math:: + + \begin{align} + \min_{x, \bar y, y} \quad & -8 x_1 - 6x_2 - 25 y_1 - 30 y_2 + 2 y_3 + 16 y_4 \\ + \text{s.t.} \quad & x_1 + x_2 \le 10, \\ + & x_1, x_2 \ge 0, \\ + & \bar y_1 + \bar y_2 + \bar y_3 + \bar y_4 \le 10 - x_1 - x_2, \\ + & -\bar y_1 + \bar y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & \bar y_2 + \bar y_4 \le 4 x_2, \\ + & \bar y_1, \bar y_2, \bar y_3, \bar y_4 \ge 0, \\ + & y \in \tilde S(x, \bar y), + \end{align} + + in which :math:`\tilde S(x)` is defined as + + .. math:: + \begin{align} + S(x) := \underset{y}{\text{arg min}} \quad & 25 y_1 + 30 y_2 - 2 y_3 - 16 y_4 \\ + \text{s.t.} \quad & y_1 + y_2 + y_3 + y_4 \le 10 - x_1 - x_2, \\ + & -y_1 + y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & y_2 + y_4 \le 4 x_2, \\ + & -10 y_1 - 10 y_2 - 10 y_3 - 10 y_4 \le -10 \bar y_1 - 10 \bar y_2 - 10 \bar y_3 - 10 \bar y_4, \\ + & y_1, y_2, y_3, y_4 \ge 0. + \end{align} + +Implementation +-------------- + +.. literalinclude:: ../../examples/bilevel/pessimistic.example.cpp + :language: cpp diff --git a/_sources/examples/facility-location-problem.rst.txt b/_sources/examples/facility-location-problem.rst.txt new file mode 100644 index 000000000..5150d706d --- /dev/null +++ b/_sources/examples/facility-location-problem.rst.txt @@ -0,0 +1,47 @@ +.. _example_flp: + +Solving a facility location problem with a custom branch-and-bound +================================================================== + +Problem Definition +------------------ + +We consider the capacitated Facility Location Problem (FLP). +Given a set of potential facility locations :math:`V_1` and a set of customers :math:`V_2`, the goal is to select +a subset of facility location to activate in order to serve all customers' demand, while minimizing the total cost. + +Each facility :math:`i\in V_1` has an opening cost :math:`f_i` and a maximum capacity :math:`q_i`. +Each customer :math:`j\in V_2` has a demand :math:`d_j`. +The unitary cost for serving customer :math:`j\in V_2` from facility :math:`i\in V_1` is :math:`t_{ij}`. + +We model the capacitated FLP with the MILP: + +.. math:: + + \begin{align*} + \min_{x,y} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j y_{ij} \le q_i, && i\in V_1, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. + \end{align*} + +Instance +-------- + +We will use an instance stored in a file called `facility.data.txt`. This file reads + +.. literalinclude:: ../../examples/mixed-integer/facility.data.txt + +On the first line, the number of facilities and the numbers of customers are specified. +Then, for each facility, the opening cost and the capacity are given. +For each customer, the demand is given. +Finally, the cost of serving each customer from each facility is given. + + +Implementation +-------------- + +.. literalinclude:: ../../examples/mixed-integer/facility.example.cpp + :language: cpp diff --git a/_sources/examples/generalized-assignment-problem-bap.rst.txt b/_sources/examples/generalized-assignment-problem-bap.rst.txt new file mode 100644 index 000000000..b3ff048ee --- /dev/null +++ b/_sources/examples/generalized-assignment-problem-bap.rst.txt @@ -0,0 +1,40 @@ +.. _example_gap_bap: + +Solving a generalized assignment problem by column generation and branch-and-price +================================================================================== + +Problem Definition +------------------ + +Given a set of :math:`m` agents and :math:`n` jobs, the goal is to assign each job to exactly one agent in such a +way that the total cost is minimized, while respecting the capacity constraints of each agent. + +Each agent :math:`i\in\{1,\dotsc,m\}` has a capacity :math:`C_i`. +Each job :math:`j\in\{1,\dotsc,n\}` has a resource consumption :math:`r_{ij}` and a cost :math:`c_{ij}` when assigned to agent :math:`i`. + +We model the GAP with the following binary linear program: + +.. math:: + + \begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij} \le C_i, && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in \{0,1\}, && i=1,\dotsc,m, j=1,\dotsc,n. + \end{align*} + +Decomposition +------------- + +In this example, we use a Dantzig-Wolfe decomposition to break down the problem into a master problem and as many subproblems as agents. +The master problem coordinates the assignment of jobs to agents, while the subproblems handle the capacity constraints for each agent individually. + +1. **Master Problem:** The master problem is responsible for ensuring that each job is assigned to exactly one agent. It maintains the overall objective of minimizing the total cost. + +2. **Subproblems:** Each subproblem corresponds to an agent and ensures that the agent's capacity constraints are respected. The subproblems are solved independently and their solutions are used to update the master problem. + +Implementation +-------------- + +.. literalinclude:: ../../examples/mixed-integer/assignment-bap.example.cpp + :language: cpp diff --git a/_sources/examples/generalized-assignment-problem-penalty-bap.rst.txt b/_sources/examples/generalized-assignment-problem-penalty-bap.rst.txt new file mode 100644 index 000000000..b11799aa0 --- /dev/null +++ b/_sources/examples/generalized-assignment-problem-penalty-bap.rst.txt @@ -0,0 +1,43 @@ +Combining branch-and-price, column generation, and a penalty method for the generalized assignment problem +========================================================================================================== + +Problem Definition +------------------ + +We consider the Generalized Assignment Problem (GAP) already studied in the :ref:`branch-and-price example `. + +In this example, we solve the continuous relaxation of the GAP using a penalty method and column generation. +Then possibly branch on the integer variables to solve the mixed-integer problem. + +First, we consider the continuous relaxation of the GAP: + +.. math:: + + \begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij}, \le C_i && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in [0,1], && i=1,\dotsc,m, j=1,\dotsc,n. + \end{align*} + +Then, we introduce penalty parameters :math:`\rho_j` to penalize the constraints :math:`\sum_{i=1}^m x_{ij} = 1` in the objective function. + +.. math:: + + \begin{align*} + \min_{x} \ & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} + \sum_{j=1}^n \rho_j \left| \sum_{i=1}^m x_{ij} - 1 \right| \\ + \text{s.t.} & \sum_{j=1}^n r_{ij} x_{ij} \le C_i && i=1,\dotsc,m \\ + & x_{ij} \in [0,1] && i=1,\dotsc,m, j=1,\dotsc,n. + \end{align*} + +Throughout the optimization process, we update the penalty parameters :math:`\rho_j` iteratively to enforce the feasibility of the solution. + +Finally, we solve the continuous relaxation of the GAP using column generation to generate new columns (variables) and improve the objective function. +That is, we iteratively solve the master problem and the subproblems to generate new columns and update the master problem. + + +Implementation with idol +------------------------ + +.. literalinclude:: ../../examples/mixed-integer/assignment-penalty-bap.example.cpp + :language: cpp diff --git a/_sources/examples/index.rst.txt b/_sources/examples/index.rst.txt new file mode 100644 index 000000000..f9172cc34 --- /dev/null +++ b/_sources/examples/index.rst.txt @@ -0,0 +1,38 @@ +.. _examples: + +Examples +======== + +Mixed-Integer Optimization +-------------------------- + +.. toctree:: + :maxdepth: 1 + + knapsack-problem + facility-location-problem + generalized-assignment-problem-bap + generalized-assignment-problem-penalty-bap + +Bilevel Optimization +-------------------- + + +.. toctree:: + :maxdepth: 1 + + bilevel-kkt + bilevel-mibs + bilevel-pessimistic + + +Robust Optimization +------------------- + + +.. toctree:: + :maxdepth: 1 + + robust-determistic + robust-adr + diff --git a/_sources/examples/knapsack-problem.rst.txt b/_sources/examples/knapsack-problem.rst.txt new file mode 100644 index 000000000..9fae0d1cc --- /dev/null +++ b/_sources/examples/knapsack-problem.rst.txt @@ -0,0 +1,40 @@ +Solving a knapsack problem with HiGHS +===================================== + +Problem Definition +------------------ + +Given a set of :math:`n` items, the goal is to select of subset of items to be put in a knapsack of limited capacity. +Each item has a weight (the amount of space it takes in the knapsack) and a profit (the value of the item). +The goal is to maximize the total profit of the items in the knapsack, while not exceeding the capacity. + +For each item :math:`j\in\{1,\dotsc,n\}`, we let :math:`w_j` denote its weight and :math:`p_j` be its profit. +The capacity of the knapsack is noted :math:`C`. + +The knapsack problem can be formulated as the following binary linear problem: + +.. math:: + + \begin{align*} + \max_{x} \quad & \sum_{j=1}^n p_j x_j \\ + \text{s.t.} \quad & \sum_{j=1}^n w_j x_j \le C, \\ + & x \in \{0,1\}^n. + \end{align*} + +Instance +-------- + +We will use an instance stored in a file called `knapsack.data.txt`. This file reads + +.. literalinclude:: ../../examples/mixed-integer/knapsack.data.txt + +The first line contains the number of items :math:`n`. +Then, the following line contains the profits of each item, :math:`p_j`. +The third line contains the weights of each item, :math:`w_j`. +Finally, the last line contains the capacity of the knapsack, :math:`C`. + +Implementation +-------------- + +.. literalinclude:: ../../examples/mixed-integer/knapsack.example.cpp + :language: cpp diff --git a/_sources/examples/robust-adr.rst.txt b/_sources/examples/robust-adr.rst.txt new file mode 100644 index 000000000..f32290201 --- /dev/null +++ b/_sources/examples/robust-adr.rst.txt @@ -0,0 +1,47 @@ +Using affine decision rules to solve a two-stage facility location problem with facility disruption +=================================================================================================== + +Problem Definition +------------------ + + +We consider a facility location problem with facility disruption. +Given a set of potential facility locations :math:`V_1` and a set of customers :math:`V_2`, the goal is to select a subset of facility locations +to activate in order to serve all customers' demand, while minimizing the total cost. +This version considers random disruptions of the opened facilities making them unusable. + +Note that there is also an example for the :ref:`deterministic version of the FLP using Column Generation `. + +Each facility :math:`i\in V_1` has an opening cost :math:`f_i` and a maximum capacity :math:`q_i`. +Each customer :math:`j\in V_2` has a demand :math:`d_j`. +The unitary cost for serving customer :math:`j\in V_2` from facility :math:`i\in V_1` is :math:`t_{ij}`. +The maximum number of facilities that can be disrupted is noted :math:`\Gamma`. + +The two-stage robust facility location problem can be formulated as + +.. math:: + + \begin{align} + \min_{ x\in \{0,1\}^{|V_1|} } \quad & \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \min_{y\in Y(x,\xi)} \quad \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\}, + \end{align} +in which :math:`\Xi := \left\{ \xi\in\{0,1\}^{|V_1|} : e^\top\xi \le \Gamma \right\}` and :math:`Y(x,\xi)` is the feasible set of the second-stage problem defined as + +.. math:: + + \begin{align} + & \sum_{j\in V_2} d_j y_{ij} \le q_i, && i\in V_1,\\ + & \sum_{i\in V_1} y_{ij} \ge 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & y_{ij} \le 1 - \xi_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. + \end{align} + +In this example, we will approximate the robust problem using affine decision rules and solve it using Gurobi. +To this end, we will restrict the adjustable decisions to be affine functions of the uncertain parameters, i.e., :math:`y(\xi) = \bar y + Y\xi`. + +Implementation +-------------- + +.. literalinclude:: ../../examples/robust/adr-facility-location.example.cpp + :language: cpp diff --git a/_sources/examples/robust-determistic.rst.txt b/_sources/examples/robust-determistic.rst.txt new file mode 100644 index 000000000..68745f683 --- /dev/null +++ b/_sources/examples/robust-determistic.rst.txt @@ -0,0 +1,65 @@ +Solving a robust facility location problem by its deterministic equivalent +=========================================================================== + +Problem Definition +------------------ + +We consider a facility location problem with uncertain demand. +Given a set of potential facility locations :math:`V_1` and a set of customers :math:`V_2`, the goal is to select a subset of facility locations +to activate in order to serve all customers' demand, while minimizing the total cost. +This version introduces uncertainty in the customers' demands. + +Note that there is also an example for the :ref:`deterministic version of the FLP using Column Generation `. + +Each facility :math:`i\in V_1` has an opening cost :math:`f_i` and a maximum capacity :math:`q_i`. +Each customer :math:`j\in V_2` has a demand :math:`d_j`. +The unitary cost for serving customer :math:`j\in V_2` from facility :math:`i\in V_1` is :math:`t_{ij}`. +The uncertainty in customer demands is controlled by a parameter :math:`\Gamma`. + +In this robust variant, we consider that the demands are uncertain and can be expressed as :math:`d_j(\xi) = d_j(1 + 0.2 \xi_j)` +with :math:`\xi` being an unknown vector taken in the uncertainty set + +.. math:: + + \Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}. + +The goal is to minimize the total cost of opening facilities and serving customers, considering the worst-case demand scenario. + +The robust version can be formulated as + +.. math:: + + \begin{align*} + \min_{x,y} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j(\xi) y_{ij} \le q_i, && i\in V_1, \quad \text{for all }\xi\in\Xi, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. + \end{align*} + +In this example, we will reformulate this robust facility location problem as a deterministic one. Then, we will solve it using Gurobi. + +.. hint:: + + Here, the deterministic reformulation reads as follows. + + .. math:: + + \begin{align*} + \min_{x,y,u.v} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j y_{ij} + \Gamma u + \sum_{j\in V_2} v_j \le q_i, && i\in V_1, \\ + & u + v_j \ge 0.2 d_j y_j, && j\in V_2, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & u, v_j \ge 0, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. + \end{align*} + + +Implementation +-------------- + +.. literalinclude:: ../../examples/robust/robust-facility-location.example.cpp + :language: cpp diff --git a/_sources/examples/two-stage-robust-facility-location-problem.rst.txt b/_sources/examples/two-stage-robust-facility-location-problem.rst.txt new file mode 100644 index 000000000..35c809909 --- /dev/null +++ b/_sources/examples/two-stage-robust-facility-location-problem.rst.txt @@ -0,0 +1,49 @@ +.. _example_robust_flp_ccg: + +Two-Stage Robust Facility Location Problem (CCG) +================================================ + +Problem Description +------------------- + +We consider a robust version of the capacitated Facility Location Problem (FLP). +Given a set of potential facility locations :math:`V_1` and a set of customers :math:`V_2`, the goal is to select a subset of facility locations +to activate in order to serve all customers' demand, while minimizing the total cost. +This version introduces uncertainty in the customers' demands. + +Note that there is also an example for the :ref:`deterministic version of the FLP using Column Generation `. + +Each facility :math:`i\in V_1` has an opening cost :math:`f_i` and a maximum capacity :math:`q_i`. +Each customer :math:`j\in V_2` has a demand :math:`d_j`. +The unitary cost for serving customer :math:`j\in V_2` from facility :math:`i\in V_1` is :math:`t_{ij}`. +The uncertainty in customer demands is controlled by a parameter :math:`\Gamma`. + +In this robust variant, we consider that the demands are uncertain and can be expressed as :math:`d_j(\xi) = d_j(1 + p\xi_j)` +with :math:`p` being the maximum increase in demand and :math:`\xi` being an unknown vector taken in the uncertainty set + +.. math:: + + \Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}. + +We model the two-stage robust FLP as + +.. math:: + + \min_{x\in \{0,1\}^{|V_1|}} \ \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \ \min_{y\in Y(x,\xi)} \ \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\} + +where :math:`Y(x,\xi)` is the set of feasible solutions for the second stage problem, given the first stage solution :math:`x` and the realization :math:`\xi` of the uncertain demand vector. +It is defined as the set of vectors :math:`y\in \mathbb{R}^{|V_1|\times|V_2|}` that satisfy the following constraints + +.. math:: + + \begin{align*} + & \sum_{i\in V_1} y_{ij} = d_j(\xi) && j\in V_2, \\ + & \sum_{j\in V_2} y_{ij} \le q_i x_i && i\in V_1, \\ + & y_{ij} \ge 0 && i\in V_1, j\in V_2. + \end{align*} + +Implementation +-------------- + +.. literalinclude:: ../../examples/robust/robust_ccg.example.cpp + :language: cpp diff --git a/_sources/faq/gap.rst.txt b/_sources/faq/gap.rst.txt new file mode 100644 index 000000000..ee0bdd421 --- /dev/null +++ b/_sources/faq/gap.rst.txt @@ -0,0 +1,24 @@ +.. _how_gap: + +How is the Optimality Gap Computed? +=================================== + +To assess global optimality, we use two different optimality gaps. + +The relative optimality gap is computed as + +.. math:: + + \begin{equation} + \gamma_{\text{rel}} := \frac{ UB - LB }{ 10^{-10} + |UB| }. + \end{equation} + +The absolute optimality gap is computed as + +.. math:: + + \begin{equation} + \gamma_{\text{abs}} := UB - LB. + \end{equation} + +See also :ref:`Tolerances `. \ No newline at end of file diff --git a/_sources/faq/index.rst.txt b/_sources/faq/index.rst.txt new file mode 100644 index 000000000..2c92ff373 --- /dev/null +++ b/_sources/faq/index.rst.txt @@ -0,0 +1,10 @@ +.. _faq: + +FAQ +--- + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/faq/mosek-and-eigen.rst.txt b/_sources/faq/mosek-and-eigen.rst.txt new file mode 100644 index 000000000..58bd45b1b --- /dev/null +++ b/_sources/faq/mosek-and-eigen.rst.txt @@ -0,0 +1,83 @@ +.. _mosek_and_socp: + +Why is Eigen Necessary to Solve QCQPs with Mosek? +================================================= + +In Short +-------- + +The interface of idol is based on quadratic expressions like + +.. math:: + + \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i. + +The C++ interface of Mosek, instead, is based on "conic expressions" like + +.. math:: + + (x_0, \textbf{Fx}) \in \mathcal Q^n, + +where :math:`\mathcal Q^n` denotes the second-order cone and :math:`F` is some matrix related to :math:`Q^i`. + +In order to make the conversion between the Mosek interface and +the idol interface (for instance, computing the matrix :math:`F`), +one needs to compute an eigen value decomposition. +This is automatically done by idol using `Eigen `_. +This is why Eigen is necessary if one wants to use Mosek with idol to solve QPs or QCQPs. + +Detailed Answer +--------------- + +Consider the quadratic expression + +.. math:: + + \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i. + +It can be written as + +.. math:: + + a_{(i)}^\top x + x^\top Q^i x \le b_i. + +The first task is to compute an eigen value decomposition of :math:`Q^i`, i.e., +to find matrices :math:`L` and :math:`D` such that :math:`Q^i = L D L^\top` +and :math:`D` is a diagonal matrix containing the eigen values of :math:`Q^i`. + +If there are more than two negative eigen values, the constraint is not convex and an exeception is thrown. + +Otherwise, we compute :math:`F` and :math:`N` so that :math:`x^\top Q^i x = \lVert Fx \rVert_2^2 + x^\top N x`. +This is done by setting :math:`F = \sqrt{D^+} L^\top` where :math:`D^+` is :math:`D` with the negative eigen values replaced by zero, +and :math:`N = L D^- L^\top`. + +Hence, we have that the constraint is expressed as + +.. math:: + + \lVert Fx \rVert_2^2 + x^\top N x \le b_i - a_{(i)}^\top x. + +If :math:`N = 0`, it can be written as + +.. math:: + + \begin{align} + & \lVert Fx \rVert_2^2 \le b_i - a_{(i)}^\top x \\ + \iff & (.5, b_i - a_{(i)}^\top x, Fx) \in\mathcal Q^{n+2}_r, + \end{align} + +where :math:`\mathcal Q^{n+2}_r` denotes the rotated second-order cone. + +Otherwise, if :math:`N` has one non-zero entry, say :math:`n_{ij}`. +Then, it must be that :math:`a_{(i)} = 0` and :math:`b_i \le 0` for the constraint to be +converted by idol. Under this assumption, the constraint can be written as + +.. math:: + + \begin{align} + & \lVert Fx \rVert_2^2 + \sqrt{-b_i}^2 \le n_{ij} x_i x_j \\ + \iff & (.5 n_{i,j} x_i, x_j, Fx, \sqrt{-b_i}) \in\mathcal Q^{n+1}_r, + \end{align} + +where it is assumed that :math:`n_{i,j} x_{i}x_{j} \ge 0` holds +(for now, a warning is printed to enlight this expectation). \ No newline at end of file diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 000000000..7d6f219d4 --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,161 @@ +.. title:: idol, a C++ Framework for Optimization + +.. raw:: html + +

    + +What is idol? +------------- + +idol is a C++ framework for **mathematical optimization** and complex decision-making problems. +It is designed to help you build new algorithms for solving complex optimization problems. +The main philosophy behind idol is interoperability and ease of use. +Hence, any algorithm can be seamlessly combined with any other algorithm to create a new one. +For instance, you can combine a Branch-and-Bound algorithm with a Column Generation algorithm to create a Branch-and-Price algorithm. + +.. code:: + + const auto branch_and_price = branch_and_bound + column_generation; + model.use(branch_and_price); + model.optimize(); + +idol offers a variety of tools to tackle many different kinds of optimization problems: + +.. raw:: html + + + +Getting Started with idol +------------------------- + +New to idol? Be sure to have a look at our :ref:`tutorials `. If you want to get a fast hands-on +start, have a look at our :ref:`local installation guideline `. It is the easiest installation process +one could think of: it automatically downloads the latest version of idol, and installs it locally in a sub-folder of your CMake project. +It's really a mater of seconds before you can start using idol. + +.. admonition:: Example + + Idol has a user-friendly interface which should look natural to people working in optimization. For instance, + here is how one solves a Knapsack Problem using the `Gurobi `_ solver. + + .. code:: cpp + + using namespace idol; + + const unsigned int n_items = 5; + const double[] profit = { 40., 50., 100., 95., 30., }; + const double[] weight = { 2., 3.14, 1.98, 5., 3., }; + const double capacity = 10.; + + Env env; + + Model model(env); + + const auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, 0., "x"); + + model.add_ctr(idol_Sum(j, Range(n_items), weight[j] * x[j]) <= capacity); + + model.set_obj_expr(idol_Sum(j, Range(n_items), -profit[j] * x[j]); + + model.use(Gurobi()); + + model.optimize(); + +Is this a MIP Solver? +--------------------- + +idol is not a MIP solver in itself. In fact, it typically needs to call external +solvers as a sub-routine of more complex algorithms such as Branch-and-Price. + +The idea is to work hand in hand with existing well-engineered optimization +software to enhance their possibilities. By doing so, we aim at solving larger and more complex problems than what is currently possible. + +Still, idol can be used to solve your favourite MILP, MIQP, or MIQCQP through the +many external solvers it interfaces with. +A clear advantage of using idol to solve these problems is that it offers a unified and common interface to every solver. +Thus, you can write your code once and test it with different solvers. +The following solvers are currently supported by idol: + +* `Gurobi `_, +* `Mosek `_, +* `GLPK `_, +* `HiGHS `_, +* `coin-or/Osi `_ (which gives access to Cplex, Symphony, or any Osi compatible solver), +* `coin-or/MibS `_. + +Table of Contents +----------------- + +.. toctree:: + :maxdepth: 1 + + installation/index + tutorials/index + examples/index + api/index + faq/index + benchmark/index + developer_guide/index + references diff --git a/_sources/installation/global-installation/index.rst.txt b/_sources/installation/global-installation/index.rst.txt new file mode 100644 index 000000000..6f9c065af --- /dev/null +++ b/_sources/installation/global-installation/index.rst.txt @@ -0,0 +1,102 @@ +.. _basics_installation: + +.. role:: bash(code) + :language: bash + +Global Installation +=================== + +This page is dedicated to the local installation of idol. It is thought for more advanced users who want to install +idol globally on their computer (e.g., in :code:`/usr/lib`). +If you simply want to "try out" idol, we advise you to opt for a :ref:`local installation `. +The installation process is managed by the CMake build system. You will therefore need to have it +installed on your computer. + +The installation process follows the classical CMake build process :code:`configure, build, install`. + +Configure +--------- + +The first step is to create a :bash:`build` directory. +This is where the library will be compiled before being it is installed (i.e., copied) on your system. + +.. code-block:: bash + + mkdir build + cd build + +Then, you should call CMake to configure the build process. +It is at this time that we let CMake look for the necessary dependencies such as, e.g., external optimization solvers. +By default, running CMake without options will cause idol to be built without any external solver. Note that options +should be specified as follows: + +.. code-block:: bash + + cmake -D= .. + +A list of **all possible options** can be found on the :ref:`complete list of options `. + +.. admonition:: Example for Gurobi + + Here is an example of a possible CMake command which will create the necessary targets for configuring idol to interface Gurobi. + + .. code-block:: bash + + cmake -DUSE_GUROBI=YES .. + + Note that this example assumes that your environment variable :bash:`GUROBI_HOME` has been correctly configured + (see `this official Gurobi page `_). + + If you want to specify the path to the Gurobi installation folder, you can use the :bash:`GUROBI_DIR` option. + + .. code-block:: bash + + cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir .. + + +Build +----- + +Now that the build process has been configured, we can build idol by running the following command. + +.. code-block:: bash + + make idol + +This will compile the idol C++ library, and make it ready to be installed (i.e., copied) on your computer. + +If you encounter any error at this stage, please, do not hesitate to contact us on our `GitHub page `_. + +Install +------- + +To install idol on your computer, run the following command. + +.. code-block:: bash + + sudo make install + +.. hint:: + + Here, you need superuser rights to install idol globally. If you want to install idol in a specific folder, + you may also use the :bash:`CMAKE_INSTALL_PREFIX` CMake option to change the destination folder. + + .. code-block:: bash + + cmake -CMAKE_INSTALL_PREFIX=/my/custom/installation/folder .. + make install + +And Then? +--------- + +That's it! idol is now installed on your computer. You can now use it in your C++ projects. To do so, you will need to +link your project against the idol library. See the related pages for more information. + +Related Pages +----------------- + +.. toctree:: + :maxdepth: 1 + :glob: + + * diff --git a/_sources/installation/global-installation/linking.rst.txt b/_sources/installation/global-installation/linking.rst.txt new file mode 100644 index 000000000..fffca91f4 --- /dev/null +++ b/_sources/installation/global-installation/linking.rst.txt @@ -0,0 +1,53 @@ +.. _linking: + +.. role:: bash(code) + :language: bash + +Linking Your C++ Project +======================== + +If you have installed idol globally, you can link your C++ project with idol using CMake. +Note that if idol was locally installed, you should refer to the :ref:`local installation guideline `, +this page is **only for global installation**. + +Idol is built with and for CMake (even though it is still possible to link using :bash:`Makefile` or pure :bash:`gcc`, :bash:`clang`, ...). + +Here is a minimal :bash:`CMakeLists.txt` which creates a new executable target linked with idol. + +.. code-block:: cmake + + cmake_minimum_required(VERSION 3.22) + project(my_project) + + set(CMAKE_CXX_STANDARD 17) + + add_executable(my_target main.cpp) + + find_package(idol REQUIRED) ## Here, we search for the installed library idol + + target_link_library(my_target PUBLIC idol) ## Here, we ask CMake to link with idol + +Note that you do not need to link with any external solver if idol was already linked with one. + +The following :bash:`main.cpp` is then a minimal example. + +.. code-block:: cpp + + #include + #include + + int main(int t_argc, const char** t_argv) { + + using namespace idol; + + Env env; + + Model model(env); + + const auto x = model.add_var(0., 1., Binary, "x"); + + // ... + + return 0; + } + diff --git a/_sources/installation/index.rst.txt b/_sources/installation/index.rst.txt new file mode 100644 index 000000000..619b8b2e8 --- /dev/null +++ b/_sources/installation/index.rst.txt @@ -0,0 +1,41 @@ +.. _installation: + +Installation +============ + +You are here on the installation guidelines. This page will guide through the installation process of idol. + +There are two ways to install idol: a local installation (easy to use) and a global installation (for more advanced users). + +Local Installation +------------------ + +:ref:`A local installation ` lets CMake automatically download and install idol in a sub-folder of your CMake project. This is the easiest way to get started. + +Global Installation +------------------- + +:ref:`A global installation ` installs idol globally on your computer (e.g., in :code:`/usr/lib`). + +.. toctree:: + :hidden: + :maxdepth: 1 + :glob: + + local_installation + global-installation/index + cmake_options + +Options (External Solvers, etc.) +-------------------------------- + +No matter which installation method you choose, you can customize the installation by setting a set of parameters accordingly. +This is particularly useful if you want to install idol with some external solver such as Gurobi. +Please refer to the :ref:`complete list of options ` for more information. + +.. toctree:: + :hidden: + :maxdepth: 1 + :glob: + + options diff --git a/_sources/installation/local_installation.rst.txt b/_sources/installation/local_installation.rst.txt new file mode 100644 index 000000000..d560c0c67 --- /dev/null +++ b/_sources/installation/local_installation.rst.txt @@ -0,0 +1,81 @@ +.. _installation_local: + +.. role:: bash(code) + :language: bash + +Local Installation +================== + +This page is dedicated to the local installation of idol. This is the easiest way to get your project working with +idol without installing it globally on your computer. +If you want to install idol globally, please read our :ref:`global installation guide `. + +The idea behind local installation is to let CMake download and manage the installation of idol in a sub-folder of your +project. This is done by using the CMake :bash:`FetchContent_*` directives. + +We provide here a minimal :bash:`CMakeLists.txt`. + +.. code-block:: cmake + + cmake_minimum_required(VERSION 3.23) + project(my_project) + + set(CMAKE_CXX_STANDARD 17) + + include(FetchContent) + + # Define your idol CMake options here + set(USE_GUROBI YES) # For instance, here, we specify that Gurobi will be used by idol + + # Tell CMake which version of idol you want to use + FetchContent_Declare( + idol + GIT_REPOSITORY https://github.com/hlefebvr/idol.git + GIT_TAG origin/main + ) + + # Ask CMake to download idol and install it to a sub-folder + FetchContent_MakeAvailable(idol) + + # Normal executable definition + add_executable(my_target main.cpp) + + # Link your CMake target with idol as classically done + target_link_libraries(my_target PUBLIC idol) + +By default, CMake will download the latest version of idol. However, you can also explicitly specify the desired version +of idol by setting the :bash:`GIT_TAG` variable in the :bash:`FetchContent_Declare` function to the specific +version, e.g., :bash:`v0.2.4-alpha`. + +.. hint:: + + As you can see in the above example, some options must be set to tell CMake to look for external solvers. Here, we + specify that Gurobi will be used by idol. You can, of course, add other solvers such as Mosek or GLPK. + + This is done with the :bash:`set` CMake function. For instance, to set the option :bash:`MY_OPTION` to the + value :bash:`MY_VALUE`. You should add :code:`set(MY_OPTION MY_VALUE)` to your :bash:`CMakeLists.txt` file. + + A list of **all possible options** can be found on the :ref:`complete list of options `. + +Then, here is a starting :bash:`main.cpp`. + +.. code-block:: cpp + + #include + #include + + int main(int t_argc, const char** t_argv) { + + using namespace idol; + + Env env; + + Model model(env); + + const auto x = model.add_var(0., 1., Binary, 0., "x"); + + // ... + + return 0; + } + diff --git a/_sources/installation/options.rst.txt b/_sources/installation/options.rst.txt new file mode 100644 index 000000000..fa5719bbf --- /dev/null +++ b/_sources/installation/options.rst.txt @@ -0,0 +1,232 @@ +.. _cmake_options: + +.. role:: bash(code) + :language: bash + +List of CMake Options +===================== + +This page contains a list of all CMake options that can be used to configure idol. In particular, this is useful to +link idol with external solvers. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Linking with External Solvers +----------------------------- + +Gurobi (Commercial Solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with Gurobi, you will need to pass the :bash:`USE_GUROBI` CMake option with value :bash:`YES`. + +By default, CMake will look for Gurobi inside the folder indicated by the environment variable :bash:`GUROBI_HOME` +(see `this official Gurobi page `_). +Note that it is also possible to pass the CMake option :bash:`GUROBI_DIR=/path/to/gurobi/install/dir` in order to specify +another directory to look for Gurobi. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with Gurobi. + + .. code-block:: bash + + cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_GUROBI YES) + set(GUROBI_DIR /path/to/gurobi/install/dir) + + +Mosek (Commercial Solver) +^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with Mosek, you will need to pass the :bash:`USE_MOSEK` CMake option with value :bash:`YES`. + +By default, CMake will look for Mosek inside the folder indicated by the environment variable :bash:`MOSEK_HOME`. +Note that it is also possible to pass the CMake option :bash:`MOSEK_DIR=/path/to/mosek/install/dir` in order to specify +another directory to look for Mosek. + +Note that :bash:`MOSEK_HOME` (or equivalently :bash:`MOSEK_DIR`) should point to the Mosek installation folder where +folders :bash:`h` and :bash:`bin` can be found. For instance, :bash:`MOSEK_HOME=~/mosek/10.0/tools/platform/linux64x86`. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with Mosek. + + .. code-block:: bash + + cmake -DUSE_MOSEK=YES -DMOSEK_DIR=/path/to/mosek/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_MOSEK YES) + set(MOSEK_DIR /path/to/mosek/install/dir) + +.. attention:: + + If you intend to use Mosek for solving QPs or SOCPs, please :ref:`read this `. + +GLPK (Open-Source Solver) +^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with GLPK, you will need to pass the :bash:`USE_GLPK` CMake option with value :bash:`YES`. + +By default, CMake will look for GLPK inside the folder indicated by the environment variable :bash:`GLPK_HOME` as well +as in the default installation folders :bash:`/usr/include` and :bash:`/usr/lib`. +Note that it is also possible to pass the CMake option :bash:`GLPK_DIR=/path/to/glpk/install/dir` in order to specify +another directory to look for GLPK. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with GLPK. + + .. code-block:: bash + + cmake -DUSE_GLPK=YES -DGLPK_DIR=/path/to/glpk/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_GLPK YES) + set(GLPK_DIR /path/to/glpk/install/dir) + + +HiGHS (Open-Source Solver) +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To link with GLPK, you will need to pass the :bash:`USE_HIGHS` CMake option with value :bash:`YES`. + +By default, CMake will look for HIGHS inside the default installation folders :bash:`/usr/include` and :bash:`/usr/lib`. +Note that it is also possible to pass the CMake option :bash:`HIGHS_DIR=/path/to/highs/install/dir` in order to specify +another directory to look for GLPK. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with GLPK. + + .. code-block:: bash + + cmake -DUSE_HIGHS=YES -DHIGHS_DIR=/path/to/glpk/install/dir .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: bash + + set(USE_HIGHS YES) + set(HIGHS_DIR /path/to/glpk/install/dir) + +coin-or (Open-Source Solvers) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +idol can be linked with some of the coin-or libraries. +Hereafter, we give a list of such libraries. For all the :code:`USE_*` options, you will need to define the environment +variable :code:`COIN_OR_HOME` or to set the CMake option :code:`COIN_OR_DIR`. It must point to the :code:`dist` directory +of coin-or. + +.. admonition:: Example + + The following will prepare CMake for linking against coin-or libraries. + + .. code-block:: + + cmake -DCOIN_OR_DIR=/path/to/coin_or/dist .. + + If you are doing a *local installation*, then the same can be achieved as follows. + + .. code-block:: + + set(COIN_OR_DIR /path/to/coin_or/dist) + +We now give the list of options which can be used in relation with coin-or libraries. + +- :code:`USE_OSI=YES`: use the Osi solver. +- :code:`USE_SYMPHONY=YES`: use the Symphony solver (can only be used through Osi). +- :code:`USE_CBC=YES`: use the Cbc solver (can only be used through Osi). +- :code:`USE_CLP=YES`: use the Clp solver (can only be used through Osi). +- :code:`USE_CPLEX=YES`: use the Cplex solver (can only be used through Osi). +- :code:`USE_MIBS=YES`: use the MibS solver (will automatically search for Alps, Bcps, Blis, and Cgl). + +Building Examples +----------------- + +:ref:`Examples :` can be found at the root level of the idol repository, inside the directory ``examples``. + +By default, CMake will not generate targets to build these example. To tell CMake to generate these, you +need to set the CMake option ``BUILD_EXAMPLE`` to ``YES``. + +.. admonition:: Example + + The following will tell CMake to create targets for examples. + + .. code-block:: + + cmake -DBUILD_EXAMPLES=YES .. + + For instance, we can now build the Knapsack Problem example, + + .. code-block:: + + make example_knapsack + + and run it. + + .. code-block:: + + cd examples && ./example_knapsack + +Other optional dependencies +--------------------------- + +Using martinus/robin-hood-hashing hash map +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Internally, idol uses unordered maps (also called hash maps). +Unfortunately, the default :code:`std` implementation is not the best choice when +it comes to performance. To avoid this, if found relevant, users can tell idol to use the hash-map implementation of +`martinus/robin-hood-hashing `_. It's actually a header-only library, so +all you have to do is to tell CMake where the :code:`robin_hood.hpp` file is. This is done through the CMake option +:code:`ROBINHOOD_DIR=/path/to/robin_hood/folder` together with :code:`USE_ROBINHOOD=YES`. + +Note that, if :code:`ROBINHOOD_DIR` is not specified, :code:`robin_hood.hpp` is searched for in :code:`/usr/include`, +:code:`/usr/include/robin_hood/`, :code:`/usr/local/include/`, :code:`/usr/local/include/robin_hood/` and in the path +stored in the environment variable :code:`ROBINHOOD_HOME`. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with martinus's robin_hood hash map + implementation. + + .. code-block:: + + cmake -DUSE_ROBINHOOD=YES -DROBINHOOD_DIR=/path/to/robin_hood/folder .. + +Using Eigen +^^^^^^^^^^^ + +Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. +It is internally used by idol for some of its functionalities. In particular, this is *necessary* for solving QPs and SOCPs +with the Mosek solver. + +Since Eigen is a header-only library, all you have to do is to tell CMake where the :code:`Eigen` folder is. This is done +through the CMake option :code:`EIGEN_DIR=/path/to/eigen/folder` together with :code:`USE_EIGEN=YES`. + +.. admonition:: Example + + The following will create an :bash:`install` target which will install idol with Eigen. + + .. code-block:: + + cmake -DUSE_EIGEN=YES -DEIGEN_DIR=/path/to/eigen/folder .. + +Building Unit and Integration Tests +----------------------------------- + +To build tests for idol, please refer to this :ref:`developer page `. \ No newline at end of file diff --git a/_sources/references.rst.txt b/_sources/references.rst.txt new file mode 100644 index 000000000..d193b70b6 --- /dev/null +++ b/_sources/references.rst.txt @@ -0,0 +1,7 @@ +References +========== + +This page contains references to the literature used in the documentation. + +.. bibliography:: + :all: diff --git a/_sources/tutorials/bilevel-optimization/files.rst.txt b/_sources/tutorials/bilevel-optimization/files.rst.txt new file mode 100644 index 000000000..145d02f04 --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/files.rst.txt @@ -0,0 +1,57 @@ +Reading and Writing Bilevel Instances (BOBILib) +=============================================== + +`BOBILib `_ is a library of instances for bilevel optimization problems. +In this tutorial, we will show how to read and write bilevel instances in the format which is used by BOBILib. +The advantage is twofold. First, we can easily access a large number of bilevel instances. +Second, we can easily share our bilevel instances with others. + +Let's get started! + +.. contents:: Table of Contents + :local: + :depth: 2 + +The Format +---------- + +The instances in BOBILib are stored in two files: + +- An :code:`.mps` or :code:`.lp` file containing the high-point relaxation of the bilevel problem, +- An :code:`.aux` file containing the description of the lower-level problem. + +For more details, we refer to the report :cite:`BOBILib`. + +Implementation +-------------- + +Reading Instances +^^^^^^^^^^^^^^^^ + +Reading a BOBILib instance is straightforward. We can use the :code:`Bilevel::read_from_file` function. +However, it requires an underlying solver to parse the :code:`.mps` file. Here, we will use Gurobi. + +.. code:: + + Env env; + auto [model, description] = + Bilevel::read_from_file(env, aux_filename); + +The function returns a pair made by the high-point relaxation model and the description of the lower-level problem. + +Writing Instances +^^^^^^^^^^^^^^^^^ + +Assume that you have a bilevel model :code:`model` and a description :code:`description` for the lower-level problem. +Writing this problem to file can be done by a single call to :code:`Bilevel::write_to_file`. +Here, no external solver is necessary. + +.. code:: + + /* + the following creates two files: + - instance-filename.mps + - instance-filename.aux + */ + Bilevel::write_to_file(model, description, "instance-filename"); + diff --git a/_sources/tutorials/bilevel-optimization/index.rst.txt b/_sources/tutorials/bilevel-optimization/index.rst.txt new file mode 100644 index 000000000..98b1640ea --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/index.rst.txt @@ -0,0 +1,72 @@ +.. _bilevel: + +Bilevel Optimization +==================== + +Bilevel optimization is a field of mathematical optimization in which two optimization problems are intertwined: the +upper-level and the lower-level problem. The upper-level problem minimizes a given objective function taking into account +the solution to the lower-level problem, which is parameterized by the upper-level’s decision. Such problems have many +applications in, e.g., economics where it is used to model non-cooperative games. + +A classic model for a bilevel problem is as follows. + +.. math:: + :label: bilevel + + \begin{align} + \text{''}\min_{x}\text{''} \quad & F(x,y) \\ + \text{s.t.} \quad & G(x,y) \ge 0, \\ + & x\in X, \\ + & y\in S(x), + \end{align} + +in which :math:`S(x)` denotes the solution set of the lower-level problem, which is parameterized by the upper-level decision +:math:`x`. The lower-level problem is defined as + +.. math:: + + \begin{align} + \min_{y} \quad & f(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y. + \end{align} + +Note that the quotes around the :math:`\min` operator in :math:numref:`bilevel` is here to highlight that the problem is +ill-defined in its current form. Indeed, in case multiple solutions to the lower-level problem exist, the upper-level problem +has to somehow "choose" one of them. To circumvent this, we typically consider the optimistic setting, where the lower-level +is assumed to pick the solution in favor of the upper-level problem, in order to break ties. + +Optimistic bilevel problems can be modeled as: + +.. math:: + + \begin{align} + \min_{x,y} \quad & F(x,y) \\ + \text{s.t.} \quad & G(x,y) \ge 0, \\ + & x\in X, \\ + & y\in S(x), + \end{align} + +Note that there exists other notions such as pessimistic bilevel problems. There, the lower-level problem is assumed to pick +the worst solution for the upper-level problem. This can be modeled as follows. + +.. math:: + + \begin{align} + \min_{x} \quad & \max_{ y\in S(x) } \ F(x,y) \\ + \text{s.t.} \quad & G(x,\bar y) \ge 0, \quad \text{for all } \bar y\in S(x), \\ + & x\in X, \\ + & S(x) \neq \emptyset. + \end{align} + +Pessimisitc bilevel problems are less studied in the literature. + +.. toctree:: + :maxdepth: 1 + :glob: + + modeling + files + kkt + mibs + pessimistic diff --git a/_sources/tutorials/bilevel-optimization/kkt.rst.txt b/_sources/tutorials/bilevel-optimization/kkt.rst.txt new file mode 100644 index 000000000..c20385166 --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/kkt.rst.txt @@ -0,0 +1,198 @@ +.. _tutorial_bilevel_kkt: + +Deriving Single-level Reformulations +==================================== + +A standard technique for solving LP-LP bilevel problems is to reformulate the problem as a single-level problem. +This can be done in several ways. In this tutorial, we will show how we can use idol to derive the +Karush-Kuhn-Tucker (KKT) reformulation and the strong-duality reformulation of a bilevel problem. + +Let's get started! + +.. contents:: Table of Contents + :local: + :depth: 2 + +Problem Formulation +------------------- + +Consider the following bilevel optimization problem: + +.. math:: + + \begin{align} + \min_{x,y} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & y \in \text{arg min} \{ f^\top y : Dy \ge b - Cx \}. + \end{align} + +In order to solve problem :math:numref:`bilevel` with a standard optimization solver, we need to reformulate it as a single-level optimization problem. +This can be automatically done by idol using the KKT reformulation or the strong-duality reformulation. + +For this tutorial, we will work on the following code snippet: + +.. code:: + + Env env; + + Model high_point_relaxation(env); + + auto x = high_point_relaxation.add_var(0, Inf, Continuous, 0., "x"); + auto y = high_point_relaxation.add_var(-Inf, Inf, Continuous, 0., "y"); + + high_point_relaxation.set_obj_expr(x + 6 * y); + auto lower_c1 = high_point_relaxation.add_ctr(2 * x - y >= 0); + auto lower_c2 = high_point_relaxation.add_ctr(-x - y >= -6); + auto lower_c3 = high_point_relaxation.add_ctr(-x + 6 * y >= -3); + auto lower_c4 = high_point_relaxation.add_ctr(x + 3 * y >= 3); + high_point_relaxation.add_ctr(-x + 5 * y <= 12.5); + + Bilevel::Description description(env); + description.set_lower_level_obj(-y); + description.make_lower_level(y); + description.make_lower_level(lower_c1); + description.make_lower_level(lower_c2); + description.make_lower_level(lower_c3); + description.make_lower_level(lower_c4); + +Here, a bilevel problem is modeled with idol. The high point relaxation is stored in :code:`high_point_relaxation`, while +the lower-level problem is described using the :code:`Bilevel::Description` object :code:`description`. + +The KKT Reformulation +--------------------- + +The KKT reformulation of a bilevel problem is obtained by replacing the lower-level problem with its KKT optimality conditions. +The KKT reformulation of the bilevel problem is as follows: + +.. math:: + :label: kkt + + \begin{align} + \min_{x,y,\lambda} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & Dy \ge b - Cx, \\ + & D^\top \lambda = f, \; \lambda \ge 0, \\ + & \lambda^\top (b - Cx - Dy) = 0. + \end{align} + +Getting the Reformulated Model +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +With idol, it is possible to generate the KKT reformulation of the bilevel problem using the :code:`Bilevel::KKT::make_model` function. + +For instance, one could do the following. + +.. code:: + + auto single_level_model = Bilevel::KKT::make_model( + high_point_relaxation, description + ); + +Then, one can solve the single-level model using a standard optimization solver. Here, we use Gurobi. + +.. code:: + + single_level.use(Gurobi()); + single_level.optimize(); + +Note that the KKT reformulation :math:numref:`kkt`, and thus :code:`single_level`, is a nonlinear problem because of the complementarity constraint. +Hence, we use the nonlinear solving features of Gurobi here. + +A common approach to handle the complementarity constraints is to linearize them by introducing binary variables. +This can also be done in idol. To do this, we will need to provide some valid bounds on the dual variables. +This is done by annotating the lower-level problem constraints. The constraints associated with the variables +bounds can also have their big-M values by annotating the corresponding variable. + +In the following code, we will simply use a default value for the big-M values of :math:`10^{4}`. + +.. code:: + + Annotation big_M(env, "big_M", 1e4); + auto single_level_model = Bilevel::KKT::make_model( + high_point_relaxation, description, big_M + ); + +The returned model is now a mixed-integer linear program that can be solved using a standard optimization solver. + +Now, say that constraint :code:`lower_c1` is known to have a dual variable bounded by, say, 10. One could do the following. + +.. code:: + + Annotation big_M(env, "big_M", 1e4); + lower_c1.set(big_M, 10); + + auto single_level_model = Bilevel::KKT::make_model( + high_point_relaxation, description, big_M + ); + +Solving the KKT Reformulation directly +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +In the previous section, we showed how to generate the KKT reformulation of a bilevel problem. +However, idol also provides a function to solve the KKT reformulation directly. +This can be done by using the :code:`Bilevel::KKT` optimizer. + +Here is a code snippet that shows how to solve the KKT reformulation directly. + +.. code:: + + high_point_relaxation.use(Bilevel::KKT(description) + Gurobi()); + +Note that big-M values can also be provided to the :code:`Bilevel::KKT` optimizer. Here is an example. + +.. code:: + + high_point_relaxation.use( + Bilevel::KKT(description) + .with_single_level_optimizer(Gurobi()) + .with_big_M(big_M) + ); + +Calling the :code:`optimize` method on the model will solve the KKT reformulation of the bilevel problem. + +The Strong-duality Reformulation +-------------------------------- + +Another single-level reformulation is the so-called strong-duality reformulation which reads + +.. math:: + + \begin{align} + \min_{x,y,\lambda} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & Dy \ge b - Cx, \\ + & D^\top \lambda = f, \; \lambda \ge 0, \\ + & f^\top y \le (b - Cx)^\top \lambda. + \end{align} + + +Getting the Reformulated Model +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The strong-duality reformulation can be obtained using the :code:`Bilevel::StrongDuality::make_model` function. +This function works similarly to the :code:`Bilevel::KKT::make_model` function. +Here is an example. + +.. code:: + + auto single_level_model = Bilevel::StrongDuality::make_model( + high_point_relaxation, description + ); + single_level_model.use(Gurobi()); + single_level_model.optimize(); + +Note that here, the strong-duality reformulation is a nonlinear problem because of the dual objective function. +Hence, we use the nonlinear solving features of Gurobi here. + +Solving the Strong-duality Reformulation directly +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Similarly to the KKT reformulation, idol also provides a function to solve the strong-duality reformulation directly. +This can be done by using the :code:`Bilevel::StrongDuality` optimizer as follows. + +.. code:: + + high_point_relaxation.use( + Bilevel::StrongDuality(description) + Gurobi() + ); + high_point_relaxation.optimize(); diff --git a/_sources/tutorials/bilevel-optimization/mibs.rst.txt b/_sources/tutorials/bilevel-optimization/mibs.rst.txt new file mode 100644 index 000000000..d870ac159 --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/mibs.rst.txt @@ -0,0 +1,66 @@ +Solving Mixed-Integer Bilevel Problems with coin-or/MibS +======================================================== + +MibS is an optimization solver for mixed-integer bilevel problems; for more information, please refer to the `MibS website `_. +Idol seamlessly interfaces with MibS to solve bilevel problems. + +We will see that solving bilevel problems with MibS is very similar to solving any optimization problem in idol. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Setup +----- + +We will assume that you have your bilevel problem already modeled in idol. In particular, we consider that you have +two variables: + +1. :code:`high_point_relaxation` which is a :code:`Model` representing the high-point relaxation of your bilevel problem. + +2. :code:`description` which is a :code:`Bilevel:Description` object representing the bilevel problem. If you do not know what this is or how to create it, please refer to the :ref:`previous tutorial `. + +Using MibS +---------- + +To solve your bilevel problem, you can use the :code:`MibS` optimizer factory as follows: + +.. code:: + + high_point_relaxation.use(Bilevel::MibS(description)); + + high_point_relaxation.optimize(); + + std::cout << save_primal(high_point_relaxation) << std::endl; + +Notice how the MibS optimizer factory is attached to the high-point relaxation model and that the bilevel description +is passed as an argument. + +The rest of the code is the same as with any other solver. + +.. hint:: + + To use MibS, you need to have the MibS library installed on your system and idol linked against it. + You can download MibS from `here `_. + + Then, idol should be compiled with the options :code:`USE_MIBS=YES`, :code:`USE_CLP=YES`. + +Using CPLEX for Feasibility Check +--------------------------------- + +Note that it is also possible to use MibS in combination with CPLEX for the feasibility check. This can be done as follows: + +.. code:: + + const auto mibs = Bilevel::MibS(description) + .with_cplex_for_feasibility(true) + .with_time_limit(3600) + .with_logs(true); + + high_point_relaxation.use(mibs); + + high_point_relaxation.optimize(); + + std::cout << save_primal(high_point_relaxation) << std::endl; + +Off course, MibS must have been installed with CPLEX for this to work. diff --git a/_sources/tutorials/bilevel-optimization/modeling.rst.txt b/_sources/tutorials/bilevel-optimization/modeling.rst.txt new file mode 100644 index 000000000..f96432c08 --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/modeling.rst.txt @@ -0,0 +1,136 @@ +.. _tutorial_optimistic_bilevel: + +Modeling a Bilevel Problem +========================== + +In this tutorial, we will see how to model a bilevel problem in idol. + +To follow this tutorial, you should be familiar with bilevel optimization and modeling optimization problems in idol. +If this is not the case, we recommend you to read the tutorial on :ref:`MIP modeling `. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Problem Definition and Main Steps +---------------------------------- + +We consider the optimistic bilevel problem + +.. math:: + + \begin{align} + \min_{x, y} \quad & -x + -10 y \\ + \text{s.t.} \quad & x \in \mathbb Z_{\ge 0} \\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & y \\ + \text{s.t.} \quad & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_{\ge 0}. + \end{array} + \end{align} + +This is an ILP-ILP bilevel problem which is taken from :cite:`Moore1990` (Example 1). + +To model this problem in idol, there are three main steps: + +1. Define the high-point relaxation (HPR) model, + +2. Describe which variables and constraints are part of the lower-level problem, + +3. Define the lower-level objective function. + +Modeling the High-Point Relaxation +---------------------------------- + +The HPR can be modeled in the same way as a classical optimization problem. +If you are not familiar with modeling optimization problems in idol, +we recommend you to read the tutorial on :ref:`MIP modeling `. + +In our example, the HPR reads + +.. math:: + + \begin{align} + \min_{x, y} \ & -x + -10 y \\ + \text{s.t.} \ & x \in \mathbb Z_+ \\ + & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_+. + \end{align} + +Here is the code to model the HPR of the bilevel problem. + +.. code:: + + Env env; + Model high_point_relaxation(env); + + auto x = high_point_relaxation.add_var(0, Inf, Integer, 0, "x"); + auto y = high_point_relaxation.add_var(0, Inf, Integer, 0, "y"); + + high_point_relaxation.set_obj_expr(-x - 10 * y); + auto lower_c1 = high_point_relaxation.add_ctr(-25*x + 20*y <= 30); + auto lower_c2 = high_point_relaxation.add_ctr(x + 2 * y <= 10); + auto lower_c3 = high_point_relaxation.add_ctr(2 * x - y <= 15); + auto lower_c4 = high_point_relaxation.add_ctr(2 * x + 10 * y >= 15); + +Describing the Lower-Level Problem +---------------------------------- + +To describe the lower-level problem, we need to specify which variables and constraints are part of it. +This is done by creating an object of type :code:`Bilevel::Description` and calling the methods :code:`make_lower_level`. + +.. code:: + + Bilevel::Description description(env); + description.make_lower_level(y); + description.make_lower_level(lower_c1); + description.make_lower_level(lower_c2); + description.make_lower_level(lower_c3); + description.make_lower_level(lower_c4); + +Note that this does nothing more but to create a new :code:`Annotation` to indicate variables and constraints that are part of the lower-level problem. +These annotations are used by the bilevel solvers to identify the lower-level problem. +In particular, all variables and constraints that are not annotated as lower-level variables or constraints are considered as upper-level variables or constraints, respectively. +Upper-level variables and constraints have an annotation which is set to :code:`MasterId` by default. + +Also note that it is possible to create and use your own annotation. For instance, the following code is equivalent to the previous one. + + +.. code:: + + Annotation lower_level(env, MasterId, "lower_level"); + + y.set(lower_level, 0); + lower_c1.set(lower_level, 0); + lower_c2.set(lower_level, 0); + lower_c3.set(lower_level, 0); + lower_c4.set(lower_level, 0); + + + Bilevel::Description description(lower_level); + + +Defining the Lower-Level Objective Function +------------------------------------------- + +Finally, we need to define the lower-level objective function. +This is done by calling the method :code:`set_lower_level_obj` on the object of type :code:`Bilevel::Description`. +A :code:`QuadExpr` object is passed as argument to this method. + +.. code:: + + description.set_lower_level_obj(y); + +Complete Example +---------------- + +A complete example is available :ref:`here ` and uses the MibS solver. diff --git a/_sources/tutorials/bilevel-optimization/pessimistic.rst.txt b/_sources/tutorials/bilevel-optimization/pessimistic.rst.txt new file mode 100644 index 000000000..f1fd6cbf6 --- /dev/null +++ b/_sources/tutorials/bilevel-optimization/pessimistic.rst.txt @@ -0,0 +1,104 @@ +.. _tutorial_pessimistic_bilevel: + +From Pessimistic Bilevel Optimization to Optimistic Bilevel Optimization +======================================================================== + +Most of the litereature on bilevel optimization focuses on the optimistic setting, where the lower-level problem is assumed to +pick the solution in favor of the upper-level problem. +However, there exists other notions such as pessimistic bilevel problems. + +A pessimistic problem reads as follows: + +.. math:: + :label: pessimistic + + \begin{align} + \min_{x} \quad & \max_{ y\in S(x) } \ F(x,y) \\ + \text{s.t.} \quad & x\in X, \\ + & S(x) \neq \emptyset, + \end{align} + +with :math:`S(x)` the solution set of + +.. math:: + + \begin{align} + \min_{y} \quad & f(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y. + \end{align} + + +In this tutorial, we will show how a pessimistic bilevel problem can be automatically transformed into an optimistic bilevel problem. +This transformation is due to :cite:`Zeng2020`. + +.. hint:: + + Here, :math:numref:`pessimistic` does not have coupling constraints for simplicity. + However, the transformation can be extended to bilevel problems with coupling constraints. + +.. contents:: Table of Contents + :local: + :depth: 2 + +The Equivalent Optimistic Problem +--------------------------------- + +In :cite:`Zeng2020`, the authors show that the pessimistic bilevel problem :math:numref:`pessimistic` is equivalent to the following optimistic bilevel problem: + +.. math:: + :label: optimistic + + \begin{align} + \min_{x,\bar y} \quad & F(x,y) \\ + \text{s.t.} \quad & x\in X, \ \bar y\in Y, \\ + & g(x,\bar y) \ge 0, \\ + & y\in \tilde S(x, \bar y), + \end{align} + +in which :math:`\tilde S(x, \bar y)` is the solution set of + +.. math:: + + \begin{align} + \min_y \quad & -F(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y, \\ + & f(x,y) \le f(x, \bar y). + \end{align} + +Note that :math:numref:`optimistic` is an optimistic bilevel problem. + +Implementation +-------------- + +Deriving the equivalent optimistic bilevel problem from a pessimistic bilevel problem can be done easily in idol. + +To this end, let us assume that you have your bilevel problem already modeled in idol. In particular, let us consider that you have +two variables: + +1. :code:`high_point_relaxation` which is a :code:`Model` representing the high-point relaxation of your bilevel problem. + +2. :code:`description` which is a :code:`Bilevel:Description` object representing the bilevel problem. If you do not know what this is or how to create it, please refer to the :ref:`previous tutorial `. + +Then, you can derive the equivalent optimistic bilevel problem as follows: + +.. code:: + + auto [opt_model, opt_description] = + Bilevel::PessimisticAsOptimistic::make_model( + high_point_relaxation, + description + ); + +Here, :code:`opt_model` is the high-point relaxation of :math:numref:`optimistic` and :code:`opt_description` is the bilevel description of :math:numref:`optimistic`. + +The rest of the code is the same as with any other solver. For instance, you can solve the optimistic bilevel problem with MibS as follows: + +.. code:: + + opt_model.use(Bilevel::MibS(opt_description)); + + opt_model.optimize(); + + std::cout << save_primal(opt_model) << std::endl; diff --git a/_sources/tutorials/index.rst.txt b/_sources/tutorials/index.rst.txt new file mode 100644 index 000000000..9ac7e0374 --- /dev/null +++ b/_sources/tutorials/index.rst.txt @@ -0,0 +1,38 @@ +.. _tutorials: + +Tutorials +========= + +On this page, you will find a collection of tutorials that demonstrate how to use idol to solve various optimization problems. +The tutorials are organized by topic. + +Mixed-Integer Optimization +-------------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + :titlesonly: + + mixed-integer-programming/index + +Bilevel Optimization +-------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + :titlesonly: + + bilevel-optimization/index + +Robust Optimization +------------------- + +.. toctree:: + :maxdepth: 3 + :glob: + :titlesonly: + + robust-optimization/index + diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.rst.txt new file mode 100644 index 000000000..c05735358 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.rst.txt @@ -0,0 +1,6 @@ +Creating Your Own Branching Rule (Advanced) [TODO] +================================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-callback.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-callback.rst.txt new file mode 100644 index 000000000..aec7ac3de --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-callback.rst.txt @@ -0,0 +1,8 @@ +.. _tutorial_create_bb_callback: + +Create Your Own Callback (Advanced) [TODO] +========================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.rst.txt new file mode 100644 index 000000000..e0c4c8531 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.rst.txt @@ -0,0 +1,6 @@ +Creating Your Own Node Selection Rule (Advanced) [TODO] +======================================================= + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node.rst.txt new file mode 100644 index 000000000..2a76e7d3a --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/create-node.rst.txt @@ -0,0 +1,6 @@ +Creating Your Own Node Class (Advanced) [TODO] +============================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/index.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/index.rst.txt new file mode 100644 index 000000000..1e28154f6 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/index.rst.txt @@ -0,0 +1,12 @@ +Branch-and-Bound Algorithm +========================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. + +.. toctree:: + :maxdepth: 1 + :glob: + + write-branch-and-bound diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.rst.txt new file mode 100644 index 000000000..8bca15398 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.rst.txt @@ -0,0 +1,6 @@ +Adding User Cuts and Lazy Constraints [TODO] +============================================ + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.rst.txt b/_sources/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.rst.txt new file mode 100644 index 000000000..c031523be --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.rst.txt @@ -0,0 +1,6 @@ +Writing an LP-based Branch-and-Bound [TODO] +=========================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.rst.txt new file mode 100644 index 000000000..3c5d38b7e --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.rst.txt @@ -0,0 +1,217 @@ +.. _tutorial_column_generation: + +Solving A Dantzig-Wolfe Reformulation +===================================== + +In this tutorial, we will see how to implement a column generation algorithm to solve a continuous relaxation of the Generalized Assignment Problem (GAP). +This relaxation is obtained by relaxing the Dantzig-Wolfe reformulation of the GAP. + +.. hint:: + + This tutorial regards the `advanced topic` of Column Generation and Dantzig-Wolfe decomposition. + Rudimentary notions in the following subjects are recommended: + + - `Column Generation algorithms `_ + - `Dantzig-Wolfe decomposition `_ + - `Generalized Assignment Problem `_. + +A complete example which includes branching is available :ref:`here `. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Problem Definition +------------------ + +Given a set of :math:`m` agents and :math:`n` jobs, the goal is to assign each job to exactly one agent in such a +way that the total cost is minimized, while respecting the capacity constraints of each agent. + +Each agent :math:`i\in\{1,\dotsc,m\}` has a capacity :math:`C_i`. +Each job :math:`j\in\{1,\dotsc,n\}` has a resource consumption :math:`r_{ij}` and a cost :math:`c_{ij}` when assigned to agent :math:`i`. + +The Natural Formulation +^^^^^^^^^^^^^^^^^^^^^^^ + +We model the GAP with the following binary linear program: + +.. math:: + + \begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij} \le C_i, && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in \{0,1\}, && i=1,\dotsc,m, j=1,\dotsc,n. + \end{align*} + +Here, variable :math:`x_{ij}` encodes the assignment decision and equals 1 if and only if task :math:`j` is assigned to +agent :math:`i`. + +The Dantzig-Wolfe Reformulation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Let us enumerate the list of all feasible assignments, i.e., let + +.. math:: + + \{\bar x^e_{ij} \}_{e\in E} = \left\{ x \in \{ 0,1 \}^{mn} : \sum_{j=1}^n r_{ij}x_{ij} \le C_i \quad i=1,...,m \right\}, + +in which :math:`E` denotes a list for their indices. + +The Dantzig-Wolfe reformulation of GAP reads + +.. math:: + :label: eq-dantzig-wolfe-reformulation + + \min_{\lambda} \quad & \sum_{e\in E} \lambda_e\left( \sum_{i=1}^m\sum_{j=1}^n c_{ij}\bar x_{ij}^e \right) \\ + \textrm{s.t.} \quad & \sum_{e\in E} \lambda_e \left( \sum_{i=1}^m \bar x_{ij}^e \right) = 1 \quad j=1,...,n, \\ + & \sum_{e\in E} \lambda_e = 1, \\ + & \lambda_e \in \{ 0, 1 \} & \text{for all } e\in E. + +Though this model contains an exponential number of variables, it can be solved efficiently using +Column Generation and Branch-and-price. In such a case, the pricing problem is a Knapsack Problem. + +In this tutorial, we focus on the continuous relaxation of :math:numref:`eq-dantzig-wolfe-reformulation`. + +Automatic Reformulation +----------------------- + +The simplest way to solve a problem using Column Generation and idol is through its automatic reformulation feature. +To use this, one simply needs to give the *original space formulation* of the problem +and to indicate which constraints should be moved to the pricing problem (here, the knapsack constraints). + +We will start by modeling the problem in its natural form and then indicate which constraints should be moved to the pricing problem. + +The Natural Formulation +^^^^^^^^^^^^^^^^^^^^^^^ + +Before we start, we will use a GAP instance stored in a file. This file reads as follows. + +.. literalinclude:: ../../../../examples/mixed-integer/assignment-bap.data.txt + +To read an instance of the GAP, we need to include the header file located in :code:`idol/mixed-integer/problems/generalized-assignment-problem/GAP_Instance.h`. + +Then, we can use the :code:`Problems::GAP::read_instance` function to read the instance file. + +.. code-block:: cpp + + const auto instance = + Problems::GAP::read_instance("assignment-bap.data.txt"); + + const unsigned int n_agents = instance.n_agents(); + const unsigned int n_jobs = instance.n_jobs(); + +We are now ready to model our problem (for more details, refer to :ref:`this tutorial on modeling `) + +.. code-block:: cpp + + // Create optimization environment + Env env; + + // Create model + Model model(env); + + // Create assignment variables (x_ij binaries) + auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, "x"); + + // Create knapsack constraints (i.e., capacity constraints) + for (unsigned int i = 0 ; i < n_agents ; ++i) { + model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + } + + // Create assignment constraints + for (unsigned int j = 0 ; j < n_jobs ; ++j) { + model.add(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j)); + } + + // Set the objective function + model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j]))); + +Giving Decomposition Instructions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +We are now at the crucial step of indicating which constraint should be moved to the pricing problem. In idol, this is done by using +*annotations*. Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +Note that annotations are global, i.e., they do not relate to a given optimization model. + +Every annotation is formed with a template argument which is the value type of the annotation. Here, the Dantzig-Wolfe +decomposition expects an annotation with a value of type :code:`unsigned int` and which corresponds +to the sub-problem index to which the constraint will be moved to. + +We create the annotation as follows. + +.. code-block:: cpp + + Annotation decomposition(env, "decomposition", MasterId); + +Here, we pass three arguments to the constructor of :code:`Annotation`. First, we pass the optimization +environment which will store the annotation. Then, a name is given to the annotation: here, "decomposition". +Finally, a default value is given and is set to :code:`MasterId`. This will tell idol that constraints which have not been annotated +should remain in the master problem. + +Now, observe how the annotation is applied to the capacity constraints. + +.. code:: cpp + + for (unsigned int i = 0 ; i < n_agents ; ++i) { + auto capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + capacity.set(decomposition, i); // <== Annotating the capacity constraint + } + +Here, the first capacity constraint is moved to the first pricing problem (id: 0), +the second constraint to the second pricing problem (id: 1), and so on. + +Note that another decomposition would be materialized as follows. + +.. code:: cpp + + for (unsigned int i = 0 ; i < n_agents ; ++i) { + Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i)); + capacity.set(decomposition, 0); // <== Annotating the capacity constraint + } + +Here, all the knapsack constraints would be moved to the same pricing problem (id: 0). + +Creating the Column Generation Algorithm +---------------------------------------- + +Now that the desired decomposition has been specified, we can set the desired optimizer to solve our model. +Here, we want to solve our the continuous relaxation of the Dantzig-Wolfe reformulation using column generation. + +To begin with, we need to give some instructions about how each sub-problem will be solved. In other words, we need +to specify the optimizer(s) used for pricing during the column generation process. This is done by first creating a +:code:`DantzigWolfe::SubProblem` object. + +.. code:: cpp + + const auto sub_problem_specifications = DantzigWolfe::SubProblem() + .add_optimizer(Gurobi()); + +Then, we can create the column generation algorithm (factory) in the following way. + +.. code:: cpp + + const auto column_generation = DantzigWolfeDecomposition(decomposition) + .with_master_optimizer(Gurobi::ContinuousRelaxation()) + .with_default_sub_problem_spec(sub_problem_specifications); + +We can now tell idol to use this algorithm for solving our model by using the :code:`Model::use` method. + +.. code:: cpp + + model.use(column_generation); + +Solving +------- + +As usual, one can simply call the :code:`Model::optimize` method to solve the problem. + +.. code:: cpp + + model.optimize(); + + +That's it! The problem is being solved by column generation, and possibly branching on fractional variables. + +The rest remains unchanged and one can retrieve the solution +through the usual methods such as :code:`Model::get_status` and :code:`Model::get_var_primal`. diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.rst.txt new file mode 100644 index 000000000..0c900febc --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.rst.txt @@ -0,0 +1,6 @@ +Using In-Out Stabilization [TODO] +================================= + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/index.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/index.rst.txt new file mode 100644 index 000000000..752cf2b03 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/index.rst.txt @@ -0,0 +1,31 @@ +.. _tutorial_DantzigWolfe: + +Column Generation and Branch-and-Price Algorithm +================================================ + +**Column generation** is an algorithm used to solve large scale optimization problems which involve a large number of variables. +Instead of solving the problem in its entirety, column generation begins with a restricted version of the problem containing only a subset of variables. It then iteratively introduces new variables (or columns) that have the potential to improve the solution, based on the problem's structure and constraints. + +In practice, column generation is particularly effective for problems with block-angular structures, such as cutting stock, vehicle routing, and generalized assignment problems. The method splits the problem into a master problem, which handles the selection of variables, and a pricing problem, which identifies the most promising variables to add to the master problem. These subproblems are solved iteratively until no further improvements are possible. + +.. figure:: https://upload.wikimedia.org/wikipedia/commons/e/ec/DW_Block_Angular_Matrix.jpg + :align: center + :target: https://en.wikipedia.org/wiki/Dantzig%E2%80%93Wolfe_decomposition + + Block-angular matrix structure particularly suited for column generation. + +The **Branch-and-Price** algorithm extends column generation to integer programming. While column generation operates on the linear relaxation of the problem, Branch-and-Price integrates it into a Branch-and-Bound framework to handle integer constraints. This combination allows efficient exploration of the solution space while exploiting the power of decomposition techniques. Each node of the Branch-and-Bound tree employs column generation to solve the relaxed problem, providing tight bounds for pruning and accelerating convergence. + +In this series of tutorials, we will see how column generation and, more precisely, **Dantzig-Wolfe decomposition** can be implemented in idol. + +.. hint:: + + For more details on column generation, we refer to the book :cite:`uchoa2024optimizing`. + +.. toctree:: + :maxdepth: 1 + :glob: + + dantzig-wolfe + writing-branch-and-price + strong-branching diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.rst.txt new file mode 100644 index 000000000..d0fbaf722 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.rst.txt @@ -0,0 +1,6 @@ +The Integer Master Heuristic [TODO] +=================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.rst.txt new file mode 100644 index 000000000..76cfacbe7 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.rst.txt @@ -0,0 +1,198 @@ +Using Strong Branching +====================== + +Strong Branching is a technique that falls into the category of *variable selection rules*, a crucial aspect of +Branch-and-Bound algorithms. + +More specifically, the task is to decide which variable to branch on at each node of the Branch-and-Bound tree, i.e, +among a set of branching candidates whose value must be integer, one must +decide which variable with fractional value in the current solution of the relaxation to choose for creating +child nodes. + +The most common rule is the so-called *Most-Infeasible* rule, which selects a variable whose fractional +part is closest to `0.5`. Unfortunately, this rule performs badly in practice. Most importantly, if solving a node is +computationally hard, it makes sense to spend some time in carefully choosing the variable to branch on. This is typically +the case when nodes are solved using Column Generation. + +.. hint:: + + Clearly, Strong Branching is not only used in the context of column generation. It is a general technique that can be + used in any context where solving a node is computationally expensive. Thus, this tutorial is not specific to the + context of column generation, though we will use it as an example. + +The idea of Strong Branching is to evaluate the effect of branching on a variable before branching actually happens. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Formal Definition +----------------- + +Let :math:`C` be a set of indices for branching candidates at a given node, i.e., for each :math:`j\in C`, +:math:`x_j` is an integer variable in the original problem but with :math:`x_j^*\notin\mathbb Z` at the current node. +Strong Branching tries to evaluate the effect of applying branching constraints :math:`x_j \le \lfloor x_j^* \rfloor` and +:math:`x_j \ge \lceil x_j^* \rceil` to the current node. To do so, it solves, before branching happens, and for each :math:`j\in C`, +both the left and right child node. Let :math:`z_i^\le` and :math:`z_i^\ge` denote the (optimal) value of the +left and right nodes if branching is performed on :math:`x_j`. The "effect of branching on :math:`x_j`" is then estimated by +computing a score, noted :math:`\text{Score}(j)`, based on :math:`z_j^\le` and :math:`z_j^\ge`. Then Strong Branching +selects the variable with an index :math:`j^*` such that (for minimization problems) + +.. math:: + + j^* \in \text{argmax}\{ \text{Score}(j) : j\in C \}. + +Empirically, Strong Branching is known to produce substantially smaller Branch-and-Bound trees compared to other +branching rules. Unfortunately, computing :math:`\text{Score}(j)` typically requires a lot of time. To avoid this, +several techniques have been designed such as *Restricted Strong Branching* and *Strong Branching with Phases* (see below). + +For more details, please refer to :cite:`ACHTERBERG200542`. + +Scoring Functions +^^^^^^^^^^^^^^^^^ + +Two common scoring functions :math:`\text{Score}(j)` are found in the literature. The *linear* formula :cite:`Linderoth1999` + +.. math:: + + \text{LinearScore}(j) := (1 - \mu) \min(\Delta_j^\le, \Delta_j^\ge) + \mu \max(\Delta_j^\le, \Delta_j^\ge), + +and the *product* formula + +.. math:: + + \text{ProductScore}(j) := \max(\Delta_j^\le, \varepsilon) \max(\Delta_j^\ge, \varepsilon), + +in which :math:`\Delta_j^\le := z_j^\le - z^*` and :math:`\Delta_j^\ge := z_j^\ge - z^*` with :math:`z^*` denoting the +(optimal) value of the current node. Parameters :math:`\mu\in[0,1]` and :math:`\varepsilon > 0` are given. +In idol, :math:`\mu = 1/6` and :math:`\varepsilon = 10^{-6}`. + +Variants +^^^^^^^^ + +There are several variants of Strong Branching. The most common ones are: + +* **Full Strong Branching** denotes the standard Strong Branching rule which solves all :math:`2|C|` nodes at each branching + decision. The drawback of this approach is that it may take a lot of time to solve all these sub-problems before branching + actually happens. +* **Restricted Strong Branching** is an attempt to reduce the computational burden of Full Strong Branching. The idea is to + consider only a maximum of :math:`K` branching candidates at each branching decision instead of the whole set :math:`C`. + Thus, :math:`C` is replaced by a smaller set :math:`R\subseteq C` such that :math:`|R| = K` with :math:`K` fixed. + The "restricted branching candidate set" :math:`R` is created by taking the :math:`K` first variables selected by, yet + another, branching rule, e.g., the most-infeasible rule. +* **Strong Branching with Look Ahead** is similar to *Restricted Strong Branching* yet differs from it by not specifying a + fixed size for the "restricted branching candidate set" :math:`R`. Instead, it considers a look ahead parameter, noted + :math:`L`, and applies the Full Strong Branching rule. However, if the branching candidate does not change after :math:`L` + iterations, the algorithm stops and the current branching candidate is returned. +* **Strong Branching with Phases** is a combination of the above three approaches which applies different schemes depending + on the level of the current node in the Branch-and-Bound tree. Additionally, it allows to solve each node only approximately + by, e.g., imposing a maximum number of iterations for the underlying Column Generation algorithm. + +Implementation +-------------- + +This section explains how to use the Strong Branching rule in idol. +It is based on the Generalized Assignment Problem example from the :ref:`Column Generation `. +More specifically, we will assume that you have a variable +:code:`model` of type :code:`Model` which has a decomposable structure specified by the annotation :code:`(Annotation) decomposition`. + +Full Strong Branching +^^^^^^^^^^^^^^^^^^^^^ + +Recall that the Branch-and-Price algorithm is created by the following code. + +.. code:: cpp + + const auto column_generation = + DantzigWolfeDecomposition(decomposition) + .with_master_optimizer(Gurobi::ContinuousRelaxation()) + .with_default_sub_problem_spec( + DantzigWolfe::SubProblem() + .add_optimizer(Gurobi()) + ); + +Now, we will show how to use Strong Branching as a branching rule. This is done while creating our Branch-and-Bound algorithm. In +particular, we will use the :code:`StrongBranching` class to define our branching rule. We can, for instance, simply +declare + +.. code:: cpp + + const auto branching_rule = + StrongBranching(); + +which will create a new Full Strong Branching rule. Just like any other branching rule, it can be used by calling the +:code:`BranchAndBound::with_branching_rule` method. + +.. code:: cpp + + const auto branch_and_bound = + BranchAndBound() + .with_branching_rule(branching_rule) + .with_node_selection_strategy(BestBound()); + +Then, we can write a Branch-and-Price algorithm and solve our problem as follows. + +.. code:: cpp + + const auto branch_and_price = branch_and_bound + column_generation; + + model.use(branch_and_price); + + model.optimize(); + +Beware that here, we only implemented Full Strong Branching which, as we saw, is not computationally convenient... +Let's see how to implemented Restricted Strong Branching. + +Restricted Strong Branching +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To implement Restricted Branching, one simply needs to call the :code:`StrongBranching::with_max_n_variables` method. +This is done as follows. + +.. code:: cpp + + const auto branching_rule = + StrongBranching() + .with_max_n_variables(50); + +Here, we set the maximum number of considered variables equal to :math:`K = 50`. + +Phases +^^^^^^ + +In this section, we will discuss how to implement phases with the strong branching rule. This is done by using the +:code:`StrongBranching::add_phase` method. This method takes three arguments: a phase type, which is used to indicate +how each node should be solved, e.g., with some iteration limit, a maximum number of variables to consider, for restricted +strong branching, and a maximum depth, used to trigger the phase based on the level of the current node in the Branch-and-Bound +tree. + +Here is an instance of strong branching with phases which, for nodes whose level is below or equal to 3, applies Full +Strong Branching, then switches to Restricted Strong Branching with :math:`K = 30` and which solves nodes with an iteration +limit of 20. + +.. code:: cpp + + const auto branching_rule = + StrongBranching() + .add_phase(StrongBranchingPhases::WithNodeOptimizer(), std::numeric_limits::max(), 3) + .add_phase(StrongBranchingPhases::WithIterationLimit(20), 30, std::numeric_limits::max()); + +Observe how we used :code:`std::numeric_limits::max()` to remove restrictions on the number of +considered variables and on the maximum depth for the final phase. Note that, by default, if no phase is triggered for a +given depth, e.g., because it was not specified, Full Strong Branching is applied. Here, however, we make sure that the +second phase is always triggered. + +Changing the Scoring Function +----------------------------- + +The scoring function can be changed by calling the :code:`StrongBranching::with_scoring_function` method. This method +takes a scoring function as an argument. The scoring function is a sub-class of :code:`NodeScoreFunction` and can be +:code:`Linear` or :code:`Product`. + +By default, idol uses the product scoring function. To change it to the linear scoring function, one can simply write + +.. code:: + + const auto branching_rule = + StrongBranching() + .with_scoring_function(NodeScoreFunctions::Linear()); diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.rst.txt new file mode 100644 index 000000000..8d6500ff4 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.rst.txt @@ -0,0 +1,6 @@ +Writing A Branch-and-Cut-and-Price Algorithm [TODO] +=================================================== + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.rst.txt b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.rst.txt new file mode 100644 index 000000000..4c8fe1392 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.rst.txt @@ -0,0 +1,81 @@ +Writing A Branch-and-Price Algorithm +==================================== + +This tutorial is a follow-up to the `Dantzig-Wolfe decomposition tutorial `_. +In this tutorial, we will see how to implement a Branch-and-Price algorithm in idol to, not only solve +the continuous relaxation of the Generalized Assignment Problem (GAP), but also handle the integrality constraints. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Prerequisites +------------- + +We will assume that you have already defined your model as well as the column generation optimizer factory. +If you haven't done so, we recommend you to read the `Dantzig-Wolfe decomposition tutorial `_. + +Hence, you should already have something like this: + +.. code:: + + + const auto sub_problem_specifications = DantzigWolfe::SubProblem() + .add_optimizer(Gurobi()); + + const auto column_generation = DantzigWolfeDecomposition(decomposition) + .with_master_optimizer(Gurobi::ContinuousRelaxation()) + .with_default_sub_problem_spec(sub_problem_specifications); + +Moreover, we will assume that your model is called :code:`model` and that the decomposition annotation is called :code:`decomposition`. + +Creating the Branch-and-Price Algorithm +--------------------------------------- + +Our remaining task is to embed our column generation routine inside of a Branch-and-Bound algorithm. + +Hence, we create a branch-and-bound algorithm as follows. + +.. code:: cpp + + const auto branch_and_bound = BranchAndBound() + + /* Variables are selected for branching using + the most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the best-bound rule */ + .with_node_selection_rule(BestBound()) + + /* The algorithm will run with a time limit of 3600 */ + .with_time_limit(3600) + + ); + +Here, variables are selected for branching using the most-infeasible rule, and nodes are selected using the best-bound rule. +We also set a time limit of one hour. + +The column generation algorithm can easily be combined with the branch-and-bound algorithm using the :code:`BranchAndBound::with_node_optimizer` +method, or by simply adding the two algorithms together. + +For instance, the following line creates a branch-and-price algorithm. + +.. code:: cpp + + model.use(branch_and_bound + column_generation); + +Solving +------- + +As usual, one can simply call the :code:`Model::optimize` method to solve the problem. + +.. code:: cpp + + model.optimize(); + + +That's it! The problem is being now solved by a branch-and-price and the integrality constraints are handled automatically! + +The rest remains unchanged and one can retrieve the solution +through the usual methods such as :code:`Model::get_status` and :code:`Model::get_var_primal`. + diff --git a/_sources/tutorials/mixed-integer-programming/index.rst.txt b/_sources/tutorials/mixed-integer-programming/index.rst.txt new file mode 100644 index 000000000..559c49ef7 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/index.rst.txt @@ -0,0 +1,41 @@ +.. _mip: + +Mixed-Integer Optimization +========================== + +Mixed-integer optimization deals with problems of the following form: + +.. math:: + :label: eq:mip + + \begin{align} + \min_{x} \quad & c^\top x + x^\top D x + c_0 \\ + \text{s.t.} \quad & a_{i\cdot}^\top x + x^\top Q^i x \le b_i, \quad i = 1, \ldots, m, \\ + & x_j \in \mathbb{Z}, \quad j \in I \subseteq \{ 1, \dotsc, n \}. + \end{align} + +Here, :math:`x` are the decision variables, while :math:`c`, :math:`D`, :math:`c_0`, :math:`a_i`, :math:`Q^i`, and :math:`b_i` are given data. +Some of the decision variables are required to be integer-valued and are indexed by :math:`I`. + +We say that :math:numref:`eq:mip` is an integer problem if :math:`I = \{ 1, \dotsc, n \}`, i.e., if all variables are required to +be integer. It is said to be mixed-integer if :math:`I \neq \emptyset`. Otherwise, we say that :math:numref:`eq:mip` is a continuous problem. + +An important class of problems is when :math:`D = 0` and :math:`Q^i = 0` for all :math:`i`, i.e., when the objective function and the constraints are linear. +In such a case, we say that :math:numref:`eq:mip` is a mixed-integer linear problem (MILP), or a linear problem (LP) if all variables are continuous. + +.. figure:: https://upload.wikimedia.org/wikipedia/commons/0/06/IP_polytope_with_LP_relaxation.svg + :align: center + :target: https://en.wikipedia.org/wiki/Integer_programming + + The feasible region of an integer problem and its linear relaxation. + +**Table of Contents** + +.. toctree:: + :maxdepth: 2 + :glob: + + modeling/index + optimizers/index + branch-and-bound/index + dantzig-wolfe/index diff --git a/_sources/tutorials/mixed-integer-programming/modeling/constraints.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/constraints.rst.txt new file mode 100644 index 000000000..34436259a --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/constraints.rst.txt @@ -0,0 +1,141 @@ +.. _api_constraints: + +Constraints +=========== + +Constraints are mathematical expressions that must be satisfied by the decision variables of an optimization problem. +They are used to model relationships between variables, and to restrict the feasible region of the problem. + +There are mainly two types of constraints: + +- **Linear Constraints**: constraints that are linear in the decision variables. +- **Quadratic Constraints**: constraints that are non-linear in the decision variables. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Linear Constraints +------------------ + +Creating Constraints +^^^^^^^^^^^^^^^^^^^^ + +Similarly to variables, constraints are easily created and added to a given ``Model``. + +Constraints can be created by calling the constructor of the :ref:`Ctr ` class and added to a model by means of +:code:`Model::add` or by calling the :code:`Model::add_ctr` method. + +Using the :code:`Ctr` class directly creates a variable that is not associated to any model. We will then need to add it +explicitly to a model. This is done by calling the :code:`Model::add` method. See for instance the following code. + +.. code:: + + Env env; + Model model(env); + + Var x_0(env, 0., Inf, Continuous, "x_0"); + Var x_1(env, 0., Inf, Continuous, "x_1"); + Ctr constraint(env, x_0 + x_1 >= 1); + + model.add(x_0); + model.add(x_1); + model.add(constraint); + +A more compact version of this code is obtained by making use of the ``Model::add_vars`` and ``Model::add_ctr`` methods. + +.. code-block:: cpp + + Env env; + Model model(env); + + const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, 0, "x"); + const auto constraint = model.add_ctr(x[0] + x[1] >= 1); + +Temporary Constraints +^^^^^^^^^^^^^^^^^^^^^ + +As you can see, a constraint is created using the pattern :code:`{expression} {sign} {expression}` where + +* :code:`{sign}` is one of :code:`<=`, :code:`>=` and :code:`==`; +* :code:`{expression}` is an expression, i.e., an instance of :code:`AffExpr`. + +Actually, the pattern :code:`{expression} {sign} {expression}` only creates a "temporary" constraint, i.e., a constraint +which is not associated to any model. This is why we need to add it to a model by calling the :code:`Model::add_ctr` method. +Temporary constraints are objects of the class :ref:`TempCtr `. An equivalent code would be. + +.. code:: cpp + + Env env; + Model model(env); + + const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x"); + const auto temporary_constraint = TempCtr(x[0] + x[1], GreaterOrEqual, 1); + + model.add_ctr(temporary_constraint); + +Here, the sign of the constraint is +specified by the second argument of the constructor of the :ref:`TempCtr ` class, and can take values +:code:`LessOrEqual`, :code:`GreaterOrEqual` and :code:`EqualTo`. + +Accessing Constraints +^^^^^^^^^^^^^^^^^^^^^ + +Information about a given constraint in a model can be accessed by calling the corresponding methods of the model. +For instance, one can access the right-hand side of a constraint by calling the :code:`Model::get_ctr_rhs` method. +Here is a list of the most common methods to access information about a constraint. + +- :code:`Model::get_ctr_rhs`: get the right-hand side of a constraint, +- :code:`Model::get_ctr_type`: get the type of a constraint, +- :code:`Model::get_ctr_row`: get the row of a constraint, +- :code:`Model::get_ctr_index`: get the index of a constraint. + +When available, the values associated to the constraint in a given solution can be accessed in a similar way. +Here is a list of the most common methods to access information about a constraint in a solution. + +- :code:`Model::get_ctr_dual`: get the dual value of a constraint, +- :code:`Model::get_ctr_farkas`: get the Farkas certificate of a constraint (for infeasible systems). + +The :code:`Model::has` method can be used to check if a given constraint is in the model. + +For more details, see the :ref:`Model ` class. + +Modifying Constraints +^^^^^^^^^^^^^^^^^^^^^ + +Similarly to accessing constraints, the attributes of a constraint can be modified by calling the corresponding methods of the model. +Here is a list of the most common methods to modify a constraint. + +- :code:`Model::set_ctr_rhs`: set the right-hand side of a constraint, +- :code:`Model::set_ctr_type`: set the type of a constraint, +- :code:`Model::set_ctr_row`: set the row of a constraint. + +The row of a constraint in the model can be modified by calling the :code:`Ctr::set_row` method. +For instance. + +.. code:: cpp + + LinExpr row; + row.set(x, coefficient_for_x_in_constraint); + row.set(y, coefficient_for_y_in_constraint); + + model.set_ctr_row(constraint, row); + +For more details, see the :ref:`Model ` class. + +Removing Constraints +^^^^^^^^^^^^^^^^^^^^ + +A constraint can be removed from a model by calling the :code:`Model::remove` method. + +Quadratic Constraints +--------------------- + +Creating, accessing and modifying quadratic constraints is similar to linear constraints. The main difference is that +quadratic constraints are created using the :ref:`QCtr ` class. Moreover, the corresponding methods in :code:`Model` +use :code:`qctr` instead of :code:`ctr`. For instance, the following code accesses the type of a quadratic constraint. + +.. code:: + + model.get_qctr_type(quadratic_constraint); + diff --git a/_sources/tutorials/mixed-integer-programming/modeling/environment.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/environment.rst.txt new file mode 100644 index 000000000..7017cfbf6 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/environment.rst.txt @@ -0,0 +1,14 @@ +The Environment +--------------- + +Every optimization object (such as variables and constraints) are managed by an "optimization environment". +It is the environment that controls the death and life of such objects. It is also through the environment that idol +manages the different versions each optimization object may have during the execution of your program. + +Typically, only one environment should be used by your code. Yet, it is not forbidden to have several environments at the same time (not advised). + +Environments are objects of the :ref:`Env ` class, and can be created as follows. + +.. code-block:: + + Env env; // Creates a new optimization environment. diff --git a/_sources/tutorials/mixed-integer-programming/modeling/expressions.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/expressions.rst.txt new file mode 100644 index 000000000..739209d6c --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/expressions.rst.txt @@ -0,0 +1,79 @@ +Expressions +=========== + +An expression generically refers to any mathematical expression involving variables or constraints. In idol, expressions +are represented by the :code:`QuadExpr`, :code:`AffExpr` and :code:`LinExpr` classes. These classes are used to represent +quadratic, affine and linear expressions, respectively. + +An expression can be created by adding, subtracting or multiplying variables together. For instance, +the following code creates the mathematical expression :math:`1 + 3 x_0 + x_1 + x_0 + 2 x_0 x_1`. + +.. code:: cpp + + const AffExpr expr = 1 + 3 * x[0] + x[1] + x[0] + 2 * x[0] * x[1]; + + std::cout << expr << std::endl; + + +.. contents:: Table of Contents + :local: + :depth: 2 + +:code:`LinExpr`: Linear Expressions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The :code:`LinExpr` class is used to represent linear expressions. A linear expression is a mathematical expression +that is linear in the variables. For instance, the following code creates the mathematical expression :math:`1 + 3 x_0 + x_1`. + +.. code:: cpp + + const LinExpr expr = 1 + 3 * x[0] + x[1]; + + std::cout << expr << std::endl; // "1 + 3 * x[0] + 1 * x[1]" + +.. admonition:: Linear in What? + + Actually, :code:`LinExpr` is a template class with one parameter, which is the type of the "variables" in the linear expression. + For instance, it is possible de create a linear expression of :code:`Ctr` objects, which are constraints. The following code + creates the mathematical expression :math:`1 + 3 c_0 + c_1`. + + .. code:: cpp + + const LinExpr expr = 1 + 3 * c[0] + c[1]; + + std::cout << expr << std::endl; // "1 + 3 * c[0] + 1 * c[1]" + +It is possible to iterate over the terms in the expression as follows. + +.. code:: + + for (const auto& [var, constant] : expr) { + std::cout << constant << " multiplied by " << var << std::endl; + } + +:code:`AffExpr`: Affine Expressions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The :code:`AffExpr` class is used to represent affine expressions. An affine expression is a mathematical expression +that is linear in the variables and has a constant term. + +The linear part of the expression is accessed by the :code:`AffExpr::linear()` method, and the constant term is accessed +by the :code:`AffExpr::constant()` method. + +:code:`QuadExpr`: Quadratic Expressions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The :code:`QuadExpr` class is used to represent quadratic expressions. A quadratic expression is a mathematical expression +which contains an affine part and a quadratic part. The affine part can be accessed by the :code:`QuadExpr::affine()` method. + +It is possible to iterate over the terms in the quadratic part of the expression as follows. + +.. code:: + + for (const auto& [pair, constant] : expr) { + std::cout << constant << " multiplied by " << pair.first << " and " << pair.second << std::endl; + } + + for (const auto& [var, constant] : expr.affine().linear()) { + std::cout << constant << " multiplied by " << var << std::endl; + } diff --git a/_sources/tutorials/mixed-integer-programming/modeling/index.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/index.rst.txt new file mode 100644 index 000000000..51f30a647 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/index.rst.txt @@ -0,0 +1,29 @@ +.. _mip_modeling: + +.. role:: cpp(code) + :language: cpp + +Modeling a MIP with idol +======================== + +This page introduces the basic concepts of modeling optimization problems in idol. +We will discuss how to create optimization models and add variables, constraints and objective functions to that model. +We will also see how to access the different components of an existing model. + +All classes which are used for modeling (standard) optimization problems can be accessed by including :code:`#include `. + +To simplify things, we will use the :code:`namespace idol` in the following examples. This dispenses us from prefixing +every class with :code:`idol::`. For instance, we will use :code:`Model` instead of :code:`idol::Model`. + +Let's get started. + +.. toctree:: + :maxdepth: 1 + :glob: + + environment + models + variables + expressions + constraints + objective-function diff --git a/_sources/tutorials/mixed-integer-programming/modeling/models.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/models.rst.txt new file mode 100644 index 000000000..8779fadb9 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/models.rst.txt @@ -0,0 +1,90 @@ +Models +====== + +The :ref:`Model ` class is used to represent a (standard) optimization model of the form + +.. math:: + + \begin{align} + \min_{x} \quad & c^\top x + x^\top D x + c_0 \\ + \text{s.t.} \quad & a_{i\cdot}^\top x + x^\top Q^i x \le b_i, \quad i = 1, \ldots, m, \\ + & x_j \in \mathbb{Z}, \quad j \in I \subseteq \{ 1, \dotsc, n \}. + \end{align} + +Here, :math:`x` are the decision variables, while :math:`c`, :math:`D`, :math:`c_0`, :math:`a_i`, :math:`Q^i`, and :math:`b_i` are given data. +Some of the decision variables are required to be integer-valued and are indexed by :math:`I`. + +In what follows, we will dive into the :cpp:`Model` class and see how to create, read, and write models to files. + + +.. contents:: Table of Contents + :local: + :depth: 2 + +Creating a Model +^^^^^^^^^^^^^^^^ + +A Model is created by calling the constructor of the :cpp:`Model` class. Note that it is necessary to pass an environment +to the constructor. + +The following code creates a new optimization model. + +.. code-block:: cpp + + Env env; + Model model(env); + +We can now define our decision variables and constraints, and add an objective function to our model. +This is detailed in the :ref:`Variables `, :ref:`Constraints ` and :ref:`Objective ` sections, respectively. + +Reading a Model from a File +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +A Model can also be created by reading a model from a file (typically, a :code:`.mps` or an :code:`.lp` file). +To do this, idol relies on an external solver. The following code reads a model from a file using Gurobi. + +.. code-block:: cpp + + Env env; + auto model = Gurobi::read_from_file(env, "/path/to/model.mps"); + // auto model = GLPK::read_from_file(env, "/path/to/model.mps"); + +Writing a Model to a File +^^^^^^^^^^^^^^^^^^^^^^^^^ + +To write an optimization model to a file, the easiest way is again to rely on an external solver. +This is done by attaching a solver to a model, then by calling the :code:`Model::write` method. + +.. code:: + + Env env; + Model model(env); + + // Add variables and constraints HERE... + + model.use(Gurobi()); // Set the optimizer as Gurobi + + model.write("instance.lp"); // Creates a new file "instance.lp" storing the model + +Iterating over the Variables and Constraints +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The :ref:`Model ` class provides methods to iterate over the variables and constraints of the model. +See for instance, the following example. + +.. code-block:: cpp + + for (const auto& var : model.vars()) { + std::cout << "Variable " << var.name() << " belongs to the model." << std::endl; + } + + for (const auto& ctr : model.ctrs()) { + std::cout << "Constraint " << ctr.name() << " belongs to the model." << std::endl; + } + +The number of variables and constraints can be obtained by doing the following. + +.. code:: cpp + + std::cout << "Nb. of variables: " << model.vars().size() << std::endl; + std::cout << "Nb. of constraints: " << model.ctrs().size() << std::endl; diff --git a/_sources/tutorials/mixed-integer-programming/modeling/objective-function.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/objective-function.rst.txt new file mode 100644 index 000000000..bee489ea9 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/objective-function.rst.txt @@ -0,0 +1,57 @@ +.. _api_objective_functions: + +Objective Functions +=================== + +The objective function of an optimization model is a quadratic expression of the decision variables. +It is used to guide the optimization process by defining the quantity to be minimized or maximized. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Adding an Objective Function +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The objective function of an optimization model can specified by the ``Model::set_obj_expr`` method. The objective function is a linear expression of the decision variables. + +Here is an example which sets the objective function to :math:`-x_0 + 2 x_1`; + +.. code-block:: + + model.set_obj_expr(-x_0 + 2 * x_1); + +Accessing the Objective Function +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Here is a list of methods to access the objective function of a given model: + +- ``Model::get_obj_expr``: Returns the objective function of the model. +- ``Model::get_obj_sense``: Returns the optimization sense of the model. + +If a given model has been solved, one can also query the best objective function value and the best bound. + +- ``Model::get_best_obj``: Returns the best objective function value. +- ``Model::get_best_bound``: Returns the best bound. + +Changing the Optimization Sense +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +To change the optimization sense, use the ``Model::set_obj_sense`` method. +The optimization sense can be either ``Minimize`` or ``Maximize``. For instance, + +.. code:: cpp + + model.set_obj_sense(Maximize); + +Alternatively, one can use the constructor of the ``Model`` class to set the optimization sense. + +.. code:: cpp + + Env env; + Model model(env, Maximize); // Creates a model for maximization + +.. warning:: + + idol offers minimal support for maximization problems. + We recommend to use minimization problems whenever possible. diff --git a/_sources/tutorials/mixed-integer-programming/modeling/variables.rst.txt b/_sources/tutorials/mixed-integer-programming/modeling/variables.rst.txt new file mode 100644 index 000000000..b7c547cb5 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/modeling/variables.rst.txt @@ -0,0 +1,201 @@ +.. _api_variables: + +Variables +========= + +Variables are the decision variables of an optimization problem. They are the objects that we want to find the best +values for, with respect to some objective function given the specified constraints. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Creating Variables +------------------ + +There are mainly two ways to create variables in idol. The first one is to use the :ref:`Var ` class directly, and the +second one is to use the :cpp:`Model::add_var` method. + +Using the :code:`Var` class and :code:`Model::add` +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Using the :cpp:`Var` class directly creates a variable that is not associated to any model. We will then need to add it +explicitly to a model. This is done by calling the :cpp:`Model::add` method. See for instance the following code which +creates a continuous variable :math:`x`, with bounds :math:`[0,\infty)`, and adds it to the model. + +.. code:: cpp + + Var x(env, 0., Inf, Continuous, 0, "x"); + + model.add(x); // Variable x is added to the model + +Note that a variable may belong to several models at the same time. Each version of the variable in each model is then independent. +For instance, one could do the following. + +.. code:: cpp + + Var x(env, 0., Inf, Continuous, "x"); + + model.add(x); + + Model model2(env); + model2.add(x); + model2.set_var_ub(x, 10.); + +In this example, the variable :math:`x` is added to two different models. The upper bound of :math:`x` in the second model +is then set to 10. The upper bound of :math:`x` in the first model is not affected by this change. + +Also, it is possible to add a variable to a model and set its attributes (bounds and type) at the same time. For instance, +the following code is equivalent to the previous one. + +.. code:: cpp + + Var x(env, 0., Inf, Continuous, "x"); + + model.add(x); + + Model model2(env); + model2.add(x, TempVar(0, 10, Continuous, 0)); + +Here, we used the class :ref:`TempVar ` to create a temporary variable. A temporary variable is a variable +which has not been instantiate yet. It is only a "template" of a variable specifying its bounds, type an objective coefficient. Here, we therefore +add the variable :math:`x` to the second model and directly set its attributes (bounds and type) accordingly. + +Using :code:`Model::add_var` +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +A more straightforward way to create variables is to call the ``add_var`` method of the ``Model`` class. +For instance, one can do: + +.. code-block:: cpp + + const auto x = model.add_var(0, Inf, Continuous, 0, "x"); + +Here, we do not need to repeat the environment since the model's environment is automatically used. Moreover, we do not need to +explicitly add the variable to the model since it is done by the ``add_var`` method. + +Again, a variable may belong to several models at the same time. And we can do as follows. + +.. code:: cpp + + const auto x = model.add_var(0, Inf, Continuous, "x"); + + Model model2(env); + model2.add(x); + model2.set_var_ub(x, 10.); + +Note that an even more compact version of the previous code is obtained by using the ``Model::add`` method with additional +parameters. For instance, the following code is equivalent to the previous one. + +.. code:: cpp + + const auto x = model.add(0, Inf, Continuous, "x"); + + Model model2(env); + model2.add(x, TempVar(0, 10, Continuous, 0)); + +Creating Several Variables at Once +---------------------------------- + +Sometimes, you will find it convenient to create several variables at once. This can be done by calling the ``Var::make_vector`` +function, or the ``Model::add_vars`` method. These functions require +an extra parameter specifying the dimension of the new variable. + +Using :code:`Var::make_vector` and :code:`Model::add_vector` +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The following code creates variables :math:`y_{ij}` with :math:`i=1,...,K` and :math:`j=1,...,T`. + +.. code:: cpp + + const auto y = Var::make_vector(env, Dim<2>(K, T), 0., Inf, Continuous, "y"); + + model.add_vector(y); + + std::cout << y[0][0] << std::endl; // "y_0_0" + +Here, we use the :ref:`Dim ` class to specify the dimension of the new variable. The :ref:`Dim ` class is a template class +that takes an integer as a template parameter. The integer specifies the dimension of the new variable. In this case, we use +2 to specify that we want to create a two-dimensional variable. Then, we specify the size of each dimension by passing the +appropriate arguments to the constructor of the :ref:`Dim ` class. Here, we specify that the first dimension has size :math:`K` and the +second dimension has size :math:`T`. + +Once the variables are created, we add them to the model by calling the :cpp:`Model::add_vector` method. + +Using :code:`Model::add_vars` +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +One alternative is to use the more direct ``Model::add_vars`` method. + +.. code:: cpp + + const auto y = model.add_vars(Dim<2>(K, T), 0., Inf, Continuous, "y"); + + std::cout << y[0][0] << std::endl; // "y_0_0" + +Note that the :ref:`Dim ` class is used in the same way as in the previous example. + +Variables Types +--------------- + +Variables can be of different types. In idol, three types of variables are available: + +- :code:`Continuous`: continuous variables, +- :code:`Binary` binary variables, +- :code:`Integer`: integer variables. + +Accessing Variables +------------------- + +Information about a given variable in a model can be accessed by calling the corresponding methods of the model. For instance, +one can access the lower bound of a variable by calling the :cpp:`Model::get_var_lb` method. Here is a list of the most common +methods to access information about a variable. + +- :code:`Model::get_var_lb`: returns the lower bound of a variable, +- :code:`Model::get_var_ub`: returns the upper bound of a variable, +- :code:`Model::get_var_type`: returns the type of a variable, +- :code:`Model::get_var_column`: returns the column of a variable, +- :code:`Model::get_var_obj`: returns the objective coefficient of a variable, +- :code:`Model::get_var_index`: returns the index of a variable. + +When available, the value of the variable in a given solution can be accessed in a similar way. +Here is a list of the most common methods to access information about a variable in a solution. + +- :code:`Model::get_var_primal`: returns the value of a variable in a solution, +- :code:`Model::get_var_reduced_cost`: returns the reduced cost of a variable in a solution, +- :code:`Model::get_var_ray`: returns the primal ray of a variable in a solution. + +The :cpp:`Model::has` method can be used to check if a given variable is in the model. + +For more details, see the :ref:`Model ` class. + +Modifying Variables +------------------- + +Similarly to accessing variables, the attributes of a variable can be modified by calling the corresponding methods of the model. +Here is a list of the most common methods to modify a variable. + +- :code:`Model::set_var_lb`: sets the lower bound of a variable, +- :code:`Model::set_var_ub`: sets the upper bound of a variable, +- :code:`Model::set_var_type`: sets the type of a variable, +- :code:`Model::set_var_obj`: sets the objective coefficient of a variable, +- :code:`Model::set_var_column`: sets the column of a variable. + +For instance, the following code updates the column of a given variable. + +.. code:: cpp + + LinExpr column(objective_coefficient_for_x); + column.set(constraint1, constraint1_coefficient_for_x); + column.set(constraint2, constraint2_coefficient_for_x); + + model.set_var_column(x, column); + +Here, we use the :cpp:`LinExpr` class to represent the column of the variable :math:`x`. + +For more details, see the :ref:`Model ` class. + +Removing Variables +------------------ + +A variable can be removed from a model by calling the :cpp:`Model::remove` method. diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/access-optimizer.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/access-optimizer.rst.txt new file mode 100644 index 000000000..e7c4b274e --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/access-optimizer.rst.txt @@ -0,0 +1,37 @@ +Getting Access to The Underlying Optimizer +========================================== + +In some advanced situations, you may want to access the underlying optimizer of an optimization model. +For instance, this could be the case if you want to get optimizer-specific information which are not exposed by the :code:`Model` interface. + +In this case, you can use the :code:`Model::optimizer` method. Note that this method +will return a reference of type :code:`Optimizer&`. + +To access optimizer-specific routines, you will need to cast the reference to the appropriate optimizer type. +This is made easier by the :code:`Optimizer::as` and :code:`Optimizer::is` methods, which allow you to cast the optimizer to a specific type or check if it is of a specific type. + +For instance, the following code shows how to access the underlying Gurobi optimizer of model. + +.. code:: + + Env env; + Model model(env); + auto x = model.add_var(0.0, 1.0, Continuous, -1, "x"); + + model.use(Gurobi()); + model.optimize(); + + if (!model.optimizer().is()) { + throw Exception("The optimizer is not Gurobi"); + } + + auto& gurobi_optimizer = model.optimizer().as(); + + // Access the optimizer-specific routines + GRBVar& var = gurobi_optimizer[x]; + +.. warning:: + + A common mistake is to try to cast the optimizer to the wrong type. In particular, to cast optimizer to its + optimizer factory type (e.g., :code:`Gurobi` instead of :code:`Optimizers::Gurobi`). + If so, this will result in a runtime error. diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/create-optimizer.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/create-optimizer.rst.txt new file mode 100644 index 000000000..f5f2e67ba --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/create-optimizer.rst.txt @@ -0,0 +1,6 @@ +Creating Your Own Optimizer (Advanced) [TODO] +============================================= + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/create-universal-callback.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/create-universal-callback.rst.txt new file mode 100644 index 000000000..5fa76129a --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/create-universal-callback.rst.txt @@ -0,0 +1,238 @@ +.. _tutorial_create_callback: + +Creating Your Own Callback +========================== + +In this page, we see how to create your own universal callback. +Universal callbacks are callbacks which are not specific to a particular optimizer. +In that sense, they are generic and can be used with different optimizers without any modification. + +Creating your own callback can useful if you want to create a callback that is not included in the +default set of callbacks implemented in idol. +If you are looking for quick and easy-to-use callbacks for separating user cuts or lazy constraints, +you can refer to :ref:`this page `. + +.. hint:: + + Note that there are also callbacks specific to the :code:`BranchAndBound` optimizer. + If you are looking for this, you can refer to :ref:`this page `. + +.. contents:: Table of Contents + :local: + :depth: 2 + +The Basics +^^^^^^^^^^ + +Creating your callback is done by creating a sub-class of the :ref:`Callback ` class and overriding the +:code:`Callack::operator()` method. It is this method that will be called by the solver whenever an incumbent is found. + +Note, however, that callbacks cannot be given "as-is" to an optimizer but must be passed through a :ref:`CallbackFactory `. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the :ref:`CallbackFactory ` class. + +The following code shows how to create a callback factory and a callback that prints the value of the primal solution at each +iteration. + +.. code:: cpp + + /* Callback factory implementation */ + class MyCallback : public CallbackFactory { + public: + + /* Actual callback implementation */ + class Strategy { + protected: + + /* This method is called whenever an event occurs + during the solution process */ + void operator()(CallbackEvent t_event) { + + if (t_event != IncumbentSolution) { + return; + } + + std::cout << primal_solution() << std::endl; + } + + } + + /* This method creates a new callback object */ + Callback* operator()() { + return new Strategy(); + } + + /* This method creates a copy of the callback factory */ + CallbackFactory* clone() const { + return new MyCallback(*this); + } + + } + +As you can see, the callback factory has two important methods: :code:`operator()` and :code:`clone()`. The :code:`operator()` +method is used to create a new callback object, while the :code:`clone()` method is used to create a copy of the callback factory. + +The nested class :code:`Strategy` is the actual callback implementation. It is a sub-class of the :ref:`Callback ` class and +overrides the :code:`operator()` method. In this example, the callback prints the value of the primal solution whenever the event +triggering the callback is :code:`IncumbentSolution`. In other words, this callback will print out all incumbent solutions found by the solver. + +As for the :ref:`UserCutCallback ` and :ref:`LazyConstraintCallback ` classes, +our new callback can be added to an optimizer as follows. + +.. code:: cpp + + model.use( + Gurobi().add_callback(MyCallback()) + ); + + model.optimize(); + +List of Optimizers Supporting Universal Callbacks +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The following solvers support universal callbacks: + +- :code:`Gurobi` +- :code:`BranchAndBound` +- :code:`Mosek` + +Hence, for these solvers, you can create your own callback and add it to the optimizer without having to +worry about the underlying solver. + +An Example: Knapsack Cover Cuts +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. hint:: + + This section is dedicated to the "advanced topic" of knapsack cover inequalities. + Rudimentary notions on `Knapsack problems `_ and + `Cover inequalities `_ are recommended. + + +In this example, we will show how to create a callback that separates knapsack cover cuts. A knapsack cover cut is a valid inequality +for the knapsack problem. It is defined as follows: + +.. math:: + + \sum_{i \in C} x_i \leq |C| - 1 + + +where :math:`C` defines a cover of the knapsack, i.e., a set of items such that the sum of their weights is greater than the capacity of the knapsack. + +Given a solution :math:`\hat x` to the continuous relaxation of the knapsack problem, we can check whether it violates a cover inequality. +This is done by solving the following separation problem. + +.. math:: + + \begin{align} + \max_{z} \quad & (1 - \hat x)^\top z \qquad \ge 1 \\ + \text{s.t.} \quad & w^\top z \ge W + 1, \\ + & z\in\{0,1\}^n. + \end{align} + +A cover inequality is violated if and only if the optimal objective value of this problem is strictly less than 1. +In such a case, a new cut should be added. + +We will write a callback that separates knapsack cover cuts. + +To this end, we first create our knapsack problem model. This is done as follows. + +.. code:: cpp + + Env env; + Model knapsack(env, Maximize); + + const auto x = knapsack.add_vars(Dim<1>(n), 0, 1, Binary, 0, "x"); + + knapsack.add_ctr(idol_Sum(i, Range(n_items), w[i] * x[i]) <= W); + knapsack.set_obj_expr(idol_Sum(i, Range(n_items), p[i] * x[i])); + +Then, we create our callback factory. It is this factory that will be used to create a new callback object when needed. +Since we need to pass some parameters to the callback, we will use the constructor of the callback factory to pass these parameters. +This is done as follows. + +.. code:: cpp + + + class KnapsackCover : public CallbackFactory { + const std::vector m_x; + const std::vector m_weights; + const std::vector m_profits; + const double m_capacity; + public: + KnapsackCover(const std::vector& t_x, + const std::vector& t_weights, + const std::vector& t_profits, + double t_capacity) + : m_x(t_x), m_weights(t_weights), + m_profits(t_profits), m_capacity(t_capacity) {} + + class Strategy; + + Callback* operator()() { + return new Strategy(m_x, m_weights, m_profits, m_capacity); + } + + CallbackFactory* clone() const { + return new MyCallback(*this); + } + + } + +The actual implementation of the callback is done in the nested class :code:`Strategy`. +This class is a sub-class of the :ref:`Callback ` class and is defined as follows. + +.. code:: cpp + + class KnapsackCover::Strategy { + const std::vector m_x; + const std::vector m_weights; + const std::vector m_profits; + const double m_capacity; + protected: + Strategy(const std::vector& t_x, + const std::vector& t_weights, + const std::vector& t_profits, + double t_capacity) + : m_x(t_x), m_weights(t_weights), + m_profits(t_profits), m_capacity(t_capacity) {} + + void operator()(CallbackEvent t_event) { + + if (t_event != InvalidSolution) { + return; + } + + auto& env = parent().env(); + const auto fractional_point = primal_solution(); + + Model separation(env, Maximize); + + const auto z = separation.add_vars(Dim<1>(m_x.size()), 0, 1, Binary, "z"); + separation.add_ctr(idol_Sum(i, Range(m_x.size()), m_weights[i] * z[i]) >= m_capacity + 1); + separation.set_obj_expr(idol_Sum(i, Range(m_x.size()), (1 - fractional_point[i]) * z[i])); + + separation.use(Gurobi()); + + separation.optimize(); + + if (separation.get_best_obj() < 1) { + return; + } + + const auto cut = idol_Sum(i, Range(m_x.size()), separation.get_var_primal(z[i]) * (1 - x[i])) >= 1; + + add_user_cut(cut); + + } + } + +Finally, we can add our callback to the optimizer as follows. + +.. code:: + + knapsack.use( + Gurobi::Continuous().add_callback(KnapsackCover(x, w, p, W)) + ); + + knapsack.optimize(); diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/index.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/index.rst.txt new file mode 100644 index 000000000..6866d4a24 --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/index.rst.txt @@ -0,0 +1,23 @@ +.. _mip_optimizers: + +.. role:: cpp(code) + :language: cpp + +Solving a MIPs +============== + +This series of tutorials covers the basics of solving mixed-integer problems (MIPs) in idol. +We assume that you already know how to create a model and add variables, constraints, and objectives to it. + +Let's get started! + +.. toctree:: + :maxdepth: 1 + :glob: + + optimizers + solving + access-optimizer + universal-callbacks + create-universal-callback + #create-optimizer diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/optimizers.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/optimizers.rst.txt new file mode 100644 index 000000000..22248b08e --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/optimizers.rst.txt @@ -0,0 +1,122 @@ +.. role:: cpp(code) + :language: cpp + +The Concept of :code:`Optimizer` and :code:`OptimizerFactory` +============================================================= + +This page discusses the concept of optimizers and optimizer factories in idol. +We will discuss how to set up an optimizer for solving a model and how to access the solution of the model. + +In idol, an optimizer is a class that is responsible for solving a given optimization problem. +It is created by an optimizer factory, which is a class that is responsible for assembling and creating optimizers. + +.. contents:: Table of Contents + :local: + :depth: 2 + +A First Example +--------------- + +We start with an example. Consider the following code, which models a simple knapsack problem: + +.. code:: cpp + + Env env; + Model model(env, Maximize); + const auto x = model.add_vars(Dim<1>(3), 0, 1, Binary, 0, "x"); + model.add_ctr(x[0] + 2 * x[1] + 3 * x[2] <= 5); + model.set_obj_expr(x[0] + x[1] + x[2]); + +The code creates a model with three binary variables, and adds a constraint and an objective function to it. +Currently, the model does not have an optimizer, so it cannot be solved. +Calling :code:`model.optimize()` will result in an exception being thrown. + +To set up an optimizer, we need to call the :code:`Model::use` method, which takes an optimizer factory as an argument. +For this example, let us use the :code:`GLPK` optimizer factory, which creates an optimizer using GLPK to solve our model; see :ref:`GLPK `. + +.. code:: cpp + + model.use(GLPK()); + +Here, we assume that idol was linked with the GLPK library during installation. If this is not the case, please, refer to +the installation guidelines. + +Now, calling :code:`model.optimize()` will cause the optimizer factory to create an optimizer, which will solve the model. +Since we are using the :ref:`GLPK ` optimizer factory, an instance of :code:`Optimizers::GLPJ` +will be created and used to solve the model; see :ref:`Optimizers::GLPK `. + +Note that we can modify the model after setting up the optimizer. The optimizer will be updated accordingly. For instance. + +.. code:: + + model.add_ctr(x[0] + x[1] <= 1); // Add a new constraint + model.optimize(); // Re-optimize + +idol provides several optimizer factories, each of which creating an optimizer using different solvers or implementing different algorithms. +For instance, the :ref:`Gurobi ` optimizer factory creates an optimizer using the Gurobi solver, +while the :ref:`BranchAndBound ` optimizer factory creates an optimizer implementing a branch-and-bound algorithm. + +Typically, users only work with optimizer factories, and do not need to create optimizers directly. +Passing arguments to an optimizer is always possible at creation time through the optimizer factory. +For instance, here is a small example showing how to pass a time limit to the :code:`GLPK` optimizer: + +.. code:: + + model.use(GLPK().with_time_limit(10)); // add time limit of 10 seconds + +As it can be seen, arguments are given by calling the :code:`with_*` methods of the optimizer factory, followed by the name of the argument. + +Combining Optimizers +-------------------- + +In some cases, it can useful to combine optimizers together. For instance, this is useful if one wants to use an optimizer +to solve a sub-problem arising in another optimizer. +The process of combining optimizers is straightforward and follows the same pattern as what we have seen so far. + +For instance, consider the following code, which implements a simple branch-and-bound algorithm to solve our knapsack problem. + +.. code:: cpp + + model.use( + /* The overall algorithm is a branch-and-bound */ + BranchAndBound() + + /* Each node is solved by the continuous relaxation + of the problem, with GLPK */ + .with_node_optimizer(GLPK::ContinuousRelaxation()) + + /* Variables are selected for branching using the + most-infeasible rule */ + .with_branching_rule(MostInfeasible()) + + /* Nodes are selected using the best-bound rule */ + .with_node_selection_rule(BestBound()) + + /* Turn on logs */ + .with_logs(true) + + /* The algorithm will run with a time limit of 3600 */ + .with_time_limit(3600) + ) + ); + +In this example, we create a branch-and-bound algorithm to solve the model, and we use GLPK to solve the continuous relaxation of the problem at each node. +Also note that we can nest optimizers as many times as we want with no restrictions. + +To simplify the writing of complex optimizer factories, it may be useful to use temporary variables to store intermediate results. +For instance. + +.. code:: cpp + + const auto continuous_relaxation = GLPK::ContinuousRelaxation(); + const auto branching_rule = MostInfeasible(); + const auto node_selection_rule = BestBound(); + + const auto branch_and_bound = BranchAndBound() + .with_node_solver(continuous_relaxation) + .with_branching_rule(branching_rule) + .with_node_selection_rule(node_selection_rule) + .with_logs(true) + .with_time_limit(3600); + + model.use(branch_and_bound); diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/solving.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/solving.rst.txt new file mode 100644 index 000000000..fd507db1d --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/solving.rst.txt @@ -0,0 +1,189 @@ +Using an External Solver and Accessing the Solution +=================================================== + +This page shows how to solve a model and access the solution. +The reader should be familiar with the concept of optimizer and optimizer factories. If this is not the case, +please refer to the page on :ref:`Optimizers `. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Modeling and Solving with an External Solver (e.g., GLPK) +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Let us consider the following code. + +.. code:: cpp + + using namespace idol; + + const unsigned int n_items = 5; + const double[] profit = { 40., 50., 100., 95., 30., }; + const double[] weight = { 2., 3.14, 1.98, 5., 3., }; + const double capacity = 10.; + + Env env; + Model model(env, Maximize); + + auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, 0, "x"); + model.add(idol_Sum(j, Range(n_items), weight[j] * x[j] ) <= capacity); + model.set_obj_expr(idol_Sum(j, Range(n_items), profit[i] * x[i]); + +This code creates a model for the knapsack problem. + +As described in the page on :ref:`this page `, +we will now set up an optimizer and solve the model. For this example, we use GLPK. + +.. code:: cpp + + model.use(GLPK()); + +Solving the model is then done by calling the :code:`optimize` method. + +.. code:: cpp + + model.optimize(); + +Accessing the Solution +^^^^^^^^^^^^^^^^^^^^^^ + +idol provides several methods to access the solution. + +First, the status of the solution can be accessed using the :code:`get_status` method. +Here is a detailed list of possible statuses and reasons: + ++-------------------+-------------------------------------------+ +| Status | Description | ++===================+===========================================+ +| Loaded | The model has been loaded but not solved. | ++-------------------+-------------------------------------------+ +| Optimal | An optimal solution has been found. | ++-------------------+-------------------------------------------+ +| Feasible | A feasible solution has been found. | ++-------------------+-------------------------------------------+ +| Infeasible | No feasible solution could be found. | ++-------------------+-------------------------------------------+ +| InfOrUnbnd | The model is infeasible or unbounded. | ++-------------------+-------------------------------------------+ +| Unbounded | The model is unbounded. | ++-------------------+-------------------------------------------+ +| Fail | The solver failed to solve the model. | ++-------------------+-------------------------------------------+ +| SubOptimal | A suboptimal solution has been found. | ++-------------------+-------------------------------------------+ + +Related to a status, the reason for the status can be accessed using the :code:`get_reason` method. + ++-----------------+--------------------------------------------------------------------+ +| Reason | Description | ++=================+====================================================================+ +| NotSpecified | No specific reason is available. | ++-----------------+--------------------------------------------------------------------+ +| Proved | The solver proved optimality. | ++-----------------+--------------------------------------------------------------------+ +| TimeLimit | The solver reached the time limit. | ++-----------------+--------------------------------------------------------------------+ +| IterLimit | The solver reached the iteration limit. | ++-----------------+--------------------------------------------------------------------+ +| ObjLimit | The solver reached the objective limit. | ++-----------------+--------------------------------------------------------------------+ +| Numerical | A numerical issue occurred during the solution process. | ++-----------------+--------------------------------------------------------------------+ +| MemoryLimit | The solver ran out of memory. | ++-----------------+--------------------------------------------------------------------+ +| Cycling | The solver encountered cycling (e.g., in simplex method). | ++-----------------+--------------------------------------------------------------------+ +| SolutionLimit | The solver reached the solution limit (e.g., number of solutions). | ++-----------------+--------------------------------------------------------------------+ + +Then, the following methods can be used to access the solution: + +- :code:`get_best_obj` returns the best known objective value (this always refers to feasible solutions), +- :code:`get_best_bound` returns the best known objective value bound, +- :code:`get_relative_gap` returns the relative optimality gap, +- :code:`get_absolute_gap` returns the absolute optimality gap; see :ref:`this page ` for more details about gaps and tolerances. + +Accessing the primal and dual values can be done with the following methods: + +- :code:`get_var_primal` returns the primal value of a given variable (Feasible and Optimal status only), +- :code:`get_var_ray` returns the primal ray value of a given variable (Unbounded status only), +- :code:`get_ctr_dual` returns the dual value of a given constraint (Continuous models only), +- :code:`get_ctr_farkas` returns the Farkas certificate value of a given constraint (Continuous models and Infeasible status only). + +Saving a Solution +^^^^^^^^^^^^^^^^^ + +Sometimes, you will find it useful to save a solution to access it later. + +idol provides the following functions to do so: +:code:`save_primal`, :code:`save_ray`, :code:`save_dual` and :code:`save_farkas`. +Each of these functions takes a model as argument and returns an object of the class :ref:`Point ` with template parameter :code:`Var` or :code:`Ctr` depending on the function. +The returned object stores the results of corresponding calls to :code:`get_var_primal`, :code:`get_var_ray`, :code:`get_ctr_dual` or :code:`get_ctr_farkas` methods. + +.. admonition:: Example + + This example shows how to solve a model using HiGHS and retrieves some piece of information about its solution. + + .. code-block:: + + model.use(HiGHS()); + + model.optimize(); + + const auto status = model.get_status(); + + if (status == Optimal) { + + std::cout << "Optimal solution found!" << std::endl; + + const auto primal_values = save_primal(model); + + std::cout << primal_values << std::endl; + + } else { + + std::cout << "An optimal solution could not be found." << std::endl; + + std::cout << "HiGHS returned status " << status << std::endl; + + std::cout << "The reason for this status is " << model.get_reason() << std::endl; + + if (status == Feasible) { + + std::cout << "The optimality gap is " << model.get_relative_gap() * 100 << " %" << std::endl; + + } else if (status == Unbounded) { + + std::cout << "An unbounded ray is" << std::endl; + + const auto primal_ray = save_ray(model); + + std::cout << primal_ray << std::endl; + + } else if (status == Infeasible) { + + std::cout << "A Farkas certificate is" << std::endl; + + const auto farkas = save_farkas(model); + + std::cout << farkas << std::endl; + + } + + } + +Saving a Projected Solution +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +In a more advanced solution scheme, you may deal with extended formulations of an original model, and may want to save +the projected solution on the original problem space. +In such a case, you can use the functions :code:`save_*` with an additional argument to specify the original model. +For instance. + +.. code:: cpp + + const auto primal_values = save_primal(original_model, higher_dimensional_model); + +This code will return an object of the class :ref:`Point ` storing the results of corresponding calls to :code:`get_var_primal` methods on the higher dimensional model +for the original model variables. diff --git a/_sources/tutorials/mixed-integer-programming/optimizers/universal-callbacks.rst.txt b/_sources/tutorials/mixed-integer-programming/optimizers/universal-callbacks.rst.txt new file mode 100644 index 000000000..af0552e8f --- /dev/null +++ b/_sources/tutorials/mixed-integer-programming/optimizers/universal-callbacks.rst.txt @@ -0,0 +1,257 @@ +.. _tutorial_user_lazy_cuts: + +Adding User Cuts and Lazy Constraints +===================================== + +When solving a mixed-integer program (MIP), the underlying optimizers typically make use of a branch-and-cut algorithm. +This algorithm iteratively solves a(n LP) relaxation of the problem, and then adds cuts to the problem to strengthen the relaxation. +Typically, these cuts are generated by the solver itself. However, the user can also add his or her own cuts to the problem. +This is useful when the user has domain-specific knowledge that can be used to strengthen the relaxation. + +Classically, there are two types of cuts that can be added to a MIP: user cuts and lazy constraints. + +* **User cuts** are cuts which are not necessary to define the feasible region of the problem, but which can be used to strengthen the relaxation. As a matter of fact, *User cuts never cut off feasible solutions to the original problem*. +* **Lazy constraints** are constraints which are necessary to define the feasible region of the problem but are either unlikely to be violated or impractical to generate in advance. Lazy constraints are only added to the problem if they are violated by a current solution. + +In both cases, user cuts and lazy constraints are added to the problem within a callback function, given to the optimizer. +Then, the optimizer will call this callback function at each node of the branch-and-cut tree, allowing to look for violated cuts and constraints that can be added to the problem. + +.. hint:: + + Though it is possible for the user to create his or her own callback functions, + the idol library provides a simple way to add user cuts and lazy constraints to a MIP, using the :ref:`UserCutCallback ` and :ref:`LazyCutCallback ` classes. + In case you are interested in creating your own callback functions, you can refer to :ref:`this page `. + +In the next section, we will show how to implement + +* a simple separation procedure for knapsack cover inequalities using the :ref:`UserCutCallback `, and +* a straightforward Bender's decomposition algorithm using the :ref:`LazyCutCallback ` class. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Introduction +------------ + +Now, both classes are derived from the :ref:`CallbackFactory ` class, and are used to create callback objects that can be passed to the optimizer. +They both have a similar interface: First, the user defines a model for the separation problem (i.e., the problem that will be solved to generate the cuts or constraints), +and the corresponding cut to be added to the original problem. +Then, the user creates a callback factory object, and passes the model and the cut to the factory. +The user also specifies which optimizer should be used to solve the separation problem. +Finally, the user passes the callback factory to the optimizer, which will manage the execution of the callback. + +The main difference between the two classes is that the :ref:`UserCutCallback ` class is called +whenever an invalid solution is found, e.g., a point which violates integer requirements, while the :ref:`LazyCutCallback ` class is called +whenever a new valid solution is found to check that it satisfies all the lazy constraints. + + +An Example of User Cuts: Knapsack Cover Inequalities +---------------------------------------------------- + +.. hint:: + + This section is dedicated to the "advanced topic" of knapsack cover inequalities. + Rudimentary notions on `Knapsack problems `_ and + `Cover inequalities `_ are recommended. + +Consider the knapsack problem: + +.. math:: + + \begin{align} + \max_{x} \quad p^\top x \quad + \text{s.t.} \quad w^\top x \le W, \; x\in\{0,1\}^n. + \end{align} + +Here, :math:`x` is a binary vector, :math:`p` is a vector of profits, :math:`w` is a vector of weights, and :math:`W` is the capacity of the knapsack. + +It is well-known that the knapsack problem can be strengthened by adding cover inequalities. A cover inequality is a constraint of the form + +.. math:: + + \sum_{i\in C} x_i \le |C| - 1, + +where :math:`C` defines a cover of the knapsack, i.e., a set of items such that the sum of their weights is greater than the capacity of the knapsack. + +Given a solution :math:`\hat x` to the continuous relaxation of the knapsack problem, we can check whether it violates a cover inequality +by solving the following separation problem. + +.. math:: + + \begin{align} + \max_{z} \quad & (1 - \hat x)^\top z \qquad \ge 1 \\ + \text{s.t.} \quad & w^\top z \ge W + 1, \\ + & z\in\{0,1\}^n. + \end{align} + +A cover inequality is violated if and only if the optimal objective value of this problem is strictly less than 1. +In such a case, a new cut should be added. + +As anticipated, we need to define three different things: + +- the original problem, i.e., the problem to be solved by the branch-and-cut algorithm; +- the feasible region of the separation problem, i.e., the set of all cover inequalities; +- the shape of the cuts to be added. + +Defining the original problem is straightforward and can be done as follows. + +.. code:: cpp + + Env env; + Model knapsack(env, Maximize); + + auto x = knapsack.add_vars(Dim<1>(n), 0, 1, Binary, 0, "x"); + + knapsack.add_ctr(idol_Sum(i, Range(n_items), w[i] * x[i]) <= W); + knapsack.set_obj_expr(idol_Sum(i, Range(n_items), p[i] * x[i])); + +Similarly, the feasible region of the separation problem can be defined as follows. + +.. code:: cpp + + Model cover(env); + + const auto z = cover.add_vars(Dim<1>(n), 0, 1, Binary, "z"); + + cover.add_ctr(idol_Sum(i, Range(n_items), w[i] * z[i]) >= W + 1); + +Finally, we need to define the cuts to be added to the original problem for a given cover inequality :math:`C`. +**Cuts are always expressed as if they were part of the original problem**. What we mean by this is that, here, :math:`x` +should be seen as a *variable* while :math:`z` should be seen as a *constant*. + +We therefore have, for a given :math:`z`, + +.. code:: cpp + + const auto cover_cut = idol_Sum(i, Range(n_items), !z[i] * x[i]) <= idol_Sum(i, Range(n_items), 1 - !z[i]); + +See how the z variables are "turned into" constants by prepending them with an "!" symbol. + +We are now ready to create the callback factory and pass it to the optimizer. This is done as follows. + +.. code:: cpp + + knapsack.use( + Gurobi::Continuous() + .add_callback( + UserCutCallback(cover, cover_cut) + .with_separation_optimizer(Gurobi()) + ) + ); + + knapsack.optimize(); + +Here, we solve the continuous relaxation of the knapsack problem using the Gurobi optimizer, and add the cover inequalities using the :ref:`UserCutCallback `. + +An Example of Lazy Cut Constraints: Benders Optimality Cuts +----------------------------------------------------------- + +.. hint:: + + This section is dedicated to the "advanced topic" of Benders Decomposition. + Rudimentary notions on `Linear Programming duality `_ and + `Benders Decomposition `_ the following subjects are recommended. + +We will base our example on the following model taken from `Blanco, V., (2016), Benders Decomposition, MINLP School: Theory +and Applications `_. + +.. math:: + + \begin{align} + \min_{x,y} \quad & 2 x_0 + 3x_1 + 2y \\ + \text{s.t.} \quad & x_0 + 2x_1 + y \ge 3, \\ + & 2x_0 - x_1 + 3y \ge 4, \\ + & x\ge 0, \ y\in \mathbb N. + \end{align} + +The Benders reformulation of this problem, by considering :math:`y` as the complicating variable, leads to + +.. math:: + + \begin{align} + \min_{y,z} \quad & 2y + z \\ + \text{s.t.} \quad & z \ge \lambda_1 ( 3 - y ) + \lambda_2(4 - 3y) \qquad \text{for all } \lambda \in \Lambda, \\ + & z \ge 0, \ y\in\mathbb N, + \end{align} + +with :math:`\Lambda` defined as the set of all dual feasible m_n_points_bound, i.e., those :math:`\lambda\in\mathbb R^2_+` such that + +.. math:: + + \begin{align} + & \lambda_0 + 2 \lambda_1 \le 2, \\ + & 2\lambda_0 - \lambda_1 \le 3. + \end{align} + +Now, we will show how to implement the Benders decomposition algorithm using the :ref:`LazyCutCallback ` class. +This will be done so that constraints :math:`z \ge \hat \lambda_1 ( 3 - y ) + \hat \lambda_2(4 - 3y)` are added to the master problem +whenever a violated Benders cut is found. + +As anticipated, we need to define three different things: + +- the master problem, i.e., the problem to be solved at each node of the branch-and-cut tree; +- the dual space :math:`\Lambda`, i.e., the feasible region of the separation problem; +- the shape of the cuts to be added. + +Defining the master problem is straightforward and can be done as follows. + +.. code:: cpp + + + Env env; + + Model master(env); + + const auto y = master.add_var(0, Inf, Integer, 0, "y"); + const auto z = master.add_var(0, Inf, Continuous, 0, "z"); + + master.set_obj_expr(2 * y + z); + +Similarly, the dual space :math:`\Lambda` can be defined as follows. + + +.. code:: + + Model dual_space(env); + + const auto lambda = dual_space.add_vars(Dim<1>(2), 0, Inf, Continuous, "lambda"); + + dual_space.add_ctr(lambda[0] + 2 + lambda[1] <= 2); + dual_space.add_ctr(2 * lambda[0] - lambda[1] <= 3); + + +Finally, we need to define the cuts to be added to the master problem for a given dual variable :math:`\lambda`. +**Cuts are always expressed as if they were part of the master problem**. What we mean by this is that, here, :math:`y` +should be seen as a *variable* while :math:`\lambda` should be seen as a *constant*. + +We therefore have, for a given :math:`\lambda`, + +.. code:: + + const auto benders_cut = z >= !lambda[0] * (3 - y) + !lambda[1] * (4 - 3 * y); + +See how the lambda variables are "turned into" constants by prepending them with an "!" symbol. + +We are now ready to create the callback factory and pass it to the optimizer. This is done as follows. + +.. code:: + + master.use( + Gurobi() + .add_callback( + LazyCutCallback(dual_space, benders_cut) + .with_separation_optimizer(Gurobi()) + ) + .with_lazy_cut(true) + ); + + master.optimize(); + +That's it! The optimizer will now call the callback function at each node of the branch-and-cut tree, and add the cuts to the master problem whenever a violated constraint is found. + +.. hint:: + + Here, we added a call to :code:`Gurobi::with_lazy_cut`. This is because the Gurobi optimizer does not support lazy cuts by default + and one needs to explicitly enable them. + diff --git a/_sources/tutorials/robust-optimization/index.rst.txt b/_sources/tutorials/robust-optimization/index.rst.txt new file mode 100644 index 000000000..6a71c0de4 --- /dev/null +++ b/_sources/tutorials/robust-optimization/index.rst.txt @@ -0,0 +1,15 @@ +.. _robust: + +Robust Optimization +=================== + +.. warning:: + + This section is under construction. + +.. toctree:: + :maxdepth: 3 + :glob: + + single-stage/index + two-stage/index diff --git a/_sources/tutorials/robust-optimization/single-stage/index.rst.txt b/_sources/tutorials/robust-optimization/single-stage/index.rst.txt new file mode 100644 index 000000000..d8695ac5b --- /dev/null +++ b/_sources/tutorials/robust-optimization/single-stage/index.rst.txt @@ -0,0 +1,14 @@ +.. _robust_single: + +Single-stage Robust Optimization +================================ + +.. warning:: + + This section is under construction. + +.. toctree:: + :maxdepth: 3 + :glob: + + diff --git a/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.rst.txt b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.rst.txt new file mode 100644 index 000000000..dc4ccbd9a --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.rst.txt @@ -0,0 +1,10 @@ +Using Column-and-Constraint-Generation +====================================== + +.. toctree:: + :maxdepth: 1 + :glob: + + introduction + write-ccg + trust-region-stabilization diff --git a/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.rst.txt b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.rst.txt new file mode 100644 index 000000000..5977afb80 --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.rst.txt @@ -0,0 +1,165 @@ +Introduction +============ + +The Column-and-Constraint Generation (CCG) algorithm is a classical method for solving two-stage robust optimization problems. +It was originally introduced by :cite:`Zeng2013`. + +In idol, the implementation of CCG alows to solve a class of problems which is slightly more general than classical +two-stage robust optimization problems. This class of problems is defined in the following section. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Problem Definition and Notation +------------------------------- + +The CCG algorithm can solve optimization problems of the form + +.. math:: + :label: eq:original-problem + + \begin{align} + \min_x \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & \forall \xi\in\Xi, \ \exists y\in Y(x,\xi), \ G(x,y,\xi) \le 0. + \end{align} + +in which :math:`f:\mathbb R^{n_x}\rightarrow\mathbb R` is a given function, +:math:`X\subseteq\mathbb R^{n_x}` is a given set, called the *first-stage feasible set*, +:math:`\Xi\subseteq\mathbb R^{n_\xi}` is a given set, called the *uncertainty set*, typically compact, +:math:`Y(x,\xi) \subseteq \mathbb R^{n_y}` is a set, defined for all :math:`x\in X` and :math:`\xi\in\Xi`, called the *second-stage feasible set*, and +:math:`G:\mathbb R^{n_x+n_y+n_\xi}\rightarrow\mathbb R^\ell` is a given vector of functions, defining the so-called *coupling constraints* between the uncertainty, the first- and the second-stage decisions. + +.. admonition:: Regarding Coupling Constraints + + It is clear that coupling constraints are redundant since they can be incorporated into the definition of the second-stage feasible set. + However, we will see that explicitly defining *coupling constraints* may lead to different implementations of the CCG algorithm. + We will dive into this aspect after introducing the concept of *separators*. + +.. hint:: + + Consider the Min-Max-Min problem + + .. math:: + + \min_{x\in X} \ \max_{\xi\in\Xi} \ \min_{y\in Y(x,\xi)} \ \psi(x,y,\xi). + + Clearly, this is a special case of :math:numref:`eq:original-problem` since it can be written as + + .. math:: + + \begin{align} + \min_{x_0,x} \quad & x_0 \\ + \text{s.t.} \quad & (x_0,x) \in\mathbb R\times X, \\ + & \forall \xi\in\Xi, \ \exists y\in Y(x,\xi), \ \psi(x,y,\xi) \le x_0. + \end{align} + + Here, there is only one coupling constraint, which is :math:`\psi(x,y,\xi) \le x_0`. + + +The Algorithm +------------- + +Basic Idea +^^^^^^^^^^ + +The idea of the CCG algorithm is to consider a finite subset of m_n_points_bound in :math:`\Xi`, say :math:`\{ \xi^1, \dotsc, \xi^k \}`, +and to solve the following problem instead of :math:numref:`eq:original-problem`: + +.. math:: + :label: eq:master-problem + + \begin{align} + \min_{x_0,x,y^1,\dotsc,y^K} \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & G(x,y^t,\xi^t) \le 0 \qquad k=1,\dotsc,K, \\ + & y^t\in Y(x,\xi^t) \qquad k=1,\dotsc,K. + \end{align} + +Here, a new variable :math:`y^t` has been introduced for each :math:`t=1,...,k`, enforcing that, indeed, +there exists :math:`y^t\in Y(x,\xi^t)` such that :math:`G(x,y^t,\xi^t) \le 0`. + +Note that Problem :math:numref:`eq:master-problem` is a relaxation of Problem :math:numref:`eq:original-problem` since +any feasible point of :math:numref:`eq:original-problem` is also feasible for :math:numref:`eq:master-problem` (for some :math:`y^1,\dotsc,y^K`). + +Now, given a solution :math:`\hat x\in X` to the relaxed problem :math:numref:`eq:master-problem`, +one needs to check whether :math:`\hat x` is feasible for Problem :math:numref:`eq:original-problem`. +Thus, one seeks a scenario :math:`\xi^*\in\Xi` such that, either :math:`Y(\hat x, \xi^*)` is empty, or :math:`G(\hat x,y,\xi^*) > 0` for all :math:`y\in Y(\hat x, \xi^*)`. +If no such scenario exists, then :math:`\hat x` is feasible for :math:numref:`eq:original-problem`. Otherwise, the new scenario :math:`\xi^*` is added to the set of considered scenarios and the process is repeated. + +Identifying a missing scenario is called *separation*, and can be done by solving the following problem: + +.. math:: + :name: eq:separation-problem + + \max_{\xi\in \Xi} \ \max_{\ell=1,...,L} \left\{ \ \min_{ y\in Y(\hat x,\xi) } \ G_\ell(\hat x,y,\xi) \right\}. + +If the optimal value of the separation problem is non-positive, then :math:`\hat x` is feasible for :math:numref:`eq:original-problem`. +Otherwise, the solution to the separation problem gives a new scenario :math:`\xi^*` to be added to the set of scenarios. + +Note that we use the convention :math:`\max \emptyset = -\infty` and :math:`\min \emptyset = +\infty`. + +Separators +^^^^^^^^^^ + +Clearly, the separation problem :math:numref:`eq:separation-problem` can be solved in many different ways. In idol, +it is therefore possible to give a user-defined functor, called a *separator*, which solves the separation problem. +Note that the most common ways to solve the separation problem are already implemented in idol. +Yet, if you wish to implement your own separator, you should refer to :ref:`this tutorial `. + +Shortly put, the separator solves problems of the form + +.. math:: + :label: eq:single-separation-problem + + \max_{\xi\in \Xi} \ \min_{ y\in Y(\hat x,\xi) } \ G_\ell(\hat x,y,\xi), + +for a given :math:`G_\ell` (:math:`\ell\in\{1,...,L\}`). + +Note that it is ensured that the separator always solves a problem which is feasible. +Indeed, in case Problem :math:numref:`eq:separation-problem` +is not known to satisfy the *complete recourse assumption* (i.e., it is not known whether :math:`\forall x\in X, \forall\xi\in\Xi, \exists y\in Y(x,\xi)` holds), +the CCG algorithm will first solve a feasibility version of the separation problem to check whether +:math:`\hat x` is such that for all :math:`\xi\in\Xi` there exists :math:`y\in Y(\hat x,\xi)`. +Fortunately, it is also possible to specify that the complete recourse assumption holds, in which case the feasibility version of the separation problem is not solved. + +Let :math:`\xi^{\ell}` denote the solution to the separation problem :math:numref:`eq:single-separation-problem` for a given :math:`\ell\in\{1,...,L\}`. +Then, a scenario :math:`\xi^{\ell^*}` is added to Problem :math:numref:`eq:master-problem` if and only if + +.. math:: + + \ell^* \in \underset{\ell=1,...,L}{\text{argmax}} \ \min_{ y\in Y(\hat x,\xi^\ell) } \ G_\ell(\hat x,y,\xi^\ell) > \varepsilon_\text{feas}. + +See :ref:`the dedicated page ` for more details. + +On the Impact of Coupling Constraints +------------------------------------- + +We now discuss the impact of the definition of the coupling constraints :math:`G` on the implementation of the CCG algorithm. +Clearly, one obtains an equivalent problem to :math:numref:`eq:original-problem` by defining the second-stage feasible set as + +.. math:: + + \tilde Y(x,\xi) = \{ y\in Y(x,\xi) \ | \ G(x,y,\xi) \le 0 \}, + +and by considering the problem + +.. math:: + + \begin{align} + \min_x \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & \forall \xi\in\Xi, \ \exists y\in \tilde Y(\hat x,\xi). + \end{align} + +In this case, the separation problem becomes + +.. math:: + + \max_{\xi\in\Xi} \ \min_{ y\in \tilde Y(\hat x,\xi) } \ 0, + +which is a feasibility problem. + +Though the two approaches are equivalent, in the sense that they will both lead to a solution to :math:numref:`eq:original-problem`, +they may lead to different computational performances. An interested reader may refer to, e.g., :cite:`Ayoub2016` for more details. diff --git a/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.rst.txt b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.rst.txt new file mode 100644 index 000000000..d38ce8039 --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.rst.txt @@ -0,0 +1,132 @@ +Using Trust Region Stabilization +================================ + +This tutorial describes how to use the trust region stabilization in the CCG algorithm. +This stabilization technique is inspired by the work of :cite:`Baena2020` on Benders decomposition. + +.. admonition:: Assumption + + This feature is only applicable if the first-stage decisions are binary, i.e., :math:`X \subseteq \{0,1\}^{n_x}`. + +.. contents:: Table of Contents + :local: + :depth: 2 + +Introduction +------------ + +In this section, we discuss stabilization of the CCG algorithm if the first-stage decisions are binary, i.e., :math:`X \subseteq \{0,1\}^{n_x}`. + +Let :math:`\bar x` be a given stability center, i.e., a point that is thought to be a "good" solution to the problem. +The following constraint is called a *local branching constraint*: + +.. math:: + + \Delta(x,\bar x) := \sum_{i:\bar x_i = 1} (1 - x_i) + \sum_{i:\bar x_i = 0} x_i \le \rho, + +with :math:`\rho` a given radius. Additionally, we call *reversed local branching constraint* the following constraint: + +.. math:: + + \Delta(x,\bar x) \ge \rho + 1. + +At each iteration, the stabilized CCG algorithm solves the following problem instead of :math:numref:`eq:master-problem`: + +.. math:: + + \begin{align} + \min_{x_0,x} \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & G(x,y^t,\xi^t) \le 0 \quad t=1,\dotsc,k, \\ + & y^t\in Y(x,\xi^t) \quad t=1,\dotsc,k, \\ + & \Delta(x,\bar x) \le \rho, \\ + & \Delta(x,\bar x') \ge \rho' + 1 \quad \forall (\bar x', \rho') \in R, + \end{align} + +for some set :math:`R\subseteq X\times\mathbb N` of reversed local branching constraints. + +The complete stabilized CCG algorithm is described with the following pseudocode. + +.. raw:: html + + 
    +        \begin{algorithm}
+        \caption{Stabilized CCG Algorithm}
+        \begin{algorithmic}
+        \REQUIRE An initial radius \( \rho\in\{ 1,\dotsc, n_x \} \) and an initial point \( \bar x\in X \).
+        \STATE Initialize \( k \gets 0 \), \( UB \gets +\infty \), \( LB \gets -\infty \), \( R \gets \emptyset \)
+        \STATE Solve the restricted master problem (RMP)
+        \IF{the RMP is infeasible}
+            \IF{ \( \rho \ge n_x \) }
+                \STATE STOP, \( UB \) is the optimal value.
+            \ENDIF
+            \STATE Add a reversed local branching constraint, \( R \gets R \cup (\bar x, \rho) \)
+            \STATE Increase \( \rho \)
+        \ELSE
+            \STATE Let \( x^k \) be the solution of the RMP and \( v^k \) be its value
+            \STATE Solve the separation problem, let \( \xi^k \) be the solution and \( s^k \) be its value
+            \IF{ \( s^k \le \varepsilon_\text{feas} \) }
+                \STATE \( UB \gets \min\{ UB, v^k \} \)
+                \STATE Solve the RMP without the stabilization constraints, let $\underline v^k$ be its value, set \( LB \gets \underline v^k \)
+                \IF{ \( UB - LB \le \varepsilon \) }
+                    \STATE STOP, \( UB \) is the optimal value.
+                \ENDIF
+                \STATE Add a reversed local branching constraint, \( R \gets R \cup (x^k, \rho) \)
+                \STATE Update the stability center \( \bar x \gets x^k \)
+                \STATE Optionally, reset \( \rho \gets 1 \)
+            \ENDIF
+            \STATE \( k \gets k + 1 \)
+            \STATE Go back to step 2
+        \ENDIF
+        \end{algorithmic}
+        \end{algorithm}
+
    + + +Note that if :math:`\rho \ge n_x`, the stabilized CCG is exactly the CCG algorithm. + +Implementation in idol +---------------------- + +Activating the trust region stabilization in idol is done through the method :code:`with_stabilization` of the :code:`idol::Robust::ColumnAndConstraintGeneration` class. +An object of the class :code:`Robust::CCGStabilizers::TrustRegion` must be passed as an argument to the method. + +The following code shows how to use the trust region stabilization in idol. + +.. code:: + + model.use( + Robust::ColumnAndConstraintGeneration(stages, uncertainty_set) + .with_master_optimizer(Gurobi()) + .with_separator(Robust::CCGSeparators::Bilevel()) + .with_stabilization(Robust::CCGStabilizers::TrustRegion()) + .with_logs(true) + ); + + model.optimize(); + +Note that the radius :math:`\rho` is set to + +.. math:: + + \rho \gets \lceil \mu_i n_x \rceil + +where :math:`\mu_i` is a parameter controlling the size of the trust region and :math:`n_x` is the number of (binary) first-stage variables. By default, :math:`\mu_i` takes value in +::math:`\lbrace .01, .02, .5 \rbrace`. +You can set the values of :math:`\mu_i` by calling the method :code:`with_trust_factors` of the class :code:`Robust::CCGStabilizers::TrustRegion`. +For instance, the following code sets the trust factors to :math:`\lbrace .02, .5 \rbrace`. + +.. code:: + + model.use( + Robust::ColumnAndConstraintGeneration(stages, uncertainty_set) + .with_master_optimizer(Gurobi()) + .with_separator(Robust::CCGSeparators::Bilevel()) + .with_stabilization( + Robust::CCGStabilizers::TrustRegion() + .with_trust_factors({.02, .5}) + ) + .with_logs(true) + ); diff --git a/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.rst.txt b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.rst.txt new file mode 100644 index 000000000..23fdd1be9 --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.rst.txt @@ -0,0 +1,49 @@ +.. _tutorial_ccg: + +Writing a Column-and-Constraint-Generation Algorithm +==================================================== + +In this tutorial, we will see how to write a column-and-constraint-generation to solve a two-stage robust problem. + +To this end, we will assume that you have your two-stage robust problem modeled already in idol. In particular, +we consider that you have + +1. :code:`(idol::Model) model` which is the deterministic model of the problem in which the uncertain data are seen as parameters. + +2. :code:`(idol::Model) uncertainty_set` which is the uncertainty set of the robust problem. + +3. :code:`(idol::Robust::StageDescription) stages` which stores the assignments of variables and constraints to each stage. + +If you do not know what these are, please refer to the tutorial on :ref:`how to model a two-stage robust problem `. + +Then, you can solve this two-stage robust problem using a column-and-constraint-generation algorithm as follows: + +.. code:: + + model.use( + Robust::ColumnAndConstraintGeneration(stages, uncertainty_set) + .with_master_optimizer(Gurobi()) + .with_separator(Robust::CCGSeparators::Bilevel()) + .with_logs(true) + ); + + model.optimize(); + + std::cout << save_primal(model) << std::endl; + +Notice that the optimizer is attached to the deterministic model and that both the uncertainty set and the stages are passed as arguments. +An optimizer to solve the master problem is necessary and will be called when needed. Here, we use the Gurobi optimizer. + +Most importantly, it is also necessary to specify a separator. The separator is a sub-routine of the CCG algorithm +which solves the separation problem, i.e., it finds the worst-case scenario for a given solution to the master problem. +In this example, we use the Bilevel separator which calls the MibS bilevel optimization solver at each iteration. + +Finally, the method :code:`optimize` is called to solve the problem and the solution is printed. + +.. hint:: + + Here, we have assumed that the problem does not satisfy the complete recourse assumption, i.e., it is not known if + :math:`\forall x\in X, \forall\xi\in\Xi, \exists y\in Y(x,\xi)`. If, to the contrary, this assumption holds, + it can be communicated to the solver by calling the method :code:`with_complete_recourse(true)`. By doing this, + the CCG algorithms will not solve the feasibility separation problem which is most likely to result in a faster convergence. + diff --git a/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.rst.txt b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.rst.txt new file mode 100644 index 000000000..5cc62d579 --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.rst.txt @@ -0,0 +1,8 @@ +.. _tutorial_write_ccg_separator: + +Writing Your Own Separator (Advanced) [TODO] +============================================ + +.. warning:: + + This is a work in progress. Thank you for your understanding. diff --git a/_sources/tutorials/robust-optimization/two-stage/index.rst.txt b/_sources/tutorials/robust-optimization/two-stage/index.rst.txt new file mode 100644 index 000000000..e0cf41831 --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/index.rst.txt @@ -0,0 +1,13 @@ +.. _robust_single: + +Adjustable Robust Optimization (Two-stage) +========================================== + + + +.. toctree:: + :maxdepth: 3 + :glob: + + modeling + column-and-constraint-generation/index diff --git a/_sources/tutorials/robust-optimization/two-stage/modeling.rst.txt b/_sources/tutorials/robust-optimization/two-stage/modeling.rst.txt new file mode 100644 index 000000000..83c44e54f --- /dev/null +++ b/_sources/tutorials/robust-optimization/two-stage/modeling.rst.txt @@ -0,0 +1,219 @@ +.. _modeling_two_stage_robust_problem: + +Modeling Adjustable Robust Problems +=================================== + +In this tutorial, we will see how to model a two-stage robust problem in idol. + +To follow this tutorial, you should be familiar with two-stage robust optimization and modeling optimization problems in idol. +If this is not the case, we recommend you to read the tutorial on :ref:`MIP modeling `. + +.. contents:: Table of Contents + :local: + :depth: 2 + +A Two-Stage Robust Facility Location Problem +-------------------------------------------- + +We consider a two-stage robust facility location problem (FLP) where demands are uncertain. + +Given a set of potential facility locations :math:`V_1` and a set of customers :math:`V_2`, the goal is to select a subset of facility locations +to activate in order to serve all customers' demand, while minimizing the total cost. +This version introduces uncertainty in the customers' demands. + +Note that there is also an example for the :ref:`deterministic version of the FLP using Column Generation `. + +Each facility :math:`i\in V_1` has an opening cost :math:`f_i` and a maximum capacity :math:`q_i`. +Each customer :math:`j\in V_2` has a demand :math:`d_j`. +The unitary cost for serving customer :math:`j\in V_2` from facility :math:`i\in V_1` is :math:`t_{ij}`. +The uncertainty in customer demands is controlled by a parameter :math:`\Gamma`. + +In this robust variant, we consider that the demands are uncertain and can be expressed as :math:`d_j(\xi) = d_j(1 + p\xi_j)` +with :math:`p` being the maximum increase in demand and :math:`\xi` being an unknown vector taken in the uncertainty set + +.. math:: + + \Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}. + +We model the two-stage robust FLP as + +.. math:: + + \min_{x\in \{0,1\}^{|V_1|}} \ \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \ \min_{y\in Y(x,\xi)} \ \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\} + +where :math:`Y(x,\xi)` is the set of feasible solutions for the second stage problem, given the first stage solution :math:`x` and the realization :math:`\xi` of the uncertain demand vector. +It is defined as the set of vectors :math:`y\in \mathbb{R}^{|V_1|\times|V_2|}` that satisfy the following constraints + +.. math:: + + \begin{align*} + & \sum_{i\in V_1} y_{ij} = d_j(\xi) && j\in V_2, \\ + & \sum_{j\in V_2} y_{ij} \le q_i x_i && i\in V_1, \\ + & y_{ij} \ge 0 && i\in V_1, j\in V_2. + \end{align*} + +In what follows, we will assume that we have a variable :code:`instance` of type :code:`idol::Problems::FLP::Instance` +that contains the data of the problem. Most typically, you will want to read the instance from a file. This is done as follows. + +.. code:: + + // Read instance + const auto instance = Problems::FLP::read_instance_1991_Cornuejols_eal("robust_ccg.data.txt"); + +Additionally, we define an optimization environment :code:`env` and some parameters. + +.. code:: + + Env env; + + const double Gamma = 3; + const double percentage_increase = .2; + +Modeling Steps +-------------- + +To model a two-stage robust problem, one needs to perform the following steps: + +1. Define an uncertainty set :math:`\Xi`. +2. Define the deterministic model in which :math:`\xi` is a parameter. +3. Assign a stage to each variable and constraint. + +Let's see how these steps are done in idol. + +Defining the Uncertainty Set +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Modeling the uncertainty set :math:`\Xi` is done in the same way as modeling any classical optimization problem. +For instance, one can do as follows. + +.. code:: + + const unsigned int n_customers = instance.n_customers(); + + Model uncertainty_set(env); + + auto xi = uncertainty_set.add_vars(Dim<1>(n_customers), 0., 1, Binary, "xi"); + uncertainty_set.add_ctr(idol_Sum(j, Range(n_customers), xi[j]) <= Gamma); + +Note that defining an objective function is not necessary since the uncertainty set is not optimized over. +If an objective function is defined, it will be ignored by the optimizer. + +Defining the Deterministic Model +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The deterministic model underlying the two-stage robust FLP is the same as the classical FLP, except that the demand is seen as a parameter. + +Recall that a variable, e.g., :code:`xi[0]`, can be turned into a parameter by prepending it with :code:`!`. + +Hence, +we can define the deterministic model as follows. + +.. code:: + + const unsigned int n_facilities = instance.n_facilities(); + + Model model(env); + + const auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, "x"); + const auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., Inf, Continuous, "y"); + + // Capacity constraints + for (unsigned int i = 0 ; i < n_facilities ; ++i) { + model.add_ctr(idol_Sum(j, Range(n_customers), y[i][j]) <= instance.capacity(i) * x[i]); + } + + // Demand satisfaction constraints + for (unsigned int j = 0 ; j < n_customers ; ++j) { + // IMPORTANT: here we use the parameter "!xi[j]" instead of the variable "xi[j]" + model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) == instance.demand(j) * (1 + percentage_increase * !xi[j])); + } + + // Objective function + model.seobj_expr(idol_Sum(i, Range(n_facilities), + instance.fixed_cost(i) * x[i] + + idol_Sum(j, Range(n_customers), + instance.per_unit_transportation_cost(i, j) * y[i][j] + ) + ) + ); + +Assigning Stages +^^^^^^^^^^^^^^^^ + +The last step is to assign a stage to each variable and constraint. Here, variables :math:`x` are first-stage variables +and variables :math:`y` are second-stage variables, i.e., they depend on the realization of the uncertain demand. +Similarly, all constraints are second-stage constraints since they are part of the second-stage feasible region. + +Assigning stages is done by creating a new object of type :code:`idol::Robust::StageDescription`. +Under the hood, this object does nothing more but defining new annotations for variables and constraints storing +the assigned stage of each variable and constraint. It is created as follows. + +.. code:: + + Robust::StageDescription stages(env); + +By default, all variables and constraints are assigned to the first stage. +To assign a variable or constraint to the second stage, one can use the method :code:`set_stage` of the object :code:`stages`. +For instance, one can do as follows. + +.. code:: + + for (const auto& var : model.vars()) { + if (var.name().front() != 'x') { + stages.set_stage(var, 2); + } + } + +Similarly, since all constraints are second-stage constraints, one can do as follows. + +.. code:: + + for (const auto& ctr : model.ctrs()) { + stages.set_stage(ctr, 2); + } + +.. admonition:: About stage annotations + + Note that it is also possible to define your own annotations to assign variables and constraints to stages. + This is a rather advanced feature and it is your responsability to ensure that the annotations are consistent with the model. + + The annotations are based on the following conventions: all first-stage variables and constraints have the annotation evaluating to :code:`MasterId`. + All second-stage variables and constraints have the annotation evaluating to :code:`0`. + + For instance, the following code is equivalent to the previous one. + + .. code:: + + Annotation stage_vars(model, "stage_vars", MasterId); // By default, all variables are first-stage variables + Annotation stage_ctrs(model, "stage_ctrs", MasterId); // By default, all constraints are first-stage constraints + + for (const auto& var : model.vars()) { + if (var.name().front() != 'x') { + var.set(stage_vars, 0); // Assign variable to the second stage + } + } + + for (const auto& ctr : model.ctrs()) { + ctr.set(stage_ctrs, 0); // Assign constraint to the second stage + } + + idol::Robust::StageDescription stages(stage_vars, stage_ctrs); + + By doing so, a call to :code:`stages.stage(var)` will return "1" for all first-stage variables and "2" for all second-stage variables. + The underlying annotation can be obtained using + + .. code:: + + Annotation stage_vars = stages.stage_vars() + + Finally, also note the method :code:`stages.stage_index(var)` that will return "0" for all first-stage variables and "1" for all second-stage variables. + + +That's it! We have now modeled a two-stage robust FLP in idol. Note that you will now need +to attach an optimizer to the model to solve it. +To this end, be sure to check the tutorials on optimizers for two-stage robust problems, e.g., :ref:`the column-and-constraint generation tutorial `. + +Complete Example +---------------- + +A complete example is given :ref:`here ` \ No newline at end of file diff --git a/_static/basic.css b/_static/basic.css new file mode 100644 index 000000000..7ebbd6d07 --- /dev/null +++ b/_static/basic.css @@ -0,0 +1,914 @@ +/* + * Sphinx stylesheet -- basic theme. + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { + display: inline; 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+ vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a:visited { + color: #551A8B; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +aside.footnote > span, +div.citation > span { + float: left; +} +aside.footnote > span:last-of-type, +div.citation > span:last-of-type { + padding-right: 0.5em; +} +aside.footnote > p { + margin-left: 2em; +} +div.citation > p { + margin-left: 4em; +} +aside.footnote > p:last-of-type, +div.citation > p:last-of-type { + margin-bottom: 0em; +} +aside.footnote > p:last-of-type:after, +div.citation > p:last-of-type:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/_static/check-solid.svg b/_static/check-solid.svg new file mode 100644 index 000000000..92fad4b5c --- /dev/null +++ b/_static/check-solid.svg @@ -0,0 +1,4 @@ + + + + diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js new file mode 100644 index 000000000..54b3c4638 --- /dev/null +++ b/_static/clipboard.min.js @@ -0,0 +1,7 @@ +/*! + * clipboard.js v2.0.8 + * https://clipboardjs.com/ + * + * Licensed MIT © Zeno Rocha + */ +!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 + + + + diff --git a/_static/copybutton.css b/_static/copybutton.css new file mode 100644 index 000000000..f1916ec7d --- /dev/null +++ b/_static/copybutton.css @@ -0,0 +1,94 @@ +/* Copy buttons */ +button.copybtn { + position: absolute; + display: flex; + top: .3em; + right: .3em; + width: 1.7em; + height: 1.7em; + opacity: 0; + transition: opacity 0.3s, border .3s, background-color .3s; + user-select: none; + padding: 0; + border: none; + outline: none; + border-radius: 0.4em; + /* The colors that GitHub uses */ + border: #1b1f2426 1px solid; + background-color: #f6f8fa; + color: #57606a; +} + +button.copybtn.success { + border-color: #22863a; + color: #22863a; +} + +button.copybtn svg { + stroke: currentColor; + width: 1.5em; + height: 1.5em; + padding: 0.1em; +} + +div.highlight { + position: relative; +} + +/* Show the copybutton */ +.highlight:hover button.copybtn, button.copybtn.success { + opacity: 1; +} + +.highlight button.copybtn:hover { + background-color: rgb(235, 235, 235); +} + +.highlight button.copybtn:active { + background-color: rgb(187, 187, 187); +} + +/** + * A minimal CSS-only tooltip copied from: + * https://codepen.io/mildrenben/pen/rVBrpK + * + * To use, write HTML like the following: + * + *

    Short

    + */ + .o-tooltip--left { + position: relative; + } + + .o-tooltip--left:after { + opacity: 0; + visibility: hidden; + position: absolute; + content: attr(data-tooltip); + padding: .2em; + font-size: .8em; + left: -.2em; + background: grey; + color: white; + white-space: nowrap; + z-index: 2; + border-radius: 2px; + transform: translateX(-102%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); +} + +.o-tooltip--left:hover:after { + display: block; + opacity: 1; + visibility: visible; + transform: translateX(-100%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); + transition-delay: .5s; +} + +/* By default the copy button shouldn't show up when printing a page */ +@media print { + button.copybtn { + display: none; + } +} diff --git a/_static/copybutton.js b/_static/copybutton.js new file mode 100644 index 000000000..2ea7ff3e2 --- /dev/null +++ b/_static/copybutton.js @@ -0,0 +1,248 @@ +// Localization support +const messages = { + 'en': { + 'copy': 'Copy', + 'copy_to_clipboard': 'Copy to clipboard', + 'copy_success': 'Copied!', + 'copy_failure': 'Failed to copy', + }, + 'es' : { + 'copy': 'Copiar', + 'copy_to_clipboard': 'Copiar al portapapeles', + 'copy_success': '¡Copiado!', + 'copy_failure': 'Error al copiar', + }, + 'de' : { + 'copy': 'Kopieren', + 'copy_to_clipboard': 'In die Zwischenablage kopieren', + 'copy_success': 'Kopiert!', + 'copy_failure': 'Fehler beim Kopieren', + }, + 'fr' : { + 'copy': 'Copier', + 'copy_to_clipboard': 'Copier dans le presse-papier', + 'copy_success': 'Copié !', + 'copy_failure': 'Échec de la copie', + }, + 'ru': { + 'copy': 'Скопировать', + 'copy_to_clipboard': 'Скопировать в буфер', + 'copy_success': 'Скопировано!', + 'copy_failure': 'Не удалось скопировать', + }, + 'zh-CN': { + 'copy': '复制', + 'copy_to_clipboard': '复制到剪贴板', + 'copy_success': '复制成功!', + 'copy_failure': '复制失败', + }, + 'it' : { + 'copy': 'Copiare', + 'copy_to_clipboard': 'Copiato negli appunti', + 'copy_success': 'Copiato!', + 'copy_failure': 'Errore durante la copia', + } +} + +let locale = 'en' +if( document.documentElement.lang !== undefined + && messages[document.documentElement.lang] !== undefined ) { + locale = document.documentElement.lang +} + +let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; +if (doc_url_root == '#') { + doc_url_root = ''; +} + +/** + * SVG files for our copy buttons + */ +let iconCheck = ` + ${messages[locale]['copy_success']} + + +` + +// If the user specified their own SVG use that, otherwise use the default +let iconCopy = ``; +if (!iconCopy) { + iconCopy = ` + ${messages[locale]['copy_to_clipboard']} + + + +` +} + +/** + * Set up copy/paste for code blocks + */ + +const runWhenDOMLoaded = cb => { + if (document.readyState != 'loading') { + cb() + } else if (document.addEventListener) { + document.addEventListener('DOMContentLoaded', cb) + } else { + document.attachEvent('onreadystatechange', function() { + if (document.readyState == 'complete') cb() + }) + } +} + +const codeCellId = index => `codecell${index}` + +// Clears selected text since ClipboardJS will select the text when copying +const clearSelection = () => { + if (window.getSelection) { + window.getSelection().removeAllRanges() + } else if (document.selection) { + document.selection.empty() + } +} + +// Changes tooltip text for a moment, then changes it back +// We want the timeout of our `success` class to be a bit shorter than the +// tooltip and icon change, so that we can hide the icon before changing back. +var timeoutIcon = 2000; +var timeoutSuccessClass = 1500; + +const temporarilyChangeTooltip = (el, oldText, newText) => { + el.setAttribute('data-tooltip', newText) + el.classList.add('success') + // Remove success a little bit sooner than we change the tooltip + // So that we can use CSS to hide the copybutton first + setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) + setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) +} + +// Changes the copy button icon for two seconds, then changes it back +const temporarilyChangeIcon = (el) => { + el.innerHTML = iconCheck; + setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) +} + +const addCopyButtonToCodeCells = () => { + // If ClipboardJS hasn't loaded, wait a bit and try again. This + // happens because we load ClipboardJS asynchronously. + if (window.ClipboardJS === undefined) { + setTimeout(addCopyButtonToCodeCells, 250) + return + } + + // Add copybuttons to all of our code cells + const COPYBUTTON_SELECTOR = 'div.highlight pre'; + const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) + codeCells.forEach((codeCell, index) => { + const id = codeCellId(index) + codeCell.setAttribute('id', id) + + const clipboardButton = id => + `` + codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) + }) + +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} + + +var copyTargetText = (trigger) => { + var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); + + // get filtered text + let exclude = '.linenos'; + + let text = filterText(target, exclude); + return formatCopyText(text, '', false, true, true, true, '', '') +} + + // Initialize with a callback so we can modify the text before copy + const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) + + // Update UI with error/success messages + clipboard.on('success', event => { + clearSelection() + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) + temporarilyChangeIcon(event.trigger) + }) + + clipboard.on('error', event => { + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) + }) +} + +runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js new file mode 100644 index 000000000..dbe1aaad7 --- /dev/null +++ b/_static/copybutton_funcs.js @@ -0,0 +1,73 @@ +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +export function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} diff --git a/_static/design.css b/_static/design.css new file mode 100644 index 000000000..ec3e9b4fe --- /dev/null +++ b/_static/design.css @@ -0,0 +1,273 @@ + +html { + scroll-behavior: smooth; +} + +body { + font-size: 20px; +} + +#doxygen { + + .k, .n, .kt { + margin-right: 10px; + } + + .cpp > dd { + margin-bottom: 30px; + } + +} + +.content:not(.custom) { + max-width: 900px; + text-align: justify; +} + +.content img { + max-width: 100%; +} + +#cards { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(270px, 1fr)); + /* grid-template-columns: auto auto auto; */ +} + +.content .toctree-l1 { + + > ul { + margin-top: 20px; + } + + ul { + margin-bottom: 20px; + } + +} + +#cards > a { + display: block; + width: 270px; + padding:10px; + color: white; + margin-bottom: 10px; + + background-color: #1f5c88; + border: 1px solid lightgray; + border-radius: 4px; + box-shadow: 0 1px 2px rgba(0, 0, 0, 0.12), 0 3px 10px rgba(0, 0, 0, 0.08); + appearance: none; + + span { + font-weight: 400; + } + + > div { + margin: 5px; + margin-top: 10px; + background: white; + text-align: center; + height: 160px; + padding: 20px; + border: 1px solid lightgray; + + img { + max-height: 160px; + max-width: 100%; + } + } + + > p { + font-size : 16px ; + text-align: justify; + } +} + +.wy-nav-content { + font-family: -apple-system, BlinkMacSystemFont, + "Segoe UI", "Roboto", "Oxygen", + "Ubuntu", "Cantarell", "Fira Sans", + "Droid Sans", "Helvetica Neue", sans-serif; + line-height: 2.5em; +} + +* { + font-weight:300; +} + +h1, h2, h3, h4, h5, h6 { + font-weight:300; + text-align: left; + font-family: -apple-system, BlinkMacSystemFont, + "Segoe UI", "Roboto", "Oxygen", + "Ubuntu", "Cantarell", "Fira Sans", + "Droid Sans", "Helvetica Neue", sans-serif; +} + +.my-button { + display: inline-block; + box-sizing: border-box; + padding: 0.3em 1em; + margin: 5px; + font-family: inherit; + font-size: inherit; + font-weight: 500; + line-height: 1.5; + color: gray; + text-decoration: none; + vertical-align: baseline; + cursor: pointer; + background-color: #f7f7f7; + border-width: 0; + border-radius: 4px; + box-shadow: 0 1px 2px rgba(0, 0, 0, 0.12), 0 3px 10px rgba(0, 0, 0, 0.08); + appearance: none; +} + +.my-button:hover { + background-color: #f5f5f5; +} + +.my-button:visited { + color: gray; +} + +#get-started { + background-color: #1f883d; + color: white; +} + +#get-started:hover { + background-color: #1c8139; +} + +.wy-nav-content-wrap { + background-color:#fcfcfc; +} + +.wy-nav-side { + border-right: 1px solid #eeebee; + background-color:#f5f6fa; +} + +.wy-menu-vertical a { + color: #404040; +} + +.wy-side-nav-search { + background-color: initial; + margin-bottom: 20px; + + #rtd-search-form { + border-top: 1px solid #e1e4e5; + margin-top: 10px; + padding-top: 20px; + } + + a { + color: #404040; + font-family: -apple-system, BlinkMacSystemFont, + "Segoe UI", "Roboto", "Oxygen", + "Ubuntu", "Cantarell", "Fira Sans", + "Droid Sans", "Helvetica Neue", sans-serif; + font-weight:300; + font-size :2.25em; + overflow-wrap: break-word; + } + + a:before { + content: ""; + } + +} + +.wy-menu-vertical li.toctree-l1.current > a { + border-top : 1px solid #efefef; + border-bottom : 1px solid #efefef; +} + +.wy-side-nav-search input[type=text] { + border-color: #e1e4e5; +} + +.toctree-l1 a:hover { + background-color:white; +} + +.rst-content div[class^=highlight], .rst-content pre.literal-block { + border: 1px solid #e1e4e5; + border-radius: 4px; + padding: 12px; + background-color: #f8f8f8; +} + +.admonition { + border-left:4px solid #6ab0de; + border-radius:4px; + box-shadow: 0 1px 2px rgba(0, 0, 0, 0.12), 0 3px 10px rgba(0, 0, 0, 0.08); +} + +.rst-content .admonition-title, .wy-alert-title, +.rst-content .note .admonition-title, .rst-content .note .wy-alert-title, .rst-content .seealso .admonition-title, .rst-content .seealso .wy-alert-title, .rst-content .wy-alert-info.admonition-todo .admonition-title, .rst-content .wy-alert-info.admonition-todo .wy-alert-title, .rst-content .wy-alert-info.admonition .admonition-title, .rst-content .wy-alert-info.admonition .wy-alert-title, .rst-content .wy-alert-info.attention .admonition-title, .rst-content .wy-alert-info.attention .wy-alert-title, .rst-content .wy-alert-info.caution .admonition-title, .rst-content .wy-alert-info.caution .wy-alert-title, .rst-content .wy-alert-info.danger .admonition-title, .rst-content .wy-alert-info.danger .wy-alert-title, .rst-content .wy-alert-info.error .admonition-title, .rst-content .wy-alert-info.error .wy-alert-title, .rst-content .wy-alert-info.hint .admonition-title, .rst-content .wy-alert-info.hint .wy-alert-title, .rst-content .wy-alert-info.important .admonition-title, .rst-content .wy-alert-info.important .wy-alert-title, .rst-content .wy-alert-info.tip .admonition-title, .rst-content .wy-alert-info.tip .wy-alert-title, .rst-content .wy-alert-info.warning .admonition-title, .rst-content .wy-alert-info.warning .wy-alert-title, .rst-content .wy-alert.wy-alert-info .admonition-title, .wy-alert.wy-alert-info .rst-content .admonition-title, .wy-alert.wy-alert-info .wy-alert-title { + background-color: initial; + color:#6ab0de; + padding:15px; +} + +.rst-content .attention, .warning { + border-left:4px solid #f0ad4e; +} + +.rst-content .danger { + border-left:4px solid #d9534f; + + .admonition-title { + background-color: initial; + color:#d9534f; + } +} + +.hint { + border-left:4px solid #1abc9c; +} + +.rst-content .hint .admonition-title, .rst-content .hint .wy-alert-title, .rst-content .important .admonition-title, .rst-content .important .wy-alert-title, .rst-content .tip .admonition-title, .rst-content .tip .wy-alert-title, .rst-content .wy-alert-success.admonition-todo .admonition-title, .rst-content .wy-alert-success.admonition-todo .wy-alert-title, .rst-content .wy-alert-success.admonition .admonition-title, .rst-content .wy-alert-success.admonition .wy-alert-title, .rst-content .wy-alert-success.attention .admonition-title, .rst-content .wy-alert-success.attention .wy-alert-title, .rst-content .wy-alert-success.caution .admonition-title, .rst-content .wy-alert-success.caution .wy-alert-title, .rst-content .wy-alert-success.danger .admonition-title, .rst-content .wy-alert-success.danger .wy-alert-title, .rst-content .wy-alert-success.error .admonition-title, .rst-content .wy-alert-success.error .wy-alert-title, .rst-content .wy-alert-success.note .admonition-title, .rst-content .wy-alert-success.note .wy-alert-title, .rst-content .wy-alert-success.seealso .admonition-title, .rst-content .wy-alert-success.seealso .wy-alert-title, .rst-content .wy-alert-success.warning .admonition-title, .rst-content .wy-alert-success.warning .wy-alert-title, .rst-content .wy-alert.wy-alert-success .admonition-title, .wy-alert.wy-alert-success .rst-content .admonition-title, .wy-alert.wy-alert-success .wy-alert-title { + background-color: initial; + color:#1abc9c; +} + +.rst-content .attention .admonition-title, +.rst-content .caution .admonition-title, +.rst-content .warning .admonition-title { + background-color: initial; + color:#f0ad4e; +} + +.fa-exclamation-circle:before, .rst-content .admonition-title:before, .wy-inline-validate.wy-inline-validate-info .wy-input-context:before, .wy-inline-validate.wy-inline-validate-warning .wy-input-context:before { + content: ""; +} + +.document { + text-align: justify; +} + +.eqno { + float:right; +} + +@media (max-width: 767px) { + + body { + font-size: 16px; + } + + #cards > a { + width: 95%; + } + + .body-header { + display: none; + } + +} \ No newline at end of file diff --git a/_static/doctools.js b/_static/doctools.js new file mode 100644 index 000000000..0398ebb9f --- /dev/null +++ b/_static/doctools.js @@ -0,0 +1,149 @@ +/* + * Base JavaScript utilities for all Sphinx HTML documentation. + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 000000000..7e4c114f2 --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,13 @@ +const DOCUMENTATION_OPTIONS = { + VERSION: '', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + 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* namely the list of stopwords, stemmer, scorer and splitter. + */ + +var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; + + +/* Non-minified version is copied as a separate JS file, if available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; + + var step3list = { + icate: 'ic', + ative: '', + alize: 'al', + iciti: 'ic', + ical: 'ic', + ful: '', + ness: '' + }; + + var c = "[^aeiou]"; // consonant + var v = "[aeiouy]"; // vowel + var C = c + "[^aeiouy]*"; // consonant sequence + var V = v + "[aeiou]*"; // vowel sequence + + var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0 + var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff 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t=0;while(this._lexer.accept("func",["elif","elsif","elseif"])){this._lexer.expect("open");e.addChild(this._parseCond());this._lexer.expect("close");e.addChild(this._parseBlock());t++}var n=false;if(this._lexer.accept("func","else")){n=true;e.addChild(this._parseBlock())}this._lexer.expect("func","endif");e.value={numElif:t,hasElse:n};return e};i.prototype._parseLoop=function(){if(!this._lexer.accept("func",["FOR","FORALL","WHILE"]))return null;var e=this._lexer.get().text.toLowerCase();var t=new a("loop",e);this._lexer.expect("open");t.addChild(this._parseCond());this._lexer.expect("close");t.addChild(this._parseBlock());var n=e!=="forall"?`end${e}`:"endfor";this._lexer.expect("func",n);return t};i.prototype._parseRepeat=function(){if(!this._lexer.accept("func",["REPEAT"]))return null;var e=this._lexer.get().text.toLowerCase();var t=new a("repeat",e);t.addChild(this._parseBlock());this._lexer.expect("func","until");this._lexer.expect("open");t.addChild(this._parseCond());this._lexer.expect("close");return t};i.prototype._parseUpon=function(){if(!this._lexer.accept("func","upon"))return null;var e=new a("upon");this._lexer.expect("open");e.addChild(this._parseCond());this._lexer.expect("close");e.addChild(this._parseBlock());this._lexer.expect("func","endupon");return e};var l=["ensure","require","input","output"];var h=["state","print","return"];i.prototype._parseStatement=function(e){if(!this._lexer.accept("func",e))return null;var t=this._lexer.get().text.toLowerCase();var n=new a("statement",t);n.addChild(this._parseOpenText());return n};var p=["break","continue"];i.prototype._parseCommand=function(e){if(!this._lexer.accept("func",e))return null;var t=this._lexer.get().text.toLowerCase();var n=new a("command",t);return n};i.prototype._parseComment=function(){if(!this._lexer.accept("func","comment"))return null;var e=new a("comment");this._lexer.expect("open");e.addChild(this._parseCloseText());this._lexer.expect("close");return e};i.prototype._parseCall=function(){var e=this._lexer;if(!e.accept("func","call"))return null;var t=e.get().whitespace;e.expect("open");var n=e.expect("ordinary");e.expect("close");var i=new a("call");i.whitespace=t;i.value=n;e.expect("open");var r=this._parseCloseText();i.addChild(r);e.expect("close");return i};i.prototype._parseCond=i.prototype._parseCloseText=function(){return this._parseText("close")};i.prototype._parseOpenText=function(){return this._parseText("open")};i.prototype._parseText=function(e){var t=new a(`${e}-text`);var n=false;var i;while(true){i=this._parseAtom()||this._parseCall();if(i){if(n)i.whitespace|=n;t.addChild(i);continue}if(this._lexer.accept("open")){i=this._parseCloseText();n=this._lexer.get().whitespace;i.whitespace=n;t.addChild(i);this._lexer.expect("close");n=this._lexer.get().whitespace;continue}break}return t};var u={ordinary:{tokenType:"ordinary"},math:{tokenType:"math"},special:{tokenType:"special"},"cond-symbol":{tokenType:"func",tokenValues:["and","or","not","true","false","to","downto"]},"quote-symbol":{tokenType:"quote"},"sizing-dclr":{tokenType:"func",tokenValues:["tiny","scriptsize","footnotesize","small","normalsize","large","Large","LARGE","huge","Huge"]},"font-dclr":{tokenType:"func",tokenValues:["normalfont","rmfamily","sffamily","ttfamily","upshape","itshape","slshape","scshape","bfseries","mdseries","lfseries"]},"font-cmd":{tokenType:"func",tokenValues:["textnormal","textrm","textsf","texttt","textup","textit","textsl","textsc","uppercase","lowercase","textbf","textmd","textlf"]},"text-symbol":{tokenType:"func",tokenValues:["textbackslash"]}};i.prototype._parseAtom=function(){for(var e in u){var t=u[e];var n=this._lexer.accept(t.tokenType,t.tokenValues);if(n===null)continue;var i=this._lexer.get().whitespace;if(e!=="ordinary"&&e!=="math")n=n.toLowerCase();return new o(e,n,i)}return null};t.exports=i},{"./ParseError":3,"./utils":6}],5:[function(n,e,t){var a=n("./utils");function A(e){this._css={};this._fontSize=this._outerFontSize=e!==undefined?e:1}A.prototype.outerFontSize=function(e){if(e!==undefined)this._outerFontSize=e;return this._outerFontSize};A.prototype.fontSize=function(){return this._fontSize};A.prototype._fontCommandTable={normalfont:{"font-family":"KaTeX_Main"},rmfamily:{"font-family":"KaTeX_Main"},sffamily:{"font-family":"KaTeX_SansSerif"},ttfamily:{"font-family":"KaTeX_Typewriter"},bfseries:{"font-weight":"bold"},mdseries:{"font-weight":"medium"},lfseries:{"font-weight":"lighter"},upshape:{"font-style":"normal","font-variant":"normal"},itshape:{"font-style":"italic","font-variant":"normal"},scshape:{"font-style":"normal","font-variant":"small-caps"},slshape:{"font-style":"oblique","font-variant":"normal"},textnormal:{"font-family":"KaTeX_Main"},textrm:{"font-family":"KaTeX_Main"},textsf:{"font-family":"KaTeX_SansSerif"},texttt:{"font-family":"KaTeX_Typewriter"},textbf:{"font-weight":"bold"},textmd:{"font-weight":"medium"},textlf:{"font-weight":"lighter"},textup:{"font-style":"normal","font-variant":"normal"},textit:{"font-style":"italic","font-variant":"normal"},textsc:{"font-style":"normal","font-variant":"small-caps"},textsl:{"font-style":"oblique","font-variant":"normal"},uppercase:{"text-transform":"uppercase"},lowercase:{"text-transform":"lowercase"}};A.prototype._sizingScalesTable={tiny:.68,scriptsize:.8,footnotesize:.85,small:.92,normalsize:1,large:1.17,Large:1.41,LARGE:1.58,huge:1.9,Huge:2.28};A.prototype.updateByCommand=function(e){var t=this._fontCommandTable[e];if(t!==undefined){for(var n in t)this._css[n]=t[n];return}var i=this._sizingScalesTable[e];if(i!==undefined){this._outerFontSize=this._fontSize;this._fontSize=i;return}throw new ParserError("Unrecognized `text-style` command")};A.prototype.toCSS=function(){var e="";for(var t in this._css){var n=this._css[t];if(n===undefined)continue;e+=`${t}:${n};`}if(this._fontSize!==this._outerFontSize)e+=`font-size:${this._fontSize/this._outerFontSize}em;`;return e};function B(e,t){this._nodes=e;this._textStyle=t}B.prototype._renderCloseText=function(e,t){var n=new A(this._textStyle.fontSize());var i=new B(e.children,n);if(e.whitespace)this._html.putText(" ");this._html.putHTML(i.renderToHTML(t))};B.prototype.renderToHTML=function(e){this._html=new _;var t;while((t=this._nodes.shift())!==undefined){var n=t.type;var i=t.value;if(t.whitespace)this._html.putText(" ");switch(n){case"ordinary":this._html.putText(i);break;case"math":if(typeof e==="undefined"){throw EvalError("No math backend found. Please setup KaTeX or MathJax.")}else if(e.name==="katex"){this._html.putHTML(e.driver.renderToString(i))}else if(e.name==="mathjax"){if(e.version<3){this._html.putText(`$${i}$`)}else{this._html.putHTML(e.driver.tex2chtml(i,{display:false}).outerHTML)}}else{throw new EvalError(`Unknown math backend ${e}`)}break;case"cond-symbol":this._html.beginSpan("ps-keyword").putText(i.toLowerCase()).endSpan();break;case"special":if(i==="\\\\"){this._html.putHTML("
    ");break}var r={"\\{":"{","\\}":"}","\\$":"$","\\&":"&","\\#":"#","\\%":"%","\\_":"_"};var o=r[i];this._html.putText(o);break;case"text-symbol":var s={textbackslash:"\\"};var a=s[i];this._html.putText(a);break;case"quote-symbol":var l={"`":"\u2018","``":"\u201c","'":"\u2019","''":"\u201d"};var h=l[i];this._html.putText(h);break;case"call":this._html.beginSpan("ps-funcname").putText(i).endSpan();this._html.write("(");var p=t.children[0];this._renderCloseText(p,e);this._html.write(")");break;case"close-text":this._renderCloseText(t,e);break;case"font-dclr":case"sizing-dclr":this._textStyle.updateByCommand(i);this._html.beginSpan(null,this._textStyle.toCSS());var u=new B(this._nodes,this._textStyle);this._html.putHTML(u.renderToHTML(e));this._html.endSpan();break;case"font-cmd":var c=this._nodes[0];if(c.type!=="close-text")continue;var f=new A(this._textStyle.fontSize());f.updateByCommand(i);this._html.beginSpan(null,f.toCSS());var d=new B(c.children,f);this._html.putHTML(d.renderToHTML(e));this._html.endSpan();break;default:throw new ParseError(`Unexpected ParseNode of type ${t.type}`)}}return this._html.toMarkup()};function _(){this._body=[];this._textBuf=[]}_.prototype.beginDiv=function(e,t,n){this._beginTag("div",e,t,n);this._body.push("\n");return this};_.prototype.endDiv=function(){this._endTag("div");this._body.push("\n");return this};_.prototype.beginP=function(e,t,n){this._beginTag("p",e,t,n);this._body.push("\n");return this};_.prototype.endP=function(){this._flushText();this._endTag("p");this._body.push("\n");return this};_.prototype.beginSpan=function(e,t,n){this._flushText();return this._beginTag("span",e,t,n)};_.prototype.endSpan=function(){this._flushText();return this._endTag("span")};_.prototype.putHTML=function(e){this._flushText();this._body.push(e);return this};_.prototype.putText=function(e){this._textBuf.push(e);return this};_.prototype.write=function(e){this._body.push(e)};_.prototype.toMarkup=function(){this._flushText();var e=this._body.join("");return e.trim()};_.prototype.toDOM=function(){var e=this.toMarkup();var t=document.createElement("div");t.innerHTML=e;return t.firstChild};_.prototype._flushText=function(){if(this._textBuf.length===0)return;var e=this._textBuf.join("");this._body.push(this._escapeHtml(e));this._textBuf=[]};_.prototype._beginTag=function(e,t,n,i){var r=`<${e}`;if(t)r+=` class="${t}"`;if(n){var o;if(a.isString(n)){o=n}else{o="";for(var s in n){attrVal=n[s];o+=`${s}:${attrVal};`}}if(i)o+=i;r+=` style="${o}"`}r+=">";this._body.push(r);return this};_.prototype._endTag=function(e){this._body.push(``);return this};var i={"&":"&","<":"<",">":">",'"':""","'":"'","/":"/"};_.prototype._escapeHtml=function(e){return String(e).replace(/[&<>"'/]/g,e=>i[e])};function r(e){e=e||{};this.indentSize=e.indentSize?this._parseEmVal(e.indentSize):1.2;this.commentDelimiter=e.commentDelimiter!==undefined?e.commentDelimiter:" // ";this.lineNumberPunc=e.lineNumberPunc!==undefined?e.lineNumberPunc:":";this.lineNumber=e.lineNumber!==undefined?e.lineNumber:false;this.noEnd=e.noEnd!==undefined?e.noEnd:false;this.scopeLines=e.scopeLines!==undefined?e.scopeLines:false;if(e.captionCount!==undefined)F.captionCount=e.captionCount;this.titlePrefix=e.titlePrefix!==undefined?e.titlePrefix:"Algorithm"}r.prototype._parseEmVal=function(e){e=e.trim();if(e.indexOf("em")!==e.length-2)throw new TypeError("Unit error; expected `em` suffix");return Number(e.substring(0,e.length-2))};function F(e,t){this._root=e.parse();this._options=new r(t);this._openLine=false;this._blockLevel=0;this._textLevel=-1;this._globalTextStyle=new A;this.backend=undefined;try{if(typeof katex==="undefined")katex=n("katex")}catch(e){}try{if(typeof MathJax==="undefined")MathJax=n("mathjax")}catch(e){}if(typeof katex!=="undefined"){this.backend={name:"katex",driver:katex}}else if(typeof MathJax!=="undefined"){this.backend={name:"mathjax",version:parseInt(MathJax.version.split(".")[0]),driver:MathJax}}}F.captionCount=0;F.prototype.toMarkup=function(){var e=this._html=new _;this._buildTree(this._root);delete this._html;return e.toMarkup()};F.prototype.toDOM=function(){var e=this.toMarkup();var t=document.createElement("div");t.innerHTML=e;return t.firstChild};F.prototype._beginGroup=function(e,t,n){this._closeLineIfAny();this._html.beginDiv(`ps-${e}${t?` ${t}`:""}`,n)};F.prototype._endGroup=function(e){this._closeLineIfAny();this._html.endDiv()};F.prototype._beginBlock=function(){var e=this._options.lineNumber&&this._blockLevel===0?.6:0;var t=this._options.indentSize+e;if(this._options.scopeLines)t/=2;this._beginGroup("block",null,{"margin-left":`${t}em`});this._blockLevel++};F.prototype._endBlock=function(){this._closeLineIfAny();this._endGroup();this._blockLevel--};F.prototype._newLine=function(){this._closeLineIfAny();this._openLine=true;this._globalTextStyle.outerFontSize(1);var e=this._options.indentSize;if(this._blockLevel>0){this._numLOC++;this._html.beginP("ps-line ps-code",this._globalTextStyle.toCSS());var t=this._options.lineNumber?e*1.25:0;t+=this._options.scopeLines?e*.1:0;if(this._options.lineNumber){this._html.beginSpan("ps-linenum",{left:`${-((this._blockLevel-1)*t)}em`}).putText(this._numLOC+this._options.lineNumberPunc).endSpan()}}else{this._html.beginP("ps-line",{"text-indent":`${-e}em`,"padding-left":`${e}em`},this._globalTextStyle.toCSS())}};F.prototype._closeLineIfAny=function(){if(!this._openLine)return;this._html.endP();this._openLine=false};F.prototype._typeKeyword=function(e){this._html.beginSpan("ps-keyword").putText(e).endSpan()};F.prototype._typeFuncName=function(e){this._html.beginSpan("ps-funcname").putText(e).endSpan()};F.prototype._typeText=function(e){this._html.write(e)};F.prototype._buildTreeForAllChildren=function(e){var t=e.children;for(var n=0;n0&&t[0].type==="comment"){var n=t.shift();this._buildTree(n)}};F.prototype._buildTree=function(e){var t;var n;var 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kind] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +// Global search result kind enum, used by themes to style search results. +class SearchResultKind { + static get index() { return "index"; } + static get object() { return "object"; } + static get text() { return "text"; } + static get title() { return "title"; } +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename, kind] = item; + + let listItem = document.createElement("li"); + // Add a class representing the item's type: + // can be used by a theme's CSS selector for styling + // See SearchResultKind for the class names. + listItem.classList.add(`kind-${kind}`); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms, anchor) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = Documentation.ngettext( + "Search finished, found one page matching the search query.", + "Search finished, found ${resultCount} pages matching the search query.", + resultCount, + ).replace('${resultCount}', resultCount); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; +// Helper function used by query() to order search results. +// Each input is an array of [docname, title, anchor, descr, score, filename, kind]. +// Order the results by score (in opposite order of appearance, since the +// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically. +const _orderResultsByScoreThenName = (a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString, anchor) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + for (const removalQuery of [".headerlink", "script", "style"]) { + htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); + } + if (anchor) { + const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`); + if (anchorContent) return anchorContent.textContent; + + console.warn( + `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.` + ); + } + + // if anchor not specified or not found, fall back to main content + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent) return docContent.textContent; + + console.warn( + "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.setAttribute("role", "list"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + _parseQuery: (query) => { + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + return [query, searchTerms, excludedTerms, highlightTerms, objectTerms]; + }, + + /** + * execute search (requires search index to be loaded) + */ + _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // Collect multiple result groups to be sorted separately and then ordered. + // Each is an array of [docname, title, anchor, descr, score, filename, kind]. + const normalResults = []; + const nonMainIndexResults = []; + + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase().trim(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + const score = Math.round(Scorer.title * queryLower.length / title.length); + const boost = titles[file] === title ? 1 : 0; // add a boost for document titles + normalResults.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score + boost, + filenames[file], + SearchResultKind.title, + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id, isMain] of foundEntries) { + const score = Math.round(100 * queryLower.length / entry.length); + const result = [ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + SearchResultKind.index, + ]; + if (isMain) { + normalResults.push(result); + } else { + nonMainIndexResults.push(result); + } + } + } + } + + // lookup as object + objectTerms.forEach((term) => + normalResults.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) { + normalResults.forEach((item) => (item[4] = Scorer.score(item))); + nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item))); + } + + // Sort each group of results by score and then alphabetically by name. + normalResults.sort(_orderResultsByScoreThenName); + nonMainIndexResults.sort(_orderResultsByScoreThenName); + + // Combine the result groups in (reverse) order. + // Non-main index entries are typically arbitrary cross-references, + // so display them after other results. + let results = [...nonMainIndexResults, ...normalResults]; + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + return results.reverse(); + }, + + query: (query) => { + const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query); + const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + SearchResultKind.object, + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + if (!terms.hasOwnProperty(word)) { + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + } + if (!titleTerms.hasOwnProperty(word)) { + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: titleTerms[term], score: Scorer.partialTitle }); + }); + } + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (!fileMap.has(file)) fileMap.set(file, [word]); + else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + SearchResultKind.text, + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords, anchor) => { + const text = Search.htmlToText(htmlText, anchor); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_static/sphinx_highlight.js b/_static/sphinx_highlight.js new file mode 100644 index 000000000..8a96c69a1 --- /dev/null +++ b/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

    ' + + '' + + _("Hide Search Matches") + + "

    " + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/_static/theme.css b/_static/theme.css new file mode 100644 index 000000000..16c9136ba --- /dev/null +++ b/_static/theme.css @@ -0,0 +1 @@ +.theme-default-content code{color:var(--text-color-l20);padding:.25rem .5rem;margin:0;font-size:.85em;border-radius:3px}.theme-default-content code .token.deleted{color:#ec5975}.theme-default-content code .token.inserted{color:#3eaf7c}.theme-default-content pre,.theme-default-content pre[class*=language-]{line-height:1.4;padding:1.25rem 1.5rem;margin:.85rem 0;background-color:var(--code-bg-color);border-radius:6px;overflow:auto}.theme-default-content pre code,.theme-default-content pre[class*=language-] 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Ze(),Nt("header",ng,[ce(o,{onToggleSidebar:t[0]||(t[0]=c=>e.$emit("toggle-sidebar"))}),Cn(e.$slots,"default"),ce(l)])}const ig=an(tg,[["render",sg]]),rg={},og={class:"nav-links"};function lg(e,t,n,s,i,r){return Ze(),Nt("nav",og,[Cn(e.$slots,"default")])}const cg=an(rg,[["render",lg]]),ag={},fg={class:"vp-sidebar"};function ug(e,t,n,s,i,r){return Ze(),Nt("div",fg,[Cn(e.$slots,"default")])}const hg=an(ag,[["render",ug]]),dg={},pg={class:"page"};function mg(e,t,n,s,i,r){return Ze(),Nt("div",pg,[Cn(e.$slots,"default"),Cn(e.$slots,"bottom")])}const gg=an(dg,[["render",mg]]),fn=Qc(Vm);fn.component("outboundlink",jm),fn.component("navbar",ig),fn.component("navlinks",cg),fn.component("sidebar",hg),fn.component("page",gg),fn.component("router-link",{props:["to"],template:''}),fn.mount("#app",!0)})(); diff --git a/api/bilevel/external-solvers/MibS.html b/api/bilevel/external-solvers/MibS.html new file mode 100644 index 000000000..1164a23cb --- /dev/null +++ b/api/bilevel/external-solvers/MibS.html @@ -0,0 +1,580 @@ + + + + + + + Bilevel::MibS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel::MibS

    +
    +

    Doxygen

    +
    +
    +class MibS : public idol::OptimizerFactoryWithDefaultParameters<MibS>
    +
    +

    Public Functions

    +
    +
    +explicit MibS(Bilevel::Description t_description)
    +
    + +
    +
    +MibS(const MibS &t_src)
    +
    + +
    +
    +MibS(MibS&&) noexcept = delete
    +
    + +
    +
    +MibS &operator=(const MibS&) = delete
    +
    + +
    +
    +MibS &operator=(MibS&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +MibS &with_cplex_for_feasibility(bool t_value)
    +
    + +
    +
    +MibS &with_file_interface(bool t_value)
    +
    + +
    +
    +MibS &add_callback(const CallbackFactory &t_cb)
    +
    + +
    +
    +virtual MibS *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +MibS &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &conditional(bool t_conditional_value, const std::function<void(MibS&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &conditional(bool t_conditional_value, const std::function<void(MibS&)> &t_if, const std::function<void(MibS&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/external-solvers/Optimizers_MibS.html b/api/bilevel/external-solvers/Optimizers_MibS.html new file mode 100644 index 000000000..b853f441b --- /dev/null +++ b/api/bilevel/external-solvers/Optimizers_MibS.html @@ -0,0 +1,246 @@ + + + + + + + Optimizers::Bilevel::MibS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Bilevel::MibS

    +
    +

    Doxygen

    +
    +

    Warning

    +

    doxygenclass: Cannot find class “idol::Optimizers::Bilevel::MibS” in doxygen xml output for project “idol” from directory: _build/xml/

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/index.html b/api/bilevel/index.html new file mode 100644 index 000000000..bb1a419ba --- /dev/null +++ b/api/bilevel/index.html @@ -0,0 +1,265 @@ + + + + + + + Bilevel Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel Optimization

    +
    +

    Modeling

    +
    + +
    +
    +
    +

    External Solvers

    +
    + +
    +
    +
    +

    Single-level Reformulations

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/modeling/Description.html b/api/bilevel/modeling/Description.html new file mode 100644 index 000000000..2fa58a26b --- /dev/null +++ b/api/bilevel/modeling/Description.html @@ -0,0 +1,350 @@ + + + + + + + Bilevel::Description + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel::Description

    +
    +

    Doxygen

    +
    +
    +class Description
    +
    +

    Public Functions

    +
    +
    +inline Description(Env &t_env, const std::string &t_name)
    +
    + +
    +
    +inline explicit Description(Env &t_env)
    +
    + +
    +
    +inline explicit Description(const Annotation<unsigned int> &t_lower_level)
    +
    + +
    +
    +inline Description(const Annotation<unsigned int> &t_lower_level, AffExpr<Var> t_follower_objective)
    +
    + +
    +
    +inline const Annotation<unsigned int> &lower_level() const
    +
    + +
    +
    +inline const QuadExpr<Var> &follower_obj() const
    +
    + +
    +
    +inline void make_upper_level(const Var &t_var)
    +
    + +
    +
    +inline void make_upper_level(const Ctr &t_ctr)
    +
    + +
    +
    +inline void make_upper_level(const QCtr &t_ctr)
    +
    + +
    +
    +inline void make_lower_level(const Var &t_var)
    +
    + +
    +
    +template<unsigned int N>
    inline void make_lower_level(const Vector<Var, N> &t_vars)
    +
    + +
    +
    +inline void make_lower_level(const Ctr &t_ctr)
    +
    + +
    +
    +inline void make_lower_level(const QCtr &t_ctr)
    +
    + +
    +
    +inline void set_lower_level_obj(QuadExpr<Var> t_objective)
    +
    + +
    +
    +inline bool is_upper(const Var &t_var) const
    +
    + +
    +
    +inline bool is_upper(const Ctr &t_ctr) const
    +
    + +
    +
    +inline bool is_upper(const QCtr &t_ctr) const
    +
    + +
    +
    +inline bool is_lower(const Var &t_var) const
    +
    + +
    +
    +inline bool is_lower(const Ctr &t_ctr) const
    +
    + +
    +
    +inline bool is_lower(const QCtr &t_ctr) const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/single-level/KKT.html b/api/bilevel/single-level/KKT.html new file mode 100644 index 000000000..d7c895133 --- /dev/null +++ b/api/bilevel/single-level/KKT.html @@ -0,0 +1,578 @@ + + + + + + + Bilevel::KKT + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel::KKT

    +
    +

    Doxygen

    +
    +
    +class KKT : public idol::OptimizerFactoryWithDefaultParameters<KKT>
    +
    +

    Public Functions

    +
    +
    +explicit KKT(const Bilevel::Description &t_description)
    +
    + +
    +
    +KKT(const KKT &t_src)
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual OptimizerFactory *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +KKT &with_single_level_optimizer(const OptimizerFactory &t_deterministic_optimizer)
    +
    + +
    +
    +KKT &with_big_M(const Annotation<double> &t_big_M)
    +
    + +
    +
    +inline KKT &operator+=(const OptimizerFactory &t_optimizer)
    +
    + +
    +
    +KKT &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &conditional(bool t_conditional_value, const std::function<void(KKT&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +KKT &conditional(bool t_conditional_value, const std::function<void(KKT&)> &t_if, const std::function<void(KKT&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Model make_model(const Model &t_model, const Bilevel::Description &t_description)
    +
    + +
    +
    +static Model make_model(const Model &t_model, const Bilevel::Description &t_description, const Annotation<double> &t_big_M)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/single-level/Optimizers_KKT.html b/api/bilevel/single-level/Optimizers_KKT.html new file mode 100644 index 000000000..49f6ea0e3 --- /dev/null +++ b/api/bilevel/single-level/Optimizers_KKT.html @@ -0,0 +1,495 @@ + + + + + + + Optimizers::Bilevel::KKT + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Bilevel::KKT

    +
    +

    Doxygen

    +
    +
    +class KKT : public idol::Algorithm
    +
    +

    Public Functions

    +
    +
    +KKT(const Model &t_parent, const idol::Bilevel::Description &t_description, const OptimizerFactory &t_deterministic_optimizer, const std::optional<Annotation<double>> &t_big_M)
    +
    + +
    +
    +virtual std::string name() const override
    +
    + +
    +
    +virtual SolutionStatus get_status() const override
    +
    + +
    +
    +virtual SolutionReason get_reason() const override
    +
    + +
    +
    +virtual double get_best_obj() const override
    +
    + +
    +
    +virtual double get_best_bound() const override
    +
    + +
    +
    +virtual double get_var_primal(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_reduced_cost(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_ray(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_ctr_dual(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual double get_ctr_farkas(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual unsigned int get_n_solutions() const override
    +
    + +
    +
    +virtual unsigned int get_solution_index() const override
    +
    + +
    +
    +virtual double get_relative_gap() const override
    +
    + +
    +
    +virtual double get_absolute_gap() const override
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline virtual void set_param_logs(bool t_value)
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline virtual void set_param_time_limit(double t_time_limit)
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +inline virtual void set_param_threads(unsigned int t_threads)
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_obj_stop(double t_best_obj_stop)
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_bound_stop(double t_best_bound_stop)
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_relative_gap(double t_tol_mip_relative_gap)
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_absolute_gap(double t_mip_tol_absolute_gap)
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline virtual void set_tol_feasibility(double t_tol_feasibility)
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline virtual void set_tol_optimality(double t_tol_optimality)
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline virtual void set_tol_integer(double t_tol_integer)
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline virtual void set_param_presolve(bool t_value)
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline virtual void set_param_infeasible_or_unbounded_info(bool t_value)
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/single-level/Optimizers_StrongDuality.html b/api/bilevel/single-level/Optimizers_StrongDuality.html new file mode 100644 index 000000000..1857fe38a --- /dev/null +++ b/api/bilevel/single-level/Optimizers_StrongDuality.html @@ -0,0 +1,495 @@ + + + + + + + Optimizers::Bilevel::StrongDuality + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Bilevel::StrongDuality

    +
    +

    Doxygen

    +
    +
    +class StrongDuality : public idol::Algorithm
    +
    +

    Public Functions

    +
    +
    +StrongDuality(const Model &t_parent, const idol::Bilevel::Description &t_description, const OptimizerFactory &t_deterministic_optimizer)
    +
    + +
    +
    +virtual std::string name() const override
    +
    + +
    +
    +virtual SolutionStatus get_status() const override
    +
    + +
    +
    +virtual SolutionReason get_reason() const override
    +
    + +
    +
    +virtual double get_best_obj() const override
    +
    + +
    +
    +virtual double get_best_bound() const override
    +
    + +
    +
    +virtual double get_var_primal(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_reduced_cost(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_ray(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_ctr_dual(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual double get_ctr_farkas(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual unsigned int get_n_solutions() const override
    +
    + +
    +
    +virtual unsigned int get_solution_index() const override
    +
    + +
    +
    +virtual double get_relative_gap() const override
    +
    + +
    +
    +virtual double get_absolute_gap() const override
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline virtual void set_param_logs(bool t_value)
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline virtual void set_param_time_limit(double t_time_limit)
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +inline virtual void set_param_threads(unsigned int t_threads)
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_obj_stop(double t_best_obj_stop)
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_bound_stop(double t_best_bound_stop)
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_relative_gap(double t_tol_mip_relative_gap)
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_absolute_gap(double t_mip_tol_absolute_gap)
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline virtual void set_tol_feasibility(double t_tol_feasibility)
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline virtual void set_tol_optimality(double t_tol_optimality)
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline virtual void set_tol_integer(double t_tol_integer)
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline virtual void set_param_presolve(bool t_value)
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline virtual void set_param_infeasible_or_unbounded_info(bool t_value)
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/bilevel/single-level/StrongDuality.html b/api/bilevel/single-level/StrongDuality.html new file mode 100644 index 000000000..b1a52bb03 --- /dev/null +++ b/api/bilevel/single-level/StrongDuality.html @@ -0,0 +1,568 @@ + + + + + + + Bilevel::StrongDuality + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel::StrongDuality

    +
    +

    Doxygen

    +
    +
    +class StrongDuality : public idol::OptimizerFactoryWithDefaultParameters<StrongDuality>
    +
    +

    Public Functions

    +
    +
    +explicit StrongDuality(const Bilevel::Description &t_description)
    +
    + +
    +
    +StrongDuality(const StrongDuality &t_src)
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual OptimizerFactory *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +StrongDuality &with_single_level_optimizer(const OptimizerFactory &t_deterministic_optimizer)
    +
    + +
    +
    +inline StrongDuality &operator+=(const OptimizerFactory &t_optimizer)
    +
    + +
    +
    +StrongDuality &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &conditional(bool t_conditional_value, const std::function<void(StrongDuality&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +StrongDuality &conditional(bool t_conditional_value, const std::function<void(StrongDuality&)> &t_if, const std::function<void(StrongDuality&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Model make_model(const Model &t_model, const Bilevel::Description &t_description)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/external-bilevel/MibS.html b/api/classes/external-bilevel/MibS.html new file mode 100644 index 000000000..7e44046cb --- /dev/null +++ b/api/classes/external-bilevel/MibS.html @@ -0,0 +1,555 @@ + + + + + + + Bilevel::Mibs + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel::Mibs

    +
    +
    +class MibS : public idol::OptimizerFactoryWithDefaultParameters<MibS>
    +
    +

    Public Functions

    +
    +
    +explicit MibS(Bilevel::Description t_description)
    +
    + +
    +
    +MibS(const MibS &t_src)
    +
    + +
    +
    +MibS(MibS&&) noexcept = delete
    +
    + +
    +
    +MibS &operator=(const MibS&) = delete
    +
    + +
    +
    +MibS &operator=(MibS&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +MibS &with_cplex_for_feasibility(bool t_value)
    +
    + +
    +
    +MibS &with_file_interface(bool t_value)
    +
    + +
    +
    +MibS &add_callback(const CallbackFactory &t_cb)
    +
    + +
    +
    +virtual MibS *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +MibS &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &conditional(bool t_conditional_value, const std::function<void(MibS&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +MibS &conditional(bool t_conditional_value, const std::function<void(MibS&)> &t_if, const std::function<void(MibS&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/external-bilevel/Optimizers_MibS.html b/api/classes/external-bilevel/Optimizers_MibS.html new file mode 100644 index 000000000..471ecb21c --- /dev/null +++ b/api/classes/external-bilevel/Optimizers_MibS.html @@ -0,0 +1,221 @@ + + + + + + + Optimizers::Bilevel::MibS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Bilevel::MibS

    +
    +

    Warning

    +

    doxygenclass: Cannot find class “idol::Optimizers::Bilevel::MibS” in doxygen xml output for project “idol” from directory: _build/xml/

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/external-bilevel/index.html b/api/classes/external-bilevel/index.html new file mode 100644 index 000000000..d9c5b2eb5 --- /dev/null +++ b/api/classes/external-bilevel/index.html @@ -0,0 +1,223 @@ + + + + + + + External Bilevel Solvers + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    External Bilevel Solvers

    +
    + +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/index.html b/api/classes/index.html new file mode 100644 index 000000000..a3539392a --- /dev/null +++ b/api/classes/index.html @@ -0,0 +1,249 @@ + + + + + + + Class List + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Class List

    +
    +

    Mixed-Integer Programming

    +
    + +
    +
    +
    +

    Bilevel Optimization

    +
    + +
    +
    +
    +

    Robust Optimization

    +
    +
    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/universal-callbacks/Callback.html b/api/classes/universal-callbacks/Callback.html new file mode 100644 index 000000000..f235ce0c5 --- /dev/null +++ b/api/classes/universal-callbacks/Callback.html @@ -0,0 +1,406 @@ + + + + + + + Callback + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Callback

    +

    Callbacks are user-defined functions which are invoked during the execution of branch-and-bound algorithms at certain +key steps of the procedure. These key m_n_points_bound are called events in idol. +Callback functions can be used to monitor the algorithm’s progress, control its behavior, or perform additional processing.

    +
    +

    UserCutCallback and LazyCutCallback

    +

    A common use of callbacks is to implement custom cut generation procedures at each node of the branch-and-bound tree. Note that +idol offers out-of-the-box callback routines for cut separation. Namely, UserCutCallback +and LazyCutCallback. Yet, it is totally possible to define your own cut generation procedure +by using the Callback::add_user_cut and Callback::add_lazy_cut methods inside your callback.

    +

    In a nutshell, UserCutCallback (or, similarly, Callback::add_user_cut) are intended for +cuts which have a potential to improve the quality of the relaxation but whose presence in the model is not necessary for the +branch-and-bound to converge to an optimal solution. UserCutCallback callbacks are called when +a non-valid solution has been found.

    +

    LazyCutCallback (or, similarly, Callback::add_lazy_cut), +instead, are intended to generate constraints which should be part of the model but which were omitted in the model for some reason. +A typical reason for omitting constraints in a model’s definition is the large number of such constraints. +LazyCutCallback callbacks are called when a valid solution has been found.

    +
    +
    +

    Creating your own callback

    +

    If you want to create your own callback, you should first create a new class which inherits the Callback class and +overrides the operator()(CallbackEvent) method.

    +

    Note that callbacks cannot be given “as-is” to an optimizer but must be passed through a CallbackFactory. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the CallbackFactory class.

    +
    +

    Example

    +

    We now give an example of callback which prints out every valid solution found.

    +
    class MyCallback : public CallbackFactory {
+public:
+
+    class Strategy { // Real callback implementation
+    protected:
+        void operator()(CallbackEvent t_event) {
+
+               if (t_event != IncumbentSolution) {
+                    return;
+               }
+
+               std::cout << primal_solution() << std::endl;
+        }
+    }
+
+    Callback* operator()() { // Creates a new callback object
+        return new Strategy();
+    }
+
+    CallbackFactory* clone() const { // Creates a copy of the callback factory
+        return new MyCallback(*this);
+    }
+
+}
+
    +
    +

    Later, it is then possible to use this callback in compliant optimizers like Gurobi or BranchAndBound.

    +
    model.use(
+    Gurobi().with_callback(MyCallback();
+);
+
+model.optimize();
+
    +
    +
    +
    +

    Hint

    +

    Note that there also exists more advanced callbacks which are specific to idol’s branch-and-bound implementation. +For these advanced feature, see BranchAndBoundCallback.

    +
    +
    +
    +class Callback
    +

    Subclassed by idol::Heuristics::LocalBranching::Strategy, idol::Heuristics::RENS::Strategy, idol::Heuristics::SimpleRounding::Strategy, idol::Plots::OptimalityGap::Strategy, idol::impl::CutSeparation

    +
    +

    Public Functions

    +
    +
    +virtual ~Callback() = default
    +
    + +
    +
    +

    Protected Functions

    +
    +
    +virtual const Model &original_model() const
    +

    Accesses the original model given to the solver

    +
    + +
    +
    +virtual void submit_heuristic_solution(const PrimalPoint &t_solution)
    +

    Submits a new heuristic solution

    +
    + +
    +
    +virtual void add_user_cut(const TempCtr &t_cut)
    +

    Adds a user cut to the relaxation

    +
    +
    Parameters:
    +

    t_cut – the cut to be added

    +
    +
    +
    + +
    +
    +virtual void add_lazy_cut(const TempCtr &t_cut)
    +

    Adds a lazy cut to the relaxation

    +
    +
    Parameters:
    +

    t_cut – the cut to be added

    +
    +
    +
    + +
    +
    +virtual PrimalPoint primal_solution() const
    +

    Returns the solution of the node which is currently being explored (when available)

    +
    +
    Returns:
    +

    the solution of the current node

    +
    +
    +
    + +
    +
    +const Timer &time() const
    +

    Returns the current time

    +
    +
    Returns:
    +

    the optimizer’s time

    +
    +
    +
    + +
    +
    +double best_obj() const
    +

    Returns the best objective value found so far

    +
    +
    Returns:
    +

    the best objective value

    +
    +
    +
    + +
    +
    +double best_bound() const
    +

    Returns the best bound found so far

    +
    +
    Returns:
    +

    the best bound

    +
    +
    +
    + +
    +
    +void terminate()
    +

    Asks the optimizer to terminate the optimization process as soon as possible

    +
    + +
    +
    +virtual void operator()(CallbackEvent t_event) = 0
    +

    This method is left for the user to write and consists in the main execution block of the callback.

    +
    +
    Parameters:
    +

    t_event – the event which triggered the call

    +
    +
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class ::idol::CallbackI
    +
    + +
    +
    + +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/universal-callbacks/CallbackFactory.html b/api/classes/universal-callbacks/CallbackFactory.html new file mode 100644 index 000000000..ef710c0a4 --- /dev/null +++ b/api/classes/universal-callbacks/CallbackFactory.html @@ -0,0 +1,241 @@ + + + + + + + CallbackFactory + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    CallbackFactory

    +
    +
    +class CallbackFactory
    +

    Subclassed by idol::Heuristics::LocalBranching, idol::Heuristics::RENS, idol::Heuristics::SimpleRounding, idol::LazyCutCallback, idol::Plots::OptimalityGap, idol::UserCutCallback

    +
    +

    Public Functions

    +
    +
    +virtual ~CallbackFactory() = default
    +
    + +
    +
    +virtual Callback *operator()() = 0
    +
    + +
    +
    +virtual CallbackFactory *clone() const = 0
    +
    + +
    +
    + +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/universal-callbacks/LazyCutCallback.html b/api/classes/universal-callbacks/LazyCutCallback.html new file mode 100644 index 000000000..fce586540 --- /dev/null +++ b/api/classes/universal-callbacks/LazyCutCallback.html @@ -0,0 +1,297 @@ + + + + + + + LazyCutCallback + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    LazyCutCallback

    +

    Lazy cuts are essentially constraints which are part of an optimization model but which have been omitted in the current +definition of the model. Lazy cuts typically arise in models with a large number of constraints. Instead of enumerating +then all, it may be judicious to omit some of them to get a smaller optimization model. Then, the returned solution is +checked for feasibility against the whole set of constraints. If a violated constraint is identified, we add the +constraint to the model and resolve. If not, then all the constraints are satisfied and the solution is optimal for the +original model in which all constraints materializes.

    +

    The LazyCutCallback can be used to implement lazy cut constraint generation on the fly, during the optimization process.

    +

    Consider the following optimization problem:

    +
    +\[\begin{split}\begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X, \\ + & \xi^\top x \le \xi_0 \quad (\xi_0,\xi) \in \Xi, +\end{align}\end{split}\]
    +

    in which assume that \(|\Xi|\) is large (potentially infinite). The idea is to start by solving the following +relaxed master problem in which constraints associated to \((\xi_0,\xi)\) have been omitted.

    +
    +\[\begin{split}\begin{align} + \min_x \ & c^\top x \\ + \text{s.t.} \ & x\in X. +\end{align}\end{split}\]
    +

    If we assume that this problem is feasible and bounded, we can denote by \(x^*\) a solution of this problem. Then, +we search for a violated constraint “\(\xi^\top x \le \xi_0\)” for some \((\xi_0,\xi)\in\Xi\). Observe that +a constraint is violated if, and only if, the following holds:

    +
    +\[\left(\exists(\xi_0,\xi)\in\Xi, \ \xi^\top x^* > \xi_0\right) +\Leftrightarrow +\left(\max_{(\xi_0,\xi)\in\Xi} \xi_0 - \xi^\top x^* < 0\right).\]
    +

    Thus, the LazyCutCallback automatically solve the optimization problem on the right handside and checks for its value. +A new constraint is added if, and only if,

    +
    +\[\max_{\xi\in\Xi} \xi_0 - \xi^\top x^* < -\varepsilon,\]
    +

    with \(\varepsilon\) a given tolerance (by default, Tolerance::Feasibility).

    +
    +

    Hint

    +

    You may also be interested by a tutorial showing how you can implement a simple Benders Decomposition using lazy +cuts. See Benders Decomposition tutorial.

    +
    +
    +
    +class LazyCutCallback : public idol::CallbackFactory
    +
    +

    Public Functions

    +
    +
    +inline LazyCutCallback(const Model &t_model, TempCtr t_cut)
    +
    + +
    +
    +inline virtual Callback *operator()() override
    +
    + +
    +
    +inline virtual CallbackFactory *clone() const override
    +
    + +
    +
    +inline LazyCutCallback &with_separation_optimizer(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +
    +class Strategy : public idol::impl::CutSeparation
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(Model *t_separation_problem, TempCtr t_cut)
    +
    + +
    +
    + +
    + +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/universal-callbacks/UserCutCallback.html b/api/classes/universal-callbacks/UserCutCallback.html new file mode 100644 index 000000000..649996035 --- /dev/null +++ b/api/classes/universal-callbacks/UserCutCallback.html @@ -0,0 +1,258 @@ + + + + + + + UserCutCallback + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    UserCutCallback

    +
    +
    +class UserCutCallback : public idol::CallbackFactory
    +
    +

    Public Functions

    +
    +
    +inline UserCutCallback(const Model &t_model, TempCtr t_cut)
    +
    + +
    +
    +inline virtual Callback *operator()() override
    +
    + +
    +
    +inline virtual CallbackFactory *clone() const override
    +
    + +
    +
    +inline UserCutCallback &with_separation_optimizer(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +
    +class Strategy : public idol::impl::CutSeparation
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(Model *t_separation_problem, TempCtr t_cut)
    +
    + +
    +
    + +
    + +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/classes/universal-callbacks/index.html b/api/classes/universal-callbacks/index.html new file mode 100644 index 000000000..b4847efe5 --- /dev/null +++ b/api/classes/universal-callbacks/index.html @@ -0,0 +1,226 @@ + + + + + + + Universal Callbacks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Universal Callbacks

    +
    + +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/index.html b/api/index.html new file mode 100644 index 000000000..ed67f76a2 --- /dev/null +++ b/api/index.html @@ -0,0 +1,355 @@ + + + + + + + API + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    API

    +
    +

    Mixed-Integer Optimization

    +
    + +
    +
    +
    +

    Bilevel Optimization

    +
    + +
    +
    +
    +

    Robust Optimization

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/BranchAndBound.html b/api/mixed-integer/branch-and-bound/BranchAndBound.html new file mode 100644 index 000000000..a7538b4d4 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/BranchAndBound.html @@ -0,0 +1,803 @@ + + + + + + + BranchAndBound + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BranchAndBound

    +

    This class is an optimizer factory which creates a new branch-and-bound algorithm. +It can be used to create customized branch-and-bound algorithms with a large degree of freedom.

    +
    +

    See also

    +

    If you are not familiar with optimizers and optimizer factories, please refer to this page.

    +
    +
    +

    Example

    +

    Here, we create a simple branch-and-bound algorithm where branching is done on integer variables which are being +relaxed. Each node is solved by the external solver GLPK. Nodes are selected according to the “best-bound” +rule while variables are selected according to the “most-infeasible” branching rule.

    +

    The created algorithm also incorporates sub-tree exploration of maximum depth 2.

    +
    model.use(
+    BranchAndBound()
+        .with_node_optimizer( GLPK::ContinuousRelaxation() )
+        .with_branching_rule( MostInfeasible() )
+        .with_node_selection_rule( BestBound() )
+        .with_subtree_depth(2)
+);
+
    +
    +
    +
    +

    Doxygen

    +
    +
    +template<class NodeT = idol::DefaultNodeInfo>
    class BranchAndBound : public idol::OptimizerFactoryWithDefaultParameters<BranchAndBound<idol::DefaultNodeInfo>>
    +
    +
    Template Parameters:
    +

    NodeT – the class used to store nodes information. It is strongly advised to inherit from NodeVarInfo in order to create your own node type.

    +
    +
    +
    +

    Public Types

    +
    +
    +template<class ReturnT, class T>
    using only_if_has_Strategy = typename std::pair<typename T::template Strategy<NodeT>, ReturnT>::second_type
    +

    This type is used to exploit SFINAE in order to identify classes having a sub-class named Strategy<NodeInfoT>. This is used to make calls like .with_node_selection_rule(DepthFirst()); which will actually call .with_node_selection_rule(DepthFirst::Strategy<NodeInfoT>()).

    +
    + +
    +
    +

    Public Functions

    +
    +
    +BranchAndBound() = default
    +

    Creates a new branch-and-bound algorithm.

    +

    Example: 

    model.use( BranchAndBound() );
+
    +
    +

    +
    + +
    +
    +BranchAndBound(const BranchAndBound &t_rhs)
    +

    Copy constructor

    +
    +
    Parameters:
    +

    t_rhs – the object to copy

    +
    +
    +
    + +
    +
    +BranchAndBound<NodeT> &with_node_optimizer(const OptimizerFactory &t_node_optimizer)
    +

    Sets the optimizer for solving each of the branch-and-bound tree nodes

    +

    Example: 

    auto algorithm = BranchAndBound()
+                     .with_node_optimizer(GLPK::ContinuousRelaxation());
+
    +
    +

    +
    +
    Parameters:
    +

    t_node_optimizer – the optimizer factory the node problems

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +void set_node_optimizer(const OptimizerFactory &t_node_optimizer)
    +
    + +
    +
    +BranchAndBound<NodeT> &operator+=(const OptimizerFactory &t_node_optimizer)
    +
    + +
    +
    +BranchAndBound<NodeT> &with_branching_rule(const BranchingRuleFactory<NodeT> &t_branching_rule)
    +

    Sets the branching rule used to create child nodes

    +

    Example: 

    auto algorithm = BranchAndBound<NodeVarInfo>()
+                     .with_branching_rule(MostInfeasible::Strategy<NodeVarInfo>());
+
    +
    +

    +
    +
    Parameters:
    +

    t_branching_rule – the branching rule

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class BranchingRuleFactoryT>
    only_if_has_Strategy<BranchAndBound<NodeT>&, BranchingRuleFactoryT> with_branching_rule(const BranchingRuleFactoryT &t_branching_rule)
    +

    Sets the branching rule used to create child nodes.

    +

    Here, the function is called only when BranchingRuleFactoryT has a nested template class named Strategy<NodeInfoT>. In such a case, the branching rule is created by calling BranchingRuleFactoryT::Strategy<NodeInfoT>(t_branching_rule). This is used to avoid the user repeating the node type NodeInfoT being used.

    +

    Example: 

    auto algorithm = BranchAndBound<NodeVarInfo>()
+                     .with_branching_rule(MostInfeasible());
+
    +
    +

    +
    +
    Template Parameters:
    +

    BranchingRuleFactoryT – the class containing a nested template class named Strategy

    +
    +
    Parameters:
    +

    t_branching_rule – the branching rule

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +BranchAndBound<NodeT> &with_node_selection_rule(const NodeSelectionRuleFactory<NodeT> &t_node_selection)
    +

    Sets the node selection rule to explore the branch and bound tree.

    +

    auto algorithm = BranchAndBound<NodeVarInfo>()
+                     .with_node_selection(BestBound::Strategy<NodeVarInfo>());
+
    +
    +

    +
    +
    Parameters:
    +

    t_node_selection – the node selection rule

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class NodeSelectionRuleFactoryT>
    only_if_has_Strategy<BranchAndBound<NodeT>&, NodeSelectionRuleFactoryT> with_node_selection_rule(const NodeSelectionRuleFactoryT &t_node_selection_rule)
    +

    Sets the node selection rule to explore the branch and bound tree.

    +

    Here, the function is called only when NodeSelectionRuleFactoryT has a nested template class named Strategy<NodeInfoT>. In such a case, the node selection rule is created by calling NodeSelectionRuleFactoryT::Strategy<NodeInfoT>(t_node_selection_rule). This is used to avoid the user repeating the node type NodeInfoT being used.

    +

    Example: 

    auto algorithm = BranchAndBound<NodeVarInfo>()
+                     .with_node_selection_rule(BestBound());
+
    +
    +

    +
    +
    Template Parameters:
    +

    NodeSelectionRuleFactoryT – the class containing a nested template class named Strategy

    +
    +
    Parameters:
    +

    t_node_selection_rule – the node selection rule

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +BranchAndBound(BranchAndBound&&) noexcept = default
    +
    + +
    +
    +BranchAndBound &operator=(const BranchAndBound&) = delete
    +
    + +
    +
    +BranchAndBound &operator=(BranchAndBound&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual OptimizerFactory *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +BranchAndBound<NodeT> &with_subtree_depth(unsigned int t_depth)
    +

    Sets the depth for sub-tree exploration.

    +

    When a node is selected for branching, each of its children is explored. This exploration takes the form of a sub-tree exploration. When this parameter is set to 0, only the root node of this sub-tree is solved. Thus every child node are solved and the branch-and-bound algorithm is continued.

    +

    For strictly greater values of this parameter, the sub-tree is explored with a maximum depth equal to the value of this parameter.

    +

    For example, with a value of 1, each child node is solved along with its child nodes.

    +

    Example: 

    auto algorithm = BranchAndBound()
+                     .with_subtree_depth(1);
+
    +
    +

    +
    +
    Parameters:
    +

    t_depth – the maximum sub-tree exploration depth

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +BranchAndBound<NodeT> &with_logger(const Logs::BranchAndBound::Factory<NodeT> &t_log_factory)
    +
    + +
    +
    +BranchAndBound<NodeT> &add_callback(const BranchAndBoundCallbackFactory<NodeT> &t_callback)
    +

    Adds a callback which will be called by the optimizer.

    +

    Note that this method can be called multiple times so that multiple callbacks can be added.

    +

    auto algorithm = BranchAndBound()
+                     .with_callback(IntegerMaster.rst());
+
    +
    +

    +
    +
    Parameters:
    +

    t_callback – the callback factory

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +BranchAndBound<NodeT> &add_callback(const CallbackFactory &t_callback)
    +

    Adds a (solver independent) callback which will be called by the optimizer.

    +

    Note that this method can be called multiple times so that multiple callbacks can be added.

    +

    Here, the Callback is automatically converted into a BranchAndBoundCallback<NodeInfoT>.

    +

    auto algorithm = BranchAndBound()
+                     .with_callback(UserCutCallback(separation_model, my_cut));
+
    +
    +

    +
    +
    Parameters:
    +

    t_callback – the callback factory

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class NodeSelectionRuleFactoryT>
    idol::BranchAndBound<NodeT>::template only_if_has_Strategy<idol::BranchAndBound<NodeT>&, NodeSelectionRuleFactoryT> with_node_selection_rule(const NodeSelectionRuleFactoryT &t_node_selection_rule)
    +
    + +
    +
    +template<class BranchingRuleFactoryT>
    idol::BranchAndBound<NodeT>::template only_if_has_Strategy<idol::BranchAndBound<NodeT>&, BranchingRuleFactoryT> with_branching_rule(const BranchingRuleFactoryT &t_branching_rule)
    +
    + +
    +
    +CRTP &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +CRTP &conditional(bool t_conditional_value, const std::function<void(CRTP&)> &t_if, const std::function<void(CRTP&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.html b/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.html new file mode 100644 index 000000000..bb4c1ca3e --- /dev/null +++ b/api/mixed-integer/branch-and-bound/BranchAndBoundCallback.html @@ -0,0 +1,457 @@ + + + + + + + BranchAndBoundCallback + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BranchAndBoundCallback

    +

    This class can be used to create callbacks to run on idol’s branch-and-bound implementation.

    +
    +

    Warning

    +

    BranchAndBoundCallback-s is an advanced feature.

    +

    Please, make sure that what you are trying do cannot be done with +a solver-independent callback first, or with pre-existing callbacks, e.g., +UserCutCallback or LazyCutCallback.

    +

    The advantage of using a BranchAndBoundCallback instead of a standard +solver-independent Callback lies in the possibility to access specific information regarding +the execution of the branch-and-bound algorithm. For instance, accessing a node’s information, or the current +relaxation model being solved.

    +
    +
    +

    Example

    +

    Here is an example of callback which prints out the event triggering it and, when the event corresponds to NodeLoaded, +prints the node’s model to be solved.

    +
    class MyCallback : public BranchAndBoundCallbackFactory<NodeInfo> {
+public:
+    class Strategy : public BranchAndBoundCallback<NodeInfo> {
+    protected:
+        void operator()(CallbackEvent t_event) override {
+
+            std::cout << "MyCallback is called for " << t_event << std::endl;
+
+            if (t_event != NodeLoaded) {
+                return;
+            }
+
+            std::cout << "The problem being solve at node " << node().id() << std::endl;
+            std::cout << relaxation() << std::endl;
+
+        }
+    };
+
+    BranchAndBoundCallback<NodeInfo> *operator()() override {
+        return new Strategy();
+    }
+
+    [[nodiscard]] BranchAndBoundCallbackFactory<NodeInfo> *clone() const override {
+        return new MyCallback(*this);
+    }
+};
+
    +
    +

    Then, this callback can be used as follows.

    +
    model.use(
+    BranchAndBound()
+        .with_node_optimizer(GLPK::ContinuousRelaxation())
+        .with_branching_rule(MostInfeasible())
+        .with_node_selection_rule(DepthFirst())
+        .with_callback(MyCallback());
+);
+
    +
    +
    +
    +

    Hint

    +

    By default, most of the objects returned by BranchAndBoundCallback methods are const. If you wish to access non-const +versions (e.g., if you want to perform non-standard updates to the relaxed model or want to change the node’s current +information manually), you should use the advanced interface obtained by calling BranchAndBoundCallback::advanced_interface.

    +
    +
    +

    Doxygen

    +
    +
    +template<class NodeInfoT>
    class BranchAndBoundCallback
    +

    Subclassed by idol::CallbackAsBranchAndBoundCallback< NodeInfoT >::Strategy, idol::Cuts::KnapsackCover< NodeInfoT >::Strategy, idol::Heuristics::IntegerMaster< NodeInfoT >::Strategy, idol::ReducedCostFixing< NodeInfoT >::Strategy, idol::Utils::ExportBranchAndBoundTreeToCSV< NodeInfoT >::Strategy

    +
    +

    Public Functions

    +
    +
    +virtual ~BranchAndBoundCallback() = default
    +
    + +
    +
    +

    Protected Functions

    +
    +
    +inline virtual void initialize()
    +

    This method is called at the very beginning of the Branch-and-Bound algorithm

    +
    + +
    +
    +virtual void operator()(CallbackEvent t_event) = 0
    +

    This method is left for the user to write and consists in the main execution block of the callback.

    +
    +
    Parameters:
    +

    t_event – The event triggering the callback

    +
    +
    +
    + +
    +
    +inline virtual void log_after_termination()
    +
    + +
    +
    +void add_user_cut(const TempCtr &t_cut)
    +

    Adds a user cut to the relaxation

    +
    +
    Parameters:
    +

    t_cut – the cut to be added

    +
    +
    +
    + +
    +
    +void add_lazy_cut(const TempCtr &t_cut)
    +

    Adds a lazy cut to the relaxation

    +
    +
    Parameters:
    +

    t_cut – the cut to be added

    +
    +
    +
    + +
    +
    +void add_local_variable_branching(const Var &t_var, CtrType t_type, double t_rhs)
    +
    + +
    +
    +const Node<NodeInfoT> &node() const
    +

    Returns the node which is currently explored

    +
    +
    Returns:
    +

    the node which is currently explored

    +
    +
    +
    + +
    +
    +const Model &relaxation() const
    +

    Returns the current node’s model being solved

    +
    +
    Returns:
    +

    the current node’s model being solved

    +
    +
    +
    + +
    +
    +const Model &original_model() const
    +

    Returns the original model from which the branch-and-bound algorithm started (i.e., the original non-relaxed model)

    +
    +
    Returns:
    +

    the original model

    +
    +
    +
    + +
    +
    +void submit_heuristic_solution(NodeInfoT *t_info)
    +

    Submits a new solution to the branch-and-bound tree algorithm.

    +

    The solution is checked for validity according to the branch-and-bound tree branching rule and is set as incumbent if and only if it is valid and improves the current best objective.

    +
    +
    Parameters:
    +

    t_info – a node information storing the solution

    +
    +
    +
    + +
    +
    +void submit_bound(double t_bound)
    +

    Submits a new proven bound.

    +

    The given bound is set as best bound if and only if it improves the current best bound.

    +
    +
    Parameters:
    +

    t_bound – a proven bound

    +
    +
    +
    + +
    +
    +const SideEffectRegistry &side_effect_registry() const
    +

    Returns the side effect registry

    +
    +
    Returns:
    +

    the side effect registry

    +
    +
    +
    + +
    +
    +const Timer &time() const
    +
    + +
    +
    +double best_bound() const
    +
    + +
    +
    +double best_obj() const
    +
    + +
    +
    +void terminate()
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.html b/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.html new file mode 100644 index 000000000..6243cd18a --- /dev/null +++ b/api/mixed-integer/branch-and-bound/BranchAndBoundCallbackFactory.html @@ -0,0 +1,266 @@ + + + + + + + BranchAndBoundCallbackFactory + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BranchAndBoundCallbackFactory

    +
    +

    Doxygen

    +
    +
    +template<class NodeInfoT>
    class BranchAndBoundCallbackFactory
    +

    Subclassed by idol::CallbackAsBranchAndBoundCallback< NodeInfoT >, idol::Cuts::KnapsackCover< NodeInfoT >, idol::Heuristics::IntegerMaster< NodeInfoT >, idol::ReducedCostFixing< NodeInfoT >, idol::Utils::ExportBranchAndBoundTreeToCSV< NodeInfoT >

    +
    +

    Public Functions

    +
    +
    +virtual ~BranchAndBoundCallbackFactory() = default
    +
    + +
    +
    +virtual BranchAndBoundCallback<NodeInfoT> *operator()() = 0
    +
    + +
    +
    +virtual BranchAndBoundCallbackFactory<NodeInfoT> *clone() const = 0
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.html b/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.html new file mode 100644 index 000000000..bee6c5432 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/cuts/KnapsackCover.html @@ -0,0 +1,295 @@ + + + + + + + Cuts::KnapsackCover + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Cuts::KnapsackCover

    +
    +

    Doxygen

    +
    +
    +template<class NodeInfoT = idol::DefaultNodeInfo>
    class KnapsackCover : public idol::BranchAndBoundCallbackFactory<idol::DefaultNodeInfo>
    +
    +

    Public Functions

    +
    +
    +virtual BranchAndBoundCallback<NodeInfoT> *operator()() override
    +
    + +
    +
    +virtual BranchAndBoundCallbackFactory<NodeInfoT> *clone() const override
    +
    + +
    +
    +KnapsackCover &with_lifting(bool t_value)
    +
    + +
    +
    +KnapsackCover &with_tree_node_cuts(bool t_value)
    +
    + +
    +
    +KnapsackCover &with_max_pass_root_node(unsigned int t_value)
    +
    + +
    +
    +KnapsackCover &with_max_cuts_factor(double t_value)
    +
    + +
    +
    +
    +class Strategy : public idol::BranchAndBoundCallback<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy(bool t_use_lifting, bool t_apply_to_tree_nodes, unsigned int t_max_pass_root_node, double t_max_cuts_factor)
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/cuts/index.html b/api/mixed-integer/branch-and-bound/cuts/index.html new file mode 100644 index 000000000..6a3325e59 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/cuts/index.html @@ -0,0 +1,244 @@ + + + + + + + More on Cutting Planes… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on Cutting Planes…

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.html b/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.html new file mode 100644 index 000000000..1298abd58 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/heuristics/LocalBranching.html @@ -0,0 +1,285 @@ + + + + + + + Heuristics::LocalBranching + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Heuristics::LocalBranching

    +
    +

    Doxygen

    +
    +
    +class LocalBranching : public idol::CallbackFactory
    +
    +

    Public Functions

    +
    +
    +LocalBranching() = default
    +
    + +
    +
    +inline virtual Callback *operator()() override
    +
    + +
    +
    +inline virtual CallbackFactory *clone() const override
    +
    + +
    +
    +LocalBranching &with_optimizer(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +
    +class Strategy : public idol::Callback
    +
    +

    Public Functions

    +
    +
    +Strategy(unsigned int t_neighbourhood_size, OptimizerFactory *t_optimizer_factory)
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/heuristics/RENS.html b/api/mixed-integer/branch-and-bound/heuristics/RENS.html new file mode 100644 index 000000000..c49eb064a --- /dev/null +++ b/api/mixed-integer/branch-and-bound/heuristics/RENS.html @@ -0,0 +1,285 @@ + + + + + + + Heuristics::RENS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Heuristics::RENS

    +
    +

    Doxygen

    +
    +
    +class RENS : public idol::CallbackFactory
    +
    +

    Public Functions

    +
    +
    +RENS() = default
    +
    + +
    +
    +inline virtual Callback *operator()() override
    +
    + +
    +
    +inline virtual CallbackFactory *clone() const override
    +
    + +
    +
    +RENS &with_optimizer(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +
    +class Strategy : public idol::Callback
    +
    +

    Public Functions

    +
    +
    +Strategy(double t_minimum_ratio_of_integer_variables_to_fix, double t_minimum_ratio_of_variables_to_fix, OptimizerFactory *t_optimizer_factory)
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.html b/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.html new file mode 100644 index 000000000..2e587029c --- /dev/null +++ b/api/mixed-integer/branch-and-bound/heuristics/SimpleRounding.html @@ -0,0 +1,272 @@ + + + + + + + Heuristics::SimpleRounding + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Heuristics::SimpleRounding

    +
    +

    Doxygen

    +
    +
    +class SimpleRounding : public idol::CallbackFactory
    +
    +

    Public Functions

    +
    +
    +SimpleRounding() = default
    +
    + +
    +
    +inline virtual Callback *operator()() override
    +
    + +
    +
    +inline virtual CallbackFactory *clone() const override
    +
    + +
    +
    +
    +class Strategy : public idol::Callback
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/heuristics/index.html b/api/mixed-integer/branch-and-bound/heuristics/index.html new file mode 100644 index 000000000..40a571296 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/heuristics/index.html @@ -0,0 +1,246 @@ + + + + + + + More on Heuristics… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on Heuristics…

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/BestBound.html b/api/mixed-integer/branch-and-bound/node-selection/BestBound.html new file mode 100644 index 000000000..8c47a79fa --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/BestBound.html @@ -0,0 +1,272 @@ + + + + + + + BestBound + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BestBound

    +
    +

    Doxygen

    +
    +
    +class BestBound
    +
    +
    +template<class NodeT>
    class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(const BestBound &t_parent)
    +
    + +
    +
    +inline virtual NodeSelectionRules::BestBound<NodeT> *operator()(Optimizers::BranchAndBound<NodeT> &t_parent) const override
    +
    + +
    +
    +inline virtual Strategy *clone() const override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.html b/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.html new file mode 100644 index 000000000..7957ce45a --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/BestEstimate.html @@ -0,0 +1,273 @@ + + + + + + + BestEstimate + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BestEstimate

    +

    The “best estimate” node selection rule was introduced in J. J. H. Forrest, J. P. H. Hirst, J. A. Tomlin, (1974) Practical Solution of Large Mixed Integer Programming Problems with Umpire. Management Science 20(5):736-773.

    +
    +

    Doxygen

    +
    +
    +class BestEstimate
    +
    +
    +template<class NodeT>
    class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(const BestEstimate &t_parent)
    +
    + +
    +
    +inline virtual NodeSelectionRules::BestEstimate<NodeT> *operator()(Optimizers::BranchAndBound<NodeT> &t_parent) const override
    +
    + +
    +
    +inline virtual Strategy *clone() const override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.html b/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.html new file mode 100644 index 000000000..7f29ed0e2 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/BreadthFirst.html @@ -0,0 +1,272 @@ + + + + + + + BreadthFirst + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    BreadthFirst

    +
    +

    Doxygen

    +
    +
    +class BreadthFirst
    +
    +
    +template<class NodeT>
    class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(const BreadthFirst &t_parent)
    +
    + +
    +
    +inline virtual NodeSelectionRules::BreadthFirst<NodeT> *operator()(Optimizers::BranchAndBound<NodeT> &t_parent) const override
    +
    + +
    +
    +inline virtual Strategy *clone() const override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.html b/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.html new file mode 100644 index 000000000..11aeb2bb6 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/DepthFirst.html @@ -0,0 +1,272 @@ + + + + + + + DepthFirst + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DepthFirst

    +
    +

    Doxygen

    +
    +
    +class DepthFirst
    +
    +
    +template<class NodeT>
    class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(const DepthFirst &t_parent)
    +
    + +
    +
    +inline virtual NodeSelectionRules::DepthFirst<NodeT> *operator()(Optimizers::BranchAndBound<NodeT> &t_parent) const override
    +
    + +
    +
    +inline virtual Strategy *clone() const override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/WorstBound.html b/api/mixed-integer/branch-and-bound/node-selection/WorstBound.html new file mode 100644 index 000000000..dc5d25d38 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/WorstBound.html @@ -0,0 +1,272 @@ + + + + + + + WorstBound + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    WorstBound

    +
    +

    Doxygen

    +
    +
    +class WorstBound
    +
    +
    +template<class NodeT>
    class Strategy : public idol::NodeSelectionRuleFactory<NodeT>
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(const WorstBound &t_parent)
    +
    + +
    +
    +inline virtual NodeSelectionRules::WorstBound<NodeT> *operator()(Optimizers::BranchAndBound<NodeT> &t_parent) const override
    +
    + +
    +
    +inline virtual Strategy *clone() const override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/node-selection/index.html b/api/mixed-integer/branch-and-bound/node-selection/index.html new file mode 100644 index 000000000..1cd221528 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/node-selection/index.html @@ -0,0 +1,248 @@ + + + + + + + More on Node Selection Rules… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on Node Selection Rules…

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.html b/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.html new file mode 100644 index 000000000..5dc5a3af2 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/FirstInfeasibleFound.html @@ -0,0 +1,295 @@ + + + + + + + FirstInfeasibleFound + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    FirstInfeasibleFound

    +
    +

    Doxygen

    +
    +
    +class FirstInfeasibleFound : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +FirstInfeasibleFound() = default
    +
    + +
    +
    +template<class IteratorT>
    inline FirstInfeasibleFound(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +inline explicit Strategy(const FirstInfeasibleFound &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.html b/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.html new file mode 100644 index 000000000..4fe271cf0 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/LeastInfeasible.html @@ -0,0 +1,295 @@ + + + + + + + LeastInfeasible + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    LeastInfeasible

    +
    +

    Doxygen

    +
    +
    +class LeastInfeasible : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +LeastInfeasible() = default
    +
    + +
    +
    +template<class IteratorT>
    inline LeastInfeasible(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +inline explicit Strategy(const LeastInfeasible &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.html b/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.html new file mode 100644 index 000000000..e7af25c49 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/MostInfeasible.html @@ -0,0 +1,295 @@ + + + + + + + MostInfeasible + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    MostInfeasible

    +
    +

    Doxygen

    +
    +
    +class MostInfeasible : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +MostInfeasible() = default
    +
    + +
    +
    +template<class IteratorT>
    inline MostInfeasible(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +inline explicit Strategy(const MostInfeasible &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.html b/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.html new file mode 100644 index 000000000..3b39ade23 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/PseudoCost.html @@ -0,0 +1,295 @@ + + + + + + + PseudoCost + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    PseudoCost

    +
    +

    Doxygen

    +
    +
    +class PseudoCost : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +PseudoCost() = default
    +
    + +
    +
    +template<class IteratorT>
    inline PseudoCost(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +inline explicit Strategy(const PseudoCost &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.html b/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.html new file mode 100644 index 000000000..603983ed8 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/StrongBranching.html @@ -0,0 +1,315 @@ + + + + + + + StrongBranching + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    StrongBranching

    +
    +

    Doxygen

    +
    +
    +class StrongBranching : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +StrongBranching() = default
    +
    + +
    +
    +template<class IteratorT>
    inline StrongBranching(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +StrongBranching &with_max_n_variables(unsigned int t_n_variables)
    +
    + +
    +
    +StrongBranching &with_node_scoring_function(const NodeScoreFunction &t_score_function)
    +
    + +
    +
    +StrongBranching &add_phase(const StrongBranchingPhaseType &t_phase, unsigned int t_max_n_variables, unsigned int t_max_depth)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +Strategy(const Strategy<NodeInfoT> &t_src)
    +
    + +
    +
    +explicit Strategy(const StrongBranching &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.html b/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.html new file mode 100644 index 000000000..805fe20c4 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/UniformlyRandom.html @@ -0,0 +1,300 @@ + + + + + + + UniformlyRandom + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    UniformlyRandom

    +
    +

    Doxygen

    +
    +
    +class UniformlyRandom : public idol::VariableBranching
    +
    +

    Public Functions

    +
    +
    +UniformlyRandom() = default
    +
    + +
    +
    +template<class IteratorT>
    inline UniformlyRandom(IteratorT t_begin, IteratorT t_end)
    +
    + +
    +
    +inline UniformlyRandom &with_seed(unsigned int t_seed)
    +
    + +
    +
    +
    +template<class NodeInfoT>
    class Strategy : public idol::VariableBranching::Strategy<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +Strategy() = default
    +
    + +
    +
    +inline explicit Strategy(const UniformlyRandom &t_parent)
    +
    + +
    +
    +inline BranchingRules::VariableBranching<NodeInfoT> *operator()(const Optimizers::BranchAndBound<NodeInfoT> &t_parent) const override
    +
    + +
    +
    +inline virtual VariableBranching::Strategy<NodeInfoT> *clone() const override
    +
    + +
    +
    +virtual BranchingRule<NodeT> *operator()(const Optimizers::BranchAndBound<NodeT> &t_parent) const = 0
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/branch-and-bound/variable-selection/index.html b/api/mixed-integer/branch-and-bound/variable-selection/index.html new file mode 100644 index 000000000..e86fccea0 --- /dev/null +++ b/api/mixed-integer/branch-and-bound/variable-selection/index.html @@ -0,0 +1,249 @@ + + + + + + + More on Branching Rules… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on Branching Rules…

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/ArtificialCosts.html b/api/mixed-integer/column-generation/ArtificialCosts.html new file mode 100644 index 000000000..4af8733a7 --- /dev/null +++ b/api/mixed-integer/column-generation/ArtificialCosts.html @@ -0,0 +1,318 @@ + + + + + + + DantzigWolfe::ArtificialCosts + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DantzigWolfe::ArtificialCosts

    +
    +

    Doxygen

    +
    +
    +class ArtificialCosts : public idol::DantzigWolfe::InfeasibilityStrategyFactory
    +
    +

    Public Functions

    +
    +
    +inline virtual InfeasibilityStrategyFactory::Strategy *operator()() const override
    +
    + +
    +
    +inline virtual ArtificialCosts *clone() const override
    +
    + +
    +
    +ArtificialCosts &with_max_updates_before_phase_I(unsigned int t_value)
    +
    + +
    +
    +ArtificialCosts &with_update_factor(double t_value)
    +
    + +
    +
    +ArtificialCosts &with_initial_costs(double t_value)
    +
    + +
    +
    +
    +class Strategy : public idol::DantzigWolfe::InfeasibilityStrategyFactory::Strategy
    +
    +

    Public Functions

    +
    +
    +Strategy(double t_initial_costs, double t_update_factor, unsigned int t_max_updates_before_phase_I)
    +
    + +
    +
    +virtual void execute(Optimizers::DantzigWolfeDecomposition &t_parent) override
    +
    + +
    +
    +inline SolutionStatus status() const
    +
    + +
    +
    +inline SolutionReason reason() const
    +
    + +
    +
    +inline double best_obj() const
    +
    + +
    +
    +inline double best_bound() const
    +
    + +
    +
    +const PrimalPoint &primal_solution() const
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/DantzigWolfeDecomposition.html b/api/mixed-integer/column-generation/DantzigWolfeDecomposition.html new file mode 100644 index 000000000..3160b3f94 --- /dev/null +++ b/api/mixed-integer/column-generation/DantzigWolfeDecomposition.html @@ -0,0 +1,610 @@ + + + + + + + DantzigWolfeDecomposition + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DantzigWolfeDecomposition

    +
    +

    Hint

    +

    This page documents on the DantzigWolfeDecomposition optimizer factory. Note that there are also +Dantzig-Wolfe Decomposition tutorials.

    +
    +
    +

    Doxygen

    +
    +
    +class DantzigWolfeDecomposition : public idol::OptimizerFactoryWithDefaultParameters<DantzigWolfeDecomposition>
    +
    +

    Public Functions

    +
    +
    +DantzigWolfeDecomposition() = default
    +
    + +
    +
    +explicit DantzigWolfeDecomposition(Annotation<unsigned int> t_decomposition)
    +
    + +
    +
    +DantzigWolfeDecomposition(const DantzigWolfeDecomposition &t_src)
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual DantzigWolfeDecomposition *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_master_optimizer(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_default_sub_problem_spec(DantzigWolfe::SubProblem t_sub_problem)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_sub_problem_spec(unsigned int t_id, DantzigWolfe::SubProblem t_sub_problem)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_infeasibility_strategy(const DantzigWolfe::InfeasibilityStrategyFactory &t_strategy)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_hard_branching(bool t_value)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_infeasible_columns_removal(bool t_value)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_max_parallel_sub_problems(unsigned int t_n_sub_problems)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_logger(const Logs::DantzigWolfe::Factory &t_logger)
    +
    + +
    +
    +DantzigWolfeDecomposition &with_dual_price_smoothing_stabilization(const DantzigWolfe::DualPriceSmoothingStabilization &t_stabilization)
    +
    + +
    +
    +const DantzigWolfe::SubProblem &get_sub_problem_spec(unsigned int t_id) const
    +
    + +
    +
    +DantzigWolfeDecomposition &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &conditional(bool t_conditional_value, const std::function<void(DantzigWolfeDecomposition&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +DantzigWolfeDecomposition &conditional(bool t_conditional_value, const std::function<void(DantzigWolfeDecomposition&)> &t_if, const std::function<void(DantzigWolfeDecomposition&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/FarkasPricing.html b/api/mixed-integer/column-generation/FarkasPricing.html new file mode 100644 index 000000000..07742ec2c --- /dev/null +++ b/api/mixed-integer/column-generation/FarkasPricing.html @@ -0,0 +1,298 @@ + + + + + + + DantzigWolfe::FarkasPricing + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DantzigWolfe::FarkasPricing

    +
    +

    Doxygen

    +
    +
    +class FarkasPricing : public idol::DantzigWolfe::InfeasibilityStrategyFactory
    +
    +

    Public Functions

    +
    +
    +inline virtual InfeasibilityStrategyFactory::Strategy *operator()() const override
    +
    + +
    +
    +inline virtual FarkasPricing *clone() const override
    +
    + +
    +
    +
    +class Strategy : public idol::DantzigWolfe::InfeasibilityStrategyFactory::Strategy
    +
    +

    Public Functions

    +
    +
    +virtual void execute(Optimizers::DantzigWolfeDecomposition &t_parent) override
    +
    + +
    +
    +inline SolutionStatus status() const
    +
    + +
    +
    +inline SolutionReason reason() const
    +
    + +
    +
    +inline double best_obj() const
    +
    + +
    +
    +inline double best_bound() const
    +
    + +
    +
    +const PrimalPoint &primal_solution() const
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/IntegerMaster.html b/api/mixed-integer/column-generation/IntegerMaster.html new file mode 100644 index 000000000..9c41e9bf3 --- /dev/null +++ b/api/mixed-integer/column-generation/IntegerMaster.html @@ -0,0 +1,358 @@ + + + + + + + Heuristics::IntegerMaster + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Heuristics::IntegerMaster

    +
    +

    Warning

    +

    This heuristic can only be used with a BranchAndBound<NodeVarInfo> optimizer in which nodes are solved by +DantzigWolfeDecomposition.

    +
    +
    +

    Doxygen

    +
    +
    +template<class NodeInfoT = idol::DefaultNodeInfo>
    class IntegerMaster : public idol::BranchAndBoundCallbackFactory<idol::DefaultNodeInfo>
    +
    +

    Public Functions

    +
    +
    +IntegerMaster() = default
    +
    + +
    +
    +IntegerMaster(IntegerMaster&&) noexcept = default
    +
    + +
    +
    +IntegerMaster &operator=(const IntegerMaster&) = delete
    +
    + +
    +
    +IntegerMaster &operator=(IntegerMaster&&) noexcept = default
    +
    + +
    +
    +virtual BranchAndBoundCallback<NodeInfoT> *operator()() override
    +
    + +
    +
    +virtual BranchAndBoundCallbackFactory<NodeInfoT> *clone() const override
    +
    + +
    +
    +IntegerMaster &with_optimizer(const OptimizerFactory &t_optimizer)
    +
    + +
    +
    +IntegerMaster &with_integer_columns(bool t_value)
    +
    + +
    +
    +IntegerMaster &with_time_limit(double t_time_limit)
    +
    + +
    +
    +IntegerMaster &with_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +IntegerMaster &with_max_depth(unsigned int t_max_depth)
    +
    + +
    +
    +IntegerMaster &with_frequency(unsigned int t_frequency)
    +
    + +
    +
    +
    +class Strategy : public idol::BranchAndBoundCallback<NodeInfoT>
    +
    +

    Public Functions

    +
    +
    +explicit Strategy(const OptimizerFactory &t_optimizer)
    +
    + +
    +
    +inline bool with_integer_columns() const
    +
    + +
    +
    +inline void set_integer_columns(bool t_value)
    +
    + +
    +
    +inline void set_time_limit(double t_time_limit)
    +
    + +
    +
    +inline void set_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline void set_max_depth(unsigned int t_max_depth)
    +
    + +
    +
    +inline void set_frequency(unsigned int t_frequency)
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.html b/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.html new file mode 100644 index 000000000..8e85b1e87 --- /dev/null +++ b/api/mixed-integer/column-generation/Optimizers_DantzigWolfeDecomposition.html @@ -0,0 +1,528 @@ + + + + + + + Optimizers::DantzigWolfeDecomposition + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::DantzigWolfeDecomposition

    +
    +

    Doxygen

    +
    +
    +class DantzigWolfeDecomposition : public idol::Algorithm
    +
    +

    Public Functions

    +
    +
    +DantzigWolfeDecomposition(const Model &t_model, idol::DantzigWolfe::Formulation &&t_formulation, const OptimizerFactory &t_master_optimizer_factory, const DantzigWolfe::DualPriceSmoothingStabilization &t_stabilization, unsigned int t_max_parallel_pricing, bool t_use_hard_branching, bool t_remove_infeasible_columns, std::vector<DantzigWolfe::SubProblem> &&t_sub_problem_specifications, std::optional<DantzigWolfe::SubProblem> t_default_sub_problem_spec, const DantzigWolfe::InfeasibilityStrategyFactory &t_strategy, const Logs::DantzigWolfe::Factory &t_logger_factory)
    +
    + +
    +
    +virtual std::string name() const override
    +
    + +
    +
    +inline const DantzigWolfe::Formulation &formulation() const
    +
    + +
    +
    +inline DantzigWolfe::Formulation &formulation()
    +
    + +
    +
    +virtual SolutionStatus get_status() const override
    +
    + +
    +
    +virtual SolutionReason get_reason() const override
    +
    + +
    +
    +virtual double get_best_obj() const override
    +
    + +
    +
    +virtual double get_best_bound() const override
    +
    + +
    +
    +virtual double get_relative_gap() const override
    +
    + +
    +
    +virtual double get_absolute_gap() const override
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline virtual void set_param_logs(bool t_value)
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline virtual void set_param_time_limit(double t_time_limit)
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +inline virtual void set_param_threads(unsigned int t_threads)
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_obj_stop(double t_best_obj_stop)
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_bound_stop(double t_best_bound_stop)
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_relative_gap(double t_tol_mip_relative_gap)
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_absolute_gap(double t_mip_tol_absolute_gap)
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline virtual void set_tol_feasibility(double t_tol_feasibility)
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline virtual void set_tol_optimality(double t_tol_optimality)
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline virtual void set_tol_integer(double t_tol_integer)
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline virtual void set_param_presolve(bool t_value)
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline virtual void set_param_infeasible_or_unbounded_info(bool t_value)
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +
    +class ColumnGeneration
    +
    +

    Public Functions

    +
    +
    +ColumnGeneration(DantzigWolfeDecomposition &t_parent, bool t_use_farkas_for_infeasibility, double t_best_bound_stop)
    +
    + +
    +
    +inline const DantzigWolfeDecomposition &parent() const
    +
    + +
    +
    +inline DantzigWolfeDecomposition &parent()
    +
    + +
    +
    +inline SolutionStatus status() const
    +
    + +
    +
    +inline SolutionReason reason() const
    +
    + +
    +
    +inline double best_obj() const
    +
    + +
    +
    +inline double best_bound() const
    +
    + +
    +
    +inline const PrimalPoint &primal_solution() const
    +
    + +
    +
    +inline void set_best_bound_stop(double t_best_bound_stop)
    +
    + +
    +
    +void execute()
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/stabilization/Neame.html b/api/mixed-integer/column-generation/stabilization/Neame.html new file mode 100644 index 000000000..e76f3eb80 --- /dev/null +++ b/api/mixed-integer/column-generation/stabilization/Neame.html @@ -0,0 +1,295 @@ + + + + + + + DantzigWolfe::Neame + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DantzigWolfe::Neame

    +
    +

    Doxygen

    +
    +
    +class Neame : public idol::DantzigWolfe::DualPriceSmoothingStabilization
    +
    +

    Public Functions

    +
    +
    +inline explicit Neame(double t_initial_factor)
    +
    + +
    +
    +inline virtual DualPriceSmoothingStabilization::Strategy *operator()() const override
    +
    + +
    +
    +inline virtual DualPriceSmoothingStabilization *clone() const override
    +
    + +
    +
    +
    +class Strategy : public idol::DantzigWolfe::DualPriceSmoothingStabilization::Strategy
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(double t_initial_factor)
    +
    + +
    +
    +inline virtual void initialize() override
    +
    + +
    +
    +inline virtual void update_stability_center(const DualPoint &t_master_dual) override
    +
    + +
    +
    +inline virtual DualPoint compute_smoothed_dual_solution(const DualPoint &t_master_dual) override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/stabilization/Wentges.html b/api/mixed-integer/column-generation/stabilization/Wentges.html new file mode 100644 index 000000000..266c361ec --- /dev/null +++ b/api/mixed-integer/column-generation/stabilization/Wentges.html @@ -0,0 +1,295 @@ + + + + + + + DantzigWolfe::Wentges + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    DantzigWolfe::Wentges

    +
    +

    Doxygen

    +
    +
    +class Wentges : public idol::DantzigWolfe::DualPriceSmoothingStabilization
    +
    +

    Public Functions

    +
    +
    +inline explicit Wentges(double t_initial_factor)
    +
    + +
    +
    +inline virtual DualPriceSmoothingStabilization::Strategy *operator()() const override
    +
    + +
    +
    +inline virtual DualPriceSmoothingStabilization *clone() const override
    +
    + +
    +
    +
    +class Strategy : public idol::DantzigWolfe::DualPriceSmoothingStabilization::Strategy
    +
    +

    Public Functions

    +
    +
    +inline explicit Strategy(double t_initial_factor)
    +
    + +
    +
    +inline virtual void initialize() override
    +
    + +
    +
    +inline virtual void update_stability_center(const DualPoint &t_master_dual) override
    +
    + +
    +
    +inline virtual DualPoint compute_smoothed_dual_solution(const DualPoint &t_master_dual) override
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/column-generation/stabilization/index.html b/api/mixed-integer/column-generation/stabilization/index.html new file mode 100644 index 000000000..ce4e7d321 --- /dev/null +++ b/api/mixed-integer/column-generation/stabilization/index.html @@ -0,0 +1,245 @@ + + + + + + + More on Stabilization… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on Stabilization…

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/GLPK.html b/api/mixed-integer/external-solvers/GLPK.html new file mode 100644 index 000000000..729f78ed4 --- /dev/null +++ b/api/mixed-integer/external-solvers/GLPK.html @@ -0,0 +1,578 @@ + + + + + + + GLPK + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    GLPK

    +
    +

    Doxygen

    +
    +
    +class GLPK : public idol::OptimizerFactoryWithDefaultParameters<GLPK>
    +
    +

    Public Functions

    +
    +
    +GLPK() = default
    +
    + +
    +
    +GLPK(const GLPK&) = default
    +
    + +
    +
    +GLPK(GLPK&&) noexcept = default
    +
    + +
    +
    +GLPK &operator=(const GLPK&) = delete
    +
    + +
    +
    +GLPK &operator=(GLPK&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual GLPK *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +GLPK &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &conditional(bool t_conditional_value, const std::function<void(GLPK&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +GLPK &conditional(bool t_conditional_value, const std::function<void(GLPK&)> &t_if, const std::function<void(GLPK&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static GLPK ContinuousRelaxation()
    +
    + +
    +
    +static Model read_from_file(Env &t_env, const std::string &t_filename)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Gurobi.html b/api/mixed-integer/external-solvers/Gurobi.html new file mode 100644 index 000000000..4dfcd616a --- /dev/null +++ b/api/mixed-integer/external-solvers/Gurobi.html @@ -0,0 +1,608 @@ + + + + + + + Gurobi + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Gurobi

    +
    +

    Doxygen

    +
    +
    +class Gurobi : public idol::OptimizerFactoryWithDefaultParameters<Gurobi>
    +
    +

    Public Functions

    +
    +
    +Gurobi() = default
    +
    + +
    +
    +Gurobi(const Gurobi &t_src)
    +
    + +
    +
    +Gurobi(Gurobi&&) noexcept = default
    +
    + +
    +
    +Gurobi &operator=(const Gurobi&) = delete
    +
    + +
    +
    +Gurobi &operator=(Gurobi&&) noexcept = default
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +Gurobi &add_callback(const CallbackFactory &t_cb)
    +
    + +
    +
    +Gurobi &with_lazy_cut(bool t_value)
    +
    + +
    +
    +Gurobi &with_max_n_solution_in_pool(unsigned int t_value)
    +
    + +
    +
    +Gurobi &with_continuous_relaxation_only(bool t_value)
    +
    + +
    +
    +Gurobi &with_external_param(GRB_IntParam t_param, int t_value)
    +
    + +
    +
    +Gurobi &with_external_param(GRB_DoubleParam t_param, double t_value)
    +
    + +
    +
    +virtual Gurobi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Gurobi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &conditional(bool t_conditional_value, const std::function<void(Gurobi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Gurobi &conditional(bool t_conditional_value, const std::function<void(Gurobi&)> &t_if, const std::function<void(Gurobi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Gurobi ContinuousRelaxation()
    +
    + +
    +
    +static Model read_from_file(Env &t_env, const std::string &t_filename)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/HiGHS.html b/api/mixed-integer/external-solvers/HiGHS.html new file mode 100644 index 000000000..d0c87b6f8 --- /dev/null +++ b/api/mixed-integer/external-solvers/HiGHS.html @@ -0,0 +1,578 @@ + + + + + + + HiGHS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    HiGHS

    +
    +

    Doxygen

    +
    +
    +class HiGHS : public idol::OptimizerFactoryWithDefaultParameters<HiGHS>
    +
    +

    Public Functions

    +
    +
    +HiGHS() = default
    +
    + +
    +
    +HiGHS(const HiGHS&) = default
    +
    + +
    +
    +HiGHS(HiGHS&&) noexcept = default
    +
    + +
    +
    +HiGHS &operator=(const HiGHS&) = delete
    +
    + +
    +
    +HiGHS &operator=(HiGHS&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual HiGHS *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +HiGHS &with_continuous_relaxation_only(bool t_value)
    +
    + +
    +
    +HiGHS &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &conditional(bool t_conditional_value, const std::function<void(HiGHS&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +HiGHS &conditional(bool t_conditional_value, const std::function<void(HiGHS&)> &t_if, const std::function<void(HiGHS&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static HiGHS ContinuousRelaxation()
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Mosek.html b/api/mixed-integer/external-solvers/Mosek.html new file mode 100644 index 000000000..dacacaf70 --- /dev/null +++ b/api/mixed-integer/external-solvers/Mosek.html @@ -0,0 +1,598 @@ + + + + + + + Mosek + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Mosek

    +
    +

    Doxygen

    +
    +
    +class Mosek : public idol::OptimizerFactoryWithDefaultParameters<Mosek>
    +
    +

    Public Functions

    +
    +
    +Mosek() = default
    +
    + +
    +
    +Mosek(const Mosek&)
    +
    + +
    +
    +Mosek(Mosek&&) noexcept = default
    +
    + +
    +
    +Mosek &operator=(const Mosek&) = delete
    +
    + +
    +
    +Mosek &operator=(Mosek&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual Mosek *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Mosek &add_callback(const CallbackFactory &t_cb)
    +
    + +
    +
    +Mosek &with_continuous_relaxation_only(bool t_value)
    +
    + +
    +
    +Mosek &with_external_parameter(const std::string &t_param, double t_value)
    +
    + +
    +
    +Mosek &with_external_parameter(const std::string &t_param, int t_value)
    +
    + +
    +
    +Mosek &with_external_parameter(const std::string &t_param, std::string t_value)
    +
    + +
    +
    +Mosek &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &conditional(bool t_conditional_value, const std::function<void(Mosek&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Mosek &conditional(bool t_conditional_value, const std::function<void(Mosek&)> &t_if, const std::function<void(Mosek&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Mosek ContinuousRelaxation()
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Optimizers_GLPK.html b/api/mixed-integer/external-solvers/Optimizers_GLPK.html new file mode 100644 index 000000000..532974ecc --- /dev/null +++ b/api/mixed-integer/external-solvers/Optimizers_GLPK.html @@ -0,0 +1,458 @@ + + + + + + + Optimizers::GLPK + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::GLPK

    +
    +

    Doxygen

    +
    +
    +class GLPK : public idol::OptimizerWithLazyUpdates<int, int, int>
    +
    +

    Public Functions

    +
    +
    +explicit GLPK(const Model &t_model, bool t_continuous_relaxation)
    +
    + +
    +
    +inline virtual std::string name() const override
    +
    + +
    +
    +virtual void set_param_time_limit(double t_time_limit) override
    +
    + +
    +
    +virtual void set_param_best_obj_stop(double t_best_obj_stop) override
    +
    + +
    +
    +virtual void set_param_best_bound_stop(double t_best_bound_stop) override
    +
    + +
    +
    +virtual void set_param_presolve(bool t_value) override
    +
    + +
    +
    +virtual void set_param_logs(bool t_value) override
    +
    + +
    +
    +inline int &operator[](const Var &t_var)
    +
    + +
    +
    +inline const int &operator[](const Var &t_var) const
    +
    + +
    +
    +inline int &operator[](const Ctr &t_ctr)
    +
    + +
    +
    +inline const int &operator[](const Ctr &t_ctr) const
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +inline virtual void set_param_threads(unsigned int t_threads)
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_relative_gap(double t_tol_mip_relative_gap)
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_absolute_gap(double t_mip_tol_absolute_gap)
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline virtual void set_tol_feasibility(double t_tol_feasibility)
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline virtual void set_tol_optimality(double t_tol_optimality)
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline virtual void set_tol_integer(double t_tol_integer)
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline virtual void set_param_infeasible_or_unbounded_info(bool t_value)
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Model read_from_file(Env &t_env, const std::string &t_filename)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Optimizers_Gurobi.html b/api/mixed-integer/external-solvers/Optimizers_Gurobi.html new file mode 100644 index 000000000..635cd5e25 --- /dev/null +++ b/api/mixed-integer/external-solvers/Optimizers_Gurobi.html @@ -0,0 +1,516 @@ + + + + + + + Optimizers::Gurobi + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Gurobi

    +
    +

    Doxygen

    +
    +
    +class Gurobi : public idol::OptimizerWithLazyUpdates<GRBVar, GRBConstr, GRBQConstr>
    +
    +

    Public Functions

    +
    +
    +Gurobi(const Model &t_model, bool t_continuous_relaxation, GRBEnv &t_env)
    +
    + +
    +
    +inline explicit Gurobi(const Model &t_model, bool t_continuous_relaxation)
    +
    + +
    +
    +inline GRBEnv &env()
    +
    + +
    +
    +inline const GRBEnv &env() const
    +
    + +
    +
    +inline GRBModel &model()
    +
    + +
    +
    +inline const GRBModel &model() const
    +
    + +
    +
    +inline virtual std::string name() const override
    +
    + +
    +
    +virtual void set_param_time_limit(double t_time_limit) override
    +
    + +
    +
    +virtual void set_param_threads(unsigned int t_thread_limit) override
    +
    + +
    +
    +virtual void set_param_best_obj_stop(double t_best_obj_stop) override
    +
    + +
    +
    +virtual void set_param_best_bound_stop(double t_best_bound_stop) override
    +
    + +
    +
    +virtual void set_param_presolve(bool t_value) override
    +
    + +
    +
    +virtual void set_param_infeasible_or_unbounded_info(bool t_value) override
    +
    + +
    +
    +void add_callback(Callback *t_ptr_to_callback)
    +
    + +
    +
    +void set_lazy_cut(bool t_value)
    +
    + +
    +
    +void set_max_n_solution_in_pool(unsigned int t_value)
    +
    + +
    +
    +virtual void set_param_logs(bool t_value) override
    +
    + +
    +
    +void set_param(GRB_IntParam t_param, int t_value)
    +
    + +
    +
    +void set_param(GRB_DoubleParam t_param, double t_value)
    +
    + +
    +
    +virtual void set_tol_mip_relative_gap(double t_relative_gap_tolerance) override
    +
    + +
    +
    +virtual void set_tol_mip_absolute_gap(double t_absolute_gap_tolerance) override
    +
    + +
    +
    +virtual void set_tol_feasibility(double t_tol_feasibility) override
    +
    + +
    +
    +virtual void set_tol_optimality(double t_tol_optimality) override
    +
    + +
    +
    +virtual void set_tol_integer(double t_tol_integer) override
    +
    + +
    +
    +inline GRBVar &operator[](const Var &t_var)
    +
    + +
    +
    +inline const GRBVar &operator[](const Var &t_var) const
    +
    + +
    +
    +inline GRBConstr &operator[](const Ctr &t_ctr)
    +
    + +
    +
    +inline const GRBConstr &operator[](const Ctr &t_ctr) const
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Model read_from_file(Env &t_env, const std::string &t_filename)
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class ::idol::GurobiCallbackI
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Optimizers_HiGHS.html b/api/mixed-integer/external-solvers/Optimizers_HiGHS.html new file mode 100644 index 000000000..b4b48ebd2 --- /dev/null +++ b/api/mixed-integer/external-solvers/Optimizers_HiGHS.html @@ -0,0 +1,246 @@ + + + + + + + Optimizers::HiGHS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::HiGHS

    +
    +

    Doxygen

    +
    +

    Warning

    +

    doxygenclass: Cannot find class “idol::Optimizers::HiGHS” in doxygen xml output for project “idol” from directory: _build/xml/

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Optimizers_Mosek.html b/api/mixed-integer/external-solvers/Optimizers_Mosek.html new file mode 100644 index 000000000..44422447c --- /dev/null +++ b/api/mixed-integer/external-solvers/Optimizers_Mosek.html @@ -0,0 +1,246 @@ + + + + + + + Optimizers::Mosek + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::Mosek

    +
    +

    Doxygen

    +
    +

    Warning

    +

    doxygenclass: Cannot find class “idol::Optimizers::Mosek” in doxygen xml output for project “idol” from directory: _build/xml/

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Osi.html b/api/mixed-integer/external-solvers/Osi.html new file mode 100644 index 000000000..a8dc2a424 --- /dev/null +++ b/api/mixed-integer/external-solvers/Osi.html @@ -0,0 +1,610 @@ + + + + + + + More on coin-or/Osi (Cplex, Xpress, Cbc, …)… + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    More on coin-or/Osi (Cplex, Xpress, Cbc, …)…

    +

    Idol can be linked with the coin-or/Osi library (Open Solver Interface) to use any solver having an osi interface.

    +
    +

    Hint

    +

    At the moment, only Cplex has been properly tested and can be used as follows.

    +
    model.use(OsiCplex());
+
    +
    +
    +
    +

    Hint

    +

    Note that Osi can also be used with any Osi object by directly passing the interface as an argument.

    +
    model.use(Osi(OsiCpxSolverInterface())); // same as: model.use(OsiCplex());
+
    +
    +
    +
    +

    Warning

    +

    Though idol has dedicated optimizers for Symphony, Cbc and Clp, it seems that the osi interface for these solvers do not +fully fulfill the interface requirement to have a stable usage.

    +
    + +
    +

    Doxygen

    +
    +
    +class Osi : public idol::OptimizerFactoryWithDefaultParameters<Osi>
    +

    Subclassed by idol::OsiCbc, idol::OsiClp, idol::OsiCplex, idol::OsiSymphony

    +
    +

    Public Functions

    +
    +
    +Osi(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    +Osi(const Osi &t_src)
    +
    + +
    +
    +Osi(Osi&&) noexcept = default
    +
    + +
    +
    +Osi &operator=(const Osi&) = delete
    +
    + +
    +
    +Osi &operator=(Osi&&) noexcept = delete
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +OsiSolverInterface *create_osi_solver_interface() const
    +
    + +
    +
    +virtual Osi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Osi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if, const std::function<void(Osi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Osi ContinuousRelaxation(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Osi/OsiCbc.html b/api/mixed-integer/external-solvers/Osi/OsiCbc.html new file mode 100644 index 000000000..bc7b048e3 --- /dev/null +++ b/api/mixed-integer/external-solvers/Osi/OsiCbc.html @@ -0,0 +1,555 @@ + + + + + + + OsiCbc + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    OsiCbc

    +
    +

    Doxygen

    +
    +
    +class OsiCbc : public idol::Osi
    +
    +

    Public Functions

    +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +OsiSolverInterface *create_osi_solver_interface() const
    +
    + +
    +
    +virtual Osi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Osi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if, const std::function<void(Osi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Osi ContinuousRelaxation(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Osi/OsiClp.html b/api/mixed-integer/external-solvers/Osi/OsiClp.html new file mode 100644 index 000000000..561fdd094 --- /dev/null +++ b/api/mixed-integer/external-solvers/Osi/OsiClp.html @@ -0,0 +1,555 @@ + + + + + + + OsiClp + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    OsiClp

    +
    +

    Doxygen

    +
    +
    +class OsiClp : public idol::Osi
    +
    +

    Public Functions

    +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +OsiSolverInterface *create_osi_solver_interface() const
    +
    + +
    +
    +virtual Osi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Osi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if, const std::function<void(Osi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Osi ContinuousRelaxation(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Osi/OsiCplex.html b/api/mixed-integer/external-solvers/Osi/OsiCplex.html new file mode 100644 index 000000000..1ae21cc52 --- /dev/null +++ b/api/mixed-integer/external-solvers/Osi/OsiCplex.html @@ -0,0 +1,555 @@ + + + + + + + OsiCplex + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    OsiCplex

    +
    +

    Doxygen

    +
    +
    +class OsiCplex : public idol::Osi
    +
    +

    Public Functions

    +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +OsiSolverInterface *create_osi_solver_interface() const
    +
    + +
    +
    +virtual Osi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Osi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if, const std::function<void(Osi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Osi ContinuousRelaxation(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/external-solvers/Osi/OsiSymphony.html b/api/mixed-integer/external-solvers/Osi/OsiSymphony.html new file mode 100644 index 000000000..1c297555b --- /dev/null +++ b/api/mixed-integer/external-solvers/Osi/OsiSymphony.html @@ -0,0 +1,555 @@ + + + + + + + OsiSymphony + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    OsiSymphony

    +
    +

    Doxygen

    +
    +
    +class OsiSymphony : public idol::Osi
    +
    +

    Public Functions

    +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +OsiSolverInterface *create_osi_solver_interface() const
    +
    + +
    +
    +virtual Osi *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +Osi &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +Osi &conditional(bool t_conditional_value, const std::function<void(Osi&)> &t_if, const std::function<void(Osi&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +static Osi ContinuousRelaxation(const OsiSolverInterface &t_solver_interface)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/index.html b/api/mixed-integer/index.html new file mode 100644 index 000000000..ff4b9c31e --- /dev/null +++ b/api/mixed-integer/index.html @@ -0,0 +1,321 @@ + + + + + + + Mixed-integer Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Mixed-integer Optimization

    +
    +

    Modeling

    +
    + +
    +
    +
    +

    External Solvers

    +
    + +
    +
    +
    +

    Branch-and-Bound

    +
    + +
    +
    +
    +

    Branch-and-Price

    +
    + +
    +
    +
    +

    Penalty Alternating Direction Method

    +
    + +
    +
    +
    +

    Miscellaneous

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/misc/CtrType.html b/api/mixed-integer/misc/CtrType.html new file mode 100644 index 000000000..1b31d3d21 --- /dev/null +++ b/api/mixed-integer/misc/CtrType.html @@ -0,0 +1,260 @@ + + + + + + + CtrType + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    CtrType

    +
    +
    +enum idol::CtrType
    +

    Values:

    +
    +
    +enumerator LessOrEqual
    +
    + +
    +
    +enumerator GreaterOrEqual
    +
    + +
    +
    +enumerator Equal
    +
    + +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/misc/VarType.html b/api/mixed-integer/misc/VarType.html new file mode 100644 index 000000000..4f3331c3e --- /dev/null +++ b/api/mixed-integer/misc/VarType.html @@ -0,0 +1,260 @@ + + + + + + + VarType + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    VarType

    +
    +
    +enum idol::VarType
    +

    Values:

    +
    +
    +enumerator Continuous
    +
    + +
    +
    +enumerator Integer
    +
    + +
    +
    +enumerator Binary
    +
    + +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/misc/tolerances.html b/api/mixed-integer/misc/tolerances.html new file mode 100644 index 000000000..e828a35d3 --- /dev/null +++ b/api/mixed-integer/misc/tolerances.html @@ -0,0 +1,380 @@ + + + + + + + Tolerances + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Tolerances

    +
    +
    +namespace idol
    +
    +

    Functions

    +
    +
    +static bool is_pos_inf(double t_value)
    +
    + +
    +
    +static bool is_neg_inf(double t_value)
    +
    + +
    +
    +static bool is_inf(double t_value)
    +
    + +
    +
    +static bool equals(double t_a, double t_b, double t_tolerance)
    +
    + +
    +
    +static bool is(double t_a, CtrType t_type, double t_b, double t_tolerance)
    +
    + +
    +
    +static double relative_gap(double t_lb, double t_ub)
    +
    + +
    +
    +static double absolute_gap(double t_lb, double t_ub)
    +
    + +
    +
    +static bool is_zero(double t_value, double t_tolerance)
    +
    + +
    +
    +template<class T>
    decltype(std::declval<T>().is_zero(.1)) is_zero(const T &t_expr, double t_tolerance)
    +
    + +
    +
    +static bool is_integer(double t_value, double t_tolerance)
    +
    + +
    +
    +static double round(double t_value, unsigned int t_n_digits = 0)
    +
    + +
    +
    +

    Variables

    +
    +
    +static constexpr double Inf = 1e20
    +
    + +
    +
    +
    +namespace Tolerance
    +

    Stores the default high-level tolerances used in idol.

    +

    It is possible for external-mip to have additional tolerance parameters, yet, the tolerances defined in this namespace should always be taken into account by the optimizer. Apart from the Sparsity tolerance, users can also change tolerance values at a local level (i.e., at an optimizer level) rather than at a global level.

    +
    +

    Variables

    +
    +
    +static double Sparsity = 1e-8
    +

    Default: \( 10^{-8} \)

    +

    Recommended range: \( [ 10^{-10}, 10^{-5} ] \)

    +

    This tolerance is used when data is saved in a sparse manner. For instance, when a value close to zero should be stored or ignored when saving a primal point.

    +
    + +
    +
    +static unsigned int Digits = 8
    +
    + +
    +
    +static double MIPRelativeGap = 1e-4
    +

    Default: \( 10^{-4} \)

    +

    Recommended range: \( [ 0, +\infty ] \)

    +

    Used to declare optimality of a MIP solution by comparing with the current relative gap.

    +

    The relative gap is computed as follows:

    +\[ \gamma_{\text{rel}} := \frac{ |UB - LB| }{ 10^{-10} + |UB| }. \]
    +

    +
    + +
    +
    +static double MIPAbsoluteGap = 1e-5
    +

    Default: \( 10^{-5} \)

    +

    Recommended range: \( [ 0, \infty ] \)

    +

    Used to declare optimality of a MIP solution by comparing with the current absolute gap.

    +

    The absolute gap is computed as follows:

    +\[ \gamma_{\text{abs}} := |UB - LB| \]
    +

    +
    + +
    +
    +static double Integer = 10e-5
    +

    Default: \( 10^{-5} \)

    +

    Recommended range: \( [ 10^{-9}, 10^{-1} ] \)

    +

    Used to recognized integer values, i.e., a given value is considered integer when the closest integer point is closer than this tolerance.

    +
    + +
    +
    +static double Feasibility = 10e-6
    +

    Default: \( 10^{-6} \)

    +

    Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

    +

    Used to characterized constraint satisfaction, i.e., a constraint is satisfied if it is not violated by a larger amount than this tolerance.

    +
    + +
    +
    +static double Optimality = 10e-6
    +

    Default: \( 10^{-6} \)

    +

    Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

    +

    Used to characterize optimality, i.e., all reduced costs must be smaller than this tolerance.

    +
    + +
    +
    + +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Annotation.html b/api/mixed-integer/modeling/Annotation.html new file mode 100644 index 000000000..97ab8fae9 --- /dev/null +++ b/api/mixed-integer/modeling/Annotation.html @@ -0,0 +1,342 @@ + + + + + + + Annotation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Annotation

    +

    Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +The Annotation class takes one template arguments which is the value type. For instance, we +can create an annotation of type unsigned int as follows.

    +
    Env env;
+
+const unsigned int default_value = 0;
+
+Annotation<unsigned int> annotation(env, "my_annotation", default_value);
+
    +
    +

    Annotations are global, i.e., they do not relate to a given optimization model and can, therefore, be accessed +anywhere in the code. Thus, given a constraint called constraint, the value of the annotation can be accessed +by calling the Ctr::get method.

    +
    std::cout << "My annotation is " << constraint.get(annotation) << std::endl; // "0", i.e., the default_value value
+
    +
    +

    Annotations are, in particular, used to give decomposition instructions to idol when designing a Branch-and-Price algorithm. +To learn more, check our Branch-and-Price tutorials.

    +
    +

    Doxygen

    +
    +
    +template<class ValueT = unsigned int>
    class Annotation : public idol::impl::Annotation
    +
    +

    Public Functions

    +
    +
    +inline Annotation(Env &t_env, std::string t_name)
    +
    + +
    +
    +template<class ...ArgsT>
    inline Annotation(Env &t_env, std::string t_name, ArgsT&&... t_args)
    +
    + +
    +
    +inline const ValueT &default_value() const
    +
    + +
    +
    +inline unsigned int id() const
    +

    Returns the id of the annotation.

    +

    The id is unique within the environment.

    +
    +
    Returns:
    +

    The id of the annotation

    +
    +
    +
    + +
    +
    +inline const std::string &name() const
    +

    Returns the given name of the annotation.

    +
    +
    Returns:
    +

    The given name of the annotation

    +
    +
    +
    + +
    +
    +inline bool has_default() const
    +

    Returns true if the annotation has a default value, false otherwise.

    +
    +
    Returns:
    +

    true if the annotation has a default value, false otherwise

    +
    +
    +
    + +
    +
    +void free()
    +

    Frees the memory kept for the annotation in the environment.

    +
    + +
    +
    +inline Env &env() const
    +

    Returns the underlying environment of the annotation.

    +
    +
    Returns:
    +

    The underlying environment of the annotation.

    +
    +
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +template<class ...ArgsT>
    static inline Annotation<ValueT> make_with_default_value(Env &t_env, std::string t_name, ArgsT&&... t_args)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Ctr.html b/api/mixed-integer/modeling/Ctr.html new file mode 100644 index 000000000..76c2f3b27 --- /dev/null +++ b/api/mixed-integer/modeling/Ctr.html @@ -0,0 +1,427 @@ + + + + + + + Ctr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Ctr

    +
    +

    Doxygen

    +
    +
    +class Ctr : public idol::Object<CtrVersion, Ctr>
    +
    +

    Public Functions

    +
    +
    +Ctr(Env &t_env, TempCtr &&t_temp_ctr, std::string t_name = "")
    +

    Constructor.

    +

    Creates a new constraint in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_temp_ctr – The temporary constraint used to create the default version of the constraint.

      • +

    • t_name – The given name for the constraint.

      • +
    +
    +
    +
    + +
    +
    +Ctr(Env &t_env, const TempCtr &t_temp_ctr, std::string t_name = "")
    +

    Constructor.

    +

    Creates a new constraint in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_temp_ctr – The temporary constraint used to create the default version of the constraint.

      • +

    • t_name – The given name for the constraint.

      • +
    +
    +
    +
    + +
    +
    +Ctr(Env &t_env, CtrType t_type, double t_constant, std::string t_name = "")
    +

    Constructor.

    +

    Creates a new constraint in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_type – The type of the constraint in its default version.

      • +

    • t_constant – The right hand-side of the constraint in its default version.

      • +

    • t_name – The given name for the constraint.

      • +
    +
    +
    +
    + +
    +
    +unsigned int index(const Model &t_index) const
    +
    + +
    +
    +inline const std::string &name() const
    +

    Returns the name of the optimization object.

    +
    +
    Returns:
    +

    The name of the optimization object.

    +
    +
    +
    + +
    +
    +inline unsigned int id() const
    +

    Returns the id of the optimization object.

    +
    +
    Returns:
    +

    The id of the optimization object.

    +
    +
    +
    + +
    +
    +inline bool is_in(const Model &t_model) const
    +

    Returns true if the optimization object is part of the model t_model, false otherwise.

    +
    +
    Parameters:
    +

    t_model – The model.

    +
    +
    Returns:
    +

    True if the optimization object is part of the model t_model, false otherwise.

    +
    +
    +
    + +
    +
    +inline const ValueT &get(const Annotation<ValueT> &t_annotation) const
    +

    Returns the value of the given annotation t_annotation associated to the object.

    +

    If no value is found, the default value of the annotation is returned. If no default value was set, an exception is thrown.

    +
    +
    Template Parameters:
    +

    ValueT – The value type of the annotation.

    +
    +
    Parameters:
    +

    t_annotation – The annotation.

    +
    +
    Returns:
    +

    The value of the annotation.

    +
    +
    +
    + +
    +
    +inline void set(const Annotation<ValueT> &t_annotation, ArgsT&&... t_args) const
    +

    Sets the value of the given annotation t_annotation associated to the object.

    +
    +
    Template Parameters:
    +
      +

    • ValueT – The value type of the annotation.

      • +

    • ArgsT – The parameter pack types for constructing the value of the annotation.

      • +
    +
    +
    Parameters:
    +
      +

    • t_annotation – The annotation.

      • +

    • t_args – The parameter pack arguments used to construct “in place” the value of the annotation.

      • +
    +
    +
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +template<unsigned int N = 1, unsigned int I = 0>
    static inline Vector<Ctr, N - I> make_vector(Env &t_env, const Dim<N> &t_dim, CtrType t_type, double t_constant, const std::string &t_name = "")
    +

    Creates a (nested) vector of constraints.

    +

    Example:

    +

    Env env;
+
+auto constraint = Ctr::make_vector(env, Dim<2>(m, n), LessOrEqual, 0., "constraint");
+
+std::cout << constraint[1][4].name() << std::endl; // "constraint_1_4"
+
    +
    +

    +
    +
    Template Parameters:
    +
      +

    • N – The dimension of the (nested) vector.

      • +

    • I – Used for recursion.

      • +
    +
    +
    Parameters:
    +
      +

    • t_env – The environment to store the constraints.

      • +

    • t_dim – The number of elements in each dimension.

      • +

    • t_type – The type of the constraints.

      • +

    • t_constant – The right hand-side of the constraints.

      • +

    • t_name – The given name of the constraints.

      • +
    +
    +
    Returns:
    +

    A (nested) vector of constraints.

    +
    +
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class impl::Env
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Dim.html b/api/mixed-integer/modeling/Dim.html new file mode 100644 index 000000000..726349b00 --- /dev/null +++ b/api/mixed-integer/modeling/Dim.html @@ -0,0 +1,260 @@ + + + + + + + Dim + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Dim

    +
    +

    Doxygen

    +
    +
    +template<unsigned int N>
    class Dim : public std::array<unsigned int, N>
    +
    +

    Public Functions

    +
    +
    +inline explicit Dim(std::array<unsigned int, N> t_dims)
    +
    + +
    +
    +template<class ...ArgsT>
    inline explicit Dim(ArgsT&&... t_args)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Env.html b/api/mixed-integer/modeling/Env.html new file mode 100644 index 000000000..daea36b5b --- /dev/null +++ b/api/mixed-integer/modeling/Env.html @@ -0,0 +1,308 @@ + + + + + + + Env + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Env

    +
    +

    Doxygen

    +
    +
    +class Env : public idol::impl::Env
    +

    Environment class.

    +

    This class stores and manages every optimization objects and annotations in idol.

    +

    Essentially, it is the environment that controls the death and lives of such objects. It is through the environment that idol manages the different versions each optimization object may have during the execution of your program.

    +

    Important: If an optimization environment is destroyed, all of its objects are also destroyed. Trying to access them will lead to undefined behavior and, eventually, segmentation fault.

    +

    Typically, only one environment should be used by your code, though it is possible to instantiate many environment (not advised).

    +

    Environments are objects of the Env class and can be created as follows.

    +
    Env env; // Creates a new optimization environment.
+
    +
    +
    +

    Public Functions

    +
    +
    +Env() = default
    +

    Constructor.

    +

    Creates a new optimization environment.

    +
    + +
    +
    +template<class T>
    inline const auto &operator[](const T &t_object) const
    +

    Returns the default version of an optimization object.

    +
    +
    Template Parameters:
    +

    T – The type of object queried.

    +
    +
    Parameters:
    +

    t_object – The object. @returnthe The default version of an optimization object.

    +
    +
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class Model
    +
    + +
    +
    +friend class Var
    +
    + +
    +
    +friend class Ctr
    +
    + +
    +
    +friend class QCtr
    +
    + +
    +
    +friend class impl::Annotation
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Expr.html b/api/mixed-integer/modeling/Expr.html new file mode 100644 index 000000000..50689d024 --- /dev/null +++ b/api/mixed-integer/modeling/Expr.html @@ -0,0 +1,358 @@ + + + + + + + AffExpr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    AffExpr

    +
    +

    Doxygen

    +
    +
    +template<class KeyT = idol::Var, class ValueT = double>
    class AffExpr
    +
    +

    Public Functions

    +
    +
    +AffExpr()
    +
    + +
    +
    +AffExpr(ValueT t_constant)
    +
    + +
    +
    +AffExpr(const KeyT &t_key)
    +
    + +
    +
    +AffExpr(LinExpr<KeyT> t_expr)
    +
    + +
    +
    +virtual ~AffExpr() = default
    +
    + +
    +
    +AffExpr(const AffExpr &t_src) = default
    +
    + +
    +
    +AffExpr(AffExpr&&) noexcept = default
    +
    + +
    +
    +AffExpr &operator=(const AffExpr &t_rhs) = default
    +
    + +
    +
    +AffExpr &operator=(AffExpr&&) noexcept = default
    +
    + +
    +
    +AffExpr &operator+=(const AffExpr &t_rhs)
    +
    + +
    +
    +AffExpr &operator-=(const AffExpr &t_rhs)
    +
    + +
    +
    +AffExpr &operator*=(double t_rhs)
    +
    + +
    +
    +AffExpr &operator/=(double t_rhs)
    +
    + +
    +
    +AffExpr operator-() const
    +
    + +
    +
    +inline LinExpr<KeyT, ValueT> &linear()
    +
    + +
    +
    +inline const LinExpr<KeyT, ValueT> &linear() const
    +
    + +
    +
    +inline ValueT &constant()
    +
    + +
    +
    +inline const ValueT &constant() const
    +
    + +
    +
    +inline bool is_zero(double t_tolerance) const
    +
    + +
    +
    +inline void clear()
    +
    + +
    +
    +

    Public Static Attributes

    +
    +
    +static const AffExpr<KeyT, ValueT> Zero = {}
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/LinExpr.html b/api/mixed-integer/modeling/LinExpr.html new file mode 100644 index 000000000..b4f6b6214 --- /dev/null +++ b/api/mixed-integer/modeling/LinExpr.html @@ -0,0 +1,461 @@ + + + + + + + LinExpr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    LinExpr

    +

    This class is used to represent linear expressions in the modeling interface of idol.

    +

    It consists in a set of linear terms which represent products of keys (typically, variables) and scalars.

    +
    +

    Example

    +

    In this example, we create a linear expression representing the following linear expression.

    +
    +\[3 x_0 + 2 x_1\]
    +
    auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x");
+
+LinExpr lin_expr = 3 * x[0] + 2 * x[1];
+
    +
    +
    +
    +

    Doxygen

    +
    +
    +template<class KeyT = idol::Var, class ValueT = double>
    class LinExpr : public idol::SparseVector<idol::Var, double>
    +
    +
    Template Parameters:
    +

    KeyT – the class representing keys

    +
    +
    +

    Subclassed by idol::QuadExpr< idol::Var, idol::QuadExpr< idol::Var > >, idol::QuadExpr< idol::Var >, idol::QuadExpr< idol::Var, double >, idol::QuadExpr< KeyT, ValueT >

    +
    +

    Public Types

    +
    +
    +using iterator = typename map_t::iterator
    +
    + +
    +
    +using const_iterator = typename map_t::const_iterator
    +
    + +
    +
    +

    Public Functions

    +
    +
    +LinExpr() = default
    +
    + +
    +
    +LinExpr(KeyT t_key)
    +
    + +
    +
    +inline LinExpr(SparseVector<KeyT, ValueT> t_vector)
    +
    + +
    +
    +LinExpr(const ValueT &t_factor, const KeyT &t_key)
    +
    + +
    +
    +LinExpr(ValueT &&t_factor, const KeyT &t_key)
    +
    + +
    +
    +LinExpr(const LinExpr<KeyT, ValueT>&) = default
    +
    + +
    +
    +LinExpr(LinExpr<KeyT, ValueT>&&) = default
    +
    + +
    +
    +LinExpr &operator=(const LinExpr<KeyT, ValueT>&) noexcept = default
    +
    + +
    +
    +LinExpr &operator=(LinExpr<KeyT, ValueT>&&) noexcept = default
    +
    + +
    +
    +LinExpr &operator+=(const LinExpr<KeyT, ValueT> &t_rhs)
    +
    + +
    +
    +LinExpr &operator+=(const KeyT &t_rhs)
    +
    + +
    +
    +LinExpr &operator-=(const LinExpr<KeyT, ValueT> &t_rhs)
    +
    + +
    +
    +LinExpr &operator-=(const KeyT &t_rhs)
    +
    + +
    +
    +virtual SparseVector &operator+=(const SparseVector &t_vector)
    +
    + +
    +
    +virtual SparseVector &operator-=(const SparseVector &t_vector)
    +
    + +
    +
    +virtual SparseVector &operator*=(std::conditional_t<std::is_arithmetic_v<ValueT>, ValueT, double> t_scalar)
    +
    + +
    +
    +virtual SparseVector &operator/=(std::conditional_t<std::is_arithmetic_v<ValueT>, ValueT, double> t_scalar)
    +
    + +
    +
    +SparseVector operator-() const
    +
    + +
    +
    +inline unsigned int size() const
    +
    + +
    +
    +inline bool empty() const
    +
    + +
    +
    +inline bool has_index(const IndexT &t_index) const
    +
    + +
    +
    +const ValueT &get(const IndexT &t_index1) const
    +
    + +
    +
    +void set(const IndexT &t_index, const ValueT &t_value)
    +
    + +
    +
    +virtual bool is_zero(double t_tolerance) const
    +
    + +
    +
    +inline void remove(const IndexT &t_index)
    +
    + +
    +
    +inline void clear()
    +
    + +
    +
    +inline void reserve(unsigned int t_capacity)
    +
    + +
    +
    +inline iterator begin()
    +
    + +
    +
    +inline const_iterator begin() const
    +
    + +
    +
    +inline iterator end()
    +
    + +
    +
    +inline const_iterator end() const
    +
    + +
    +
    +inline const_iterator cbegin() const
    +
    + +
    +
    +inline const_iterator cend() const
    +
    + +
    +
    +SparseVector &merge_without_conflict(const SparseVector &t_vec)
    +
    + +
    +
    +

    Public Static Attributes

    +
    +
    +static LinExpr<KeyT, ValueT> Zero = {}
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Model.html b/api/mixed-integer/modeling/Model.html new file mode 100644 index 000000000..326bc1ebc --- /dev/null +++ b/api/mixed-integer/modeling/Model.html @@ -0,0 +1,785 @@ + + + + + + + Model + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Model

    +
    +

    Doxygen

    +
    +
    +class Model
    +

    This class is used to represent a mathematical optimization model.

    +
    +

    Public Types

    +
    +
    +enum Storage
    +

    Values:

    +
    +
    +enumerator ColumnOriented
    +
    + +
    +
    +enumerator RowOriented
    +
    + +
    +
    +enumerator Both
    +
    + +
    + +
    +
    +

    Public Functions

    +
    +
    +explicit Model(Env &t_env, Storage t_storage = Both)
    +
    + +
    +
    +Model(Model&&) noexcept
    +
    + +
    +
    +Model &operator=(const Model&) = delete
    +
    + +
    +
    +Model &operator=(Model&&) noexcept = delete
    +
    + +
    +
    +~Model()
    +
    + +
    +
    +Var add_var(double t_lb, double t_ub, VarType t_type, double t_obj = 0., std::string t_name = "")
    +
    + +
    +
    +Var add_var(double t_lb, double t_ub, VarType t_type, double t_obj, LinExpr<Ctr> t_column, std::string t_name = "")
    +
    + +
    +
    +template<unsigned int N>
    Vector<Var, N> add_vars(Dim<N> t_dim, double t_lb, double t_ub, VarType t_type, double t_obj = 0., const std::string &t_name = "")
    +
    + +
    +
    +void add(const Var &t_var)
    +
    + +
    +
    +void add(const Var &t_var, TempVar t_temp_var)
    +
    + +
    +
    +bool has(const Var &t_var) const
    +
    + +
    +
    +void remove(const Var &t_var)
    +
    + +
    +
    +inline ConstIteratorForward<std::vector<Var>> vars() const
    +
    + +
    +
    +Ctr add_ctr(TempCtr t_temp_ctr, std::string t_name = "")
    +
    + +
    +
    +Ctr add_ctr(LinExpr<Var> &&t_lhs, CtrType t_type, double t_rhs, std::string t_name = "")
    +
    + +
    +
    +template<unsigned int N>
    Vector<Ctr, N> add_ctrs(Dim<N> t_dim, CtrType t_type, double t_rhs, const std::string &t_name = "")
    +
    + +
    +
    +void add(const Ctr &t_ctr)
    +
    + +
    +
    +void add(const Ctr &t_ctr, TempCtr t_temp_ctr)
    +
    + +
    +
    +bool has(const Ctr &t_ctr) const
    +
    + +
    +
    +void remove(const Ctr &t_ctr)
    +
    + +
    +
    +inline ConstIteratorForward<std::vector<Ctr>> ctrs() const
    +
    + +
    +
    +QCtr add_qctr(TempQCtr t_temp_ctr, std::string t_name = "")
    +
    + +
    +
    +QCtr add_qctr(QuadExpr<Var> &&t_expr, CtrType t_type, std::string t_name = "")
    +
    + +
    +
    +template<unsigned int N>
    Vector<QCtr, N> add_qctrs(Dim<N> t_dim, CtrType t_type, const std::string &t_name = "")
    +
    + +
    +
    +void add(const QCtr &t_ctr)
    +
    + +
    +
    +void add(const QCtr &t_ctr, TempQCtr t_temp_ctr)
    +
    + +
    +
    +bool has(const QCtr &t_ctr) const
    +
    + +
    +
    +void remove(const QCtr &t_ctr)
    +
    + +
    +
    +inline ConstIteratorForward<std::vector<QCtr>> qctrs() const
    +
    + +
    +
    +inline unsigned int id() const
    +
    + +
    +
    +Model *clone() const
    +
    + +
    +
    +Model copy() const
    +
    + +
    +
    +void reserve_vars(unsigned int t_size)
    +
    + +
    +
    +void reserve_ctrs(unsigned int t_size)
    +
    + +
    +
    +void reserve_qctrs(unsigned int t_size)
    +
    + +
    +
    +inline Env &env() const
    +
    + +
    +
    +void use(const OptimizerFactory &t_optimizer_factory)
    +
    + +
    +
    +bool has_optimizer() const
    +
    + +
    +
    +inline bool has_optimizer_factory() const
    +
    + +
    +
    +inline const OptimizerFactory &optimizer_factory() const
    +
    + +
    +
    +void unuse()
    +
    + +
    +
    +template<class T, unsigned int N>
    void add_vector(const Vector<T, N> &t_vector)
    +
    + +
    +
    +inline Optimizer &optimizer()
    +
    + +
    +
    +inline const Optimizer &optimizer() const
    +
    + +
    +
    +void optimize()
    +
    + +
    +
    +void write(const std::string &t_name)
    +
    + +
    +
    +void update()
    +
    + +
    +
    +ObjectiveSense get_obj_sense() const
    +
    + +
    +
    +const QuadExpr<Var> &get_obj_expr() const
    +
    + +
    +
    +const LinExpr<Ctr> &get_rhs_expr() const
    +
    + +
    +
    +double get_mat_coeff(const Ctr &t_ctr, const Var &t_var) const
    +
    + +
    +
    +SolutionStatus get_status() const
    +
    + +
    +
    +SolutionReason get_reason() const
    +
    + +
    +
    +double get_best_obj() const
    +
    + +
    +
    +double get_best_bound() const
    +
    + +
    +
    +void set_obj_sense(ObjectiveSense t_value)
    +
    + +
    +
    +void set_obj_expr(const QuadExpr<Var> &t_objective)
    +
    + +
    +
    +void set_obj_expr(QuadExpr<Var> &&t_objective)
    +
    + +
    +
    +void set_rhs_expr(LinExpr<Ctr> &&t_rhs)
    +
    + +
    +
    +void set_rhs_expr(const LinExpr<Ctr> &t_rhs)
    +
    + +
    +
    +void set_obj_const(double t_constant)
    +
    + +
    +
    +void set_mat_coeff(const Ctr &t_ctr, const Var &t_var, double t_coeff)
    +
    + +
    +
    +QCtr get_qctr_by_index(unsigned int t_index) const
    +
    + +
    +
    +Ctr get_ctr_by_index(unsigned int t_index) const
    +
    + +
    +
    +Var get_var_by_index(unsigned int t_index) const
    +
    + +
    +
    +unsigned int get_ctr_index(const Ctr &t_ctr) const
    +
    + +
    +
    +unsigned int get_qctr_index(const QCtr &tctr) const
    +
    + +
    +
    +CtrType get_ctr_type(const Ctr &t_ctr) const
    +
    + +
    +
    +double get_ctr_rhs(const Ctr &t_ctr) const
    +
    + +
    +
    +const LinExpr<Var> &get_ctr_row(const Ctr &t_ctr) const
    +
    + +
    +
    +const QuadExpr<Var> &get_qctr_expr(const QCtr &t_ctr) const
    +
    + +
    +
    +CtrType get_qctr_type(const QCtr &t_ctr) const
    +
    + +
    +
    +double get_ctr_dual(const Ctr &t_ctr) const
    +
    + +
    +
    +double get_ctr_farkas(const Ctr &t_ctr) const
    +
    + +
    +
    +void set_ctr_rhs(const Ctr &t_ctr, double t_rhs)
    +
    + +
    +
    +void set_ctr_type(const Ctr &t_ctr, CtrType t_type)
    +
    + +
    +
    +void set_ctr_row(const Ctr &t_ctr, const LinExpr<Var> &t_row)
    +
    + +
    +
    +void set_ctr_row(const Ctr &t_ctr, LinExpr<Var> &&t_row)
    +
    + +
    +
    +unsigned int get_var_index(const Var &t_var) const
    +
    + +
    +
    +VarType get_var_type(const Var &t_var) const
    +
    + +
    +
    +double get_var_lb(const Var &t_var) const
    +
    + +
    +
    +double get_var_ub(const Var &t_var) const
    +
    + +
    +
    +double get_var_primal(const Var &t_var) const
    +
    + +
    +
    +double get_var_reduced_cost(const Var &t_var) const
    +
    + +
    +
    +double get_var_ray(const Var &t_var) const
    +
    + +
    +
    +const LinExpr<Ctr> &get_var_column(const Var &t_var) const
    +
    + +
    +
    +double get_var_obj(const Var &t_var) const
    +
    + +
    +
    +void set_var_type(const Var &t_var, VarType t_type)
    +
    + +
    +
    +void set_var_lb(const Var &t_var, double t_lb)
    +
    + +
    +
    +void set_var_ub(const Var &t_var, double t_ub)
    +
    + +
    +
    +void set_var_obj(const Var &t_var, double t_obj)
    +
    + +
    +
    +void set_var_column(const Var &t_var, const LinExpr<Ctr> &t_column)
    +
    + +
    +
    +void set_var_column(const Var &t_var, LinExpr<Ctr> &&t_column)
    +
    + +
    +
    +unsigned int get_n_solutions() const
    +
    + +
    +
    +unsigned int get_solution_index() const
    +
    + +
    +
    +void set_solution_index(unsigned int t_index)
    +
    + +
    +
    +void dump(std::ostream &t_os = std::cout) const
    +
    + +
    +
    +inline Storage storage() const
    +
    + +
    +
    +void set_storage(Storage t_storage, bool t_reset_minor_representation = false)
    +
    + +
    +
    +void reset_minor_representation()
    +
    + +
    +
    +template<unsigned int N>
    idol::Vector<idol::Var, N> add_vars(Dim<N> t_dim, double t_lb, double t_ub, VarType t_type, double t_obj, const std::string &t_name)
    +
    + +
    +
    +template<unsigned int N>
    idol::Vector<idol::Ctr, N> add_ctrs(Dim<N> t_dim, CtrType t_type, double t_rhs, const std::string &t_name)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Point.html b/api/mixed-integer/modeling/Point.html new file mode 100644 index 000000000..9daff0ac7 --- /dev/null +++ b/api/mixed-integer/modeling/Point.html @@ -0,0 +1,445 @@ + + + + + + + Point + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Point

    +
    +
    +template<class T>
    class Point : public idol::SparseVector<T, double>
    +
    +

    Public Types

    +
    +
    +using iterator = typename map_t::iterator
    +
    + +
    +
    +using const_iterator = typename map_t::const_iterator
    +
    + +
    +
    +

    Public Functions

    +
    +
    +Point() = default
    +
    + +
    +
    +inline explicit Point(const SparseVector<T, double> &t_vector)
    +
    + +
    +
    +inline explicit Point(SparseVector<T, double> &&t_vector)
    +
    + +
    +
    +inline SolutionStatus status() const
    +
    + +
    +
    +inline void set_status(SolutionStatus t_status)
    +
    + +
    +
    +inline SolutionReason reason() const
    +
    + +
    +
    +inline void set_reason(SolutionReason t_reason)
    +
    + +
    +
    +double objective_value() const
    +
    + +
    +
    +inline void set_objective_value(double t_objective_value)
    +
    + +
    +
    +inline bool has_objective_value() const
    +
    + +
    +
    +inline void reset_objective_value()
    +
    + +
    +
    +inline Point &operator*=(double t_factor) override
    +
    + +
    +
    +inline Point &operator+=(const Point &t_other)
    +
    + +
    +
    +inline Point &operator+=(Point &&t_other)
    +
    + +
    +
    +inline Point &operator-=(const Point &t_other)
    +
    + +
    +
    +inline Point &operator-=(Point &&t_other)
    +
    + +
    +
    +virtual SparseVector &operator+=(const SparseVector &t_vector)
    +
    + +
    +
    +virtual SparseVector &operator-=(const SparseVector &t_vector)
    +
    + +
    +
    +virtual SparseVector &operator*=(std::conditional_t<std::is_arithmetic_v<double>, double, double> t_scalar)
    +
    + +
    +
    +virtual SparseVector &operator/=(std::conditional_t<std::is_arithmetic_v<double>, double, double> t_scalar)
    +
    + +
    +
    +SparseVector operator-() const
    +
    + +
    +
    +inline unsigned int size() const
    +
    + +
    +
    +inline bool empty() const
    +
    + +
    +
    +inline bool has_index(const T &t_index) const
    +
    + +
    +
    +const double &get(const T &t_index1) const
    +
    + +
    +
    +void set(const T &t_index, const double &t_value)
    +
    + +
    +
    +virtual bool is_zero(double t_tolerance) const
    +
    + +
    +
    +inline void remove(const T &t_index)
    +
    + +
    +
    +inline void clear()
    +
    + +
    +
    +inline void reserve(unsigned int t_capacity)
    +
    + +
    +
    +inline iterator begin()
    +
    + +
    +
    +inline const_iterator begin() const
    +
    + +
    +
    +inline iterator end()
    +
    + +
    +
    +inline const_iterator end() const
    +
    + +
    +
    +inline const_iterator cbegin() const
    +
    + +
    +
    +inline const_iterator cend() const
    +
    + +
    +
    +SparseVector &merge_without_conflict(const SparseVector &t_vec)
    +
    + +
    +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/QCtr.html b/api/mixed-integer/modeling/QCtr.html new file mode 100644 index 000000000..be6147b06 --- /dev/null +++ b/api/mixed-integer/modeling/QCtr.html @@ -0,0 +1,360 @@ + + + + + + + QCtr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    QCtr

    +
    +

    Doxygen

    +
    +
    +class QCtr : public idol::Object<QCtrVersion, QCtr>
    +
    +

    Public Functions

    +
    +
    +QCtr(Env &t_env, TempQCtr &&t_temp_ctr, std::string t_name = "")
    +
    + +
    +
    +QCtr(Env &t_env, const TempQCtr &t_temp_ctr, std::string t_name = "")
    +
    + +
    +
    +QCtr(Env &t_env, CtrType t_type, std::string t_name = "")
    +
    + +
    +
    +unsigned int index(const Model &t_model) const
    +
    + +
    +
    +inline const std::string &name() const
    +

    Returns the name of the optimization object.

    +
    +
    Returns:
    +

    The name of the optimization object.

    +
    +
    +
    + +
    +
    +inline unsigned int id() const
    +

    Returns the id of the optimization object.

    +
    +
    Returns:
    +

    The id of the optimization object.

    +
    +
    +
    + +
    +
    +inline bool is_in(const Model &t_model) const
    +

    Returns true if the optimization object is part of the model t_model, false otherwise.

    +
    +
    Parameters:
    +

    t_model – The model.

    +
    +
    Returns:
    +

    True if the optimization object is part of the model t_model, false otherwise.

    +
    +
    +
    + +
    +
    +inline const ValueT &get(const Annotation<ValueT> &t_annotation) const
    +

    Returns the value of the given annotation t_annotation associated to the object.

    +

    If no value is found, the default value of the annotation is returned. If no default value was set, an exception is thrown.

    +
    +
    Template Parameters:
    +

    ValueT – The value type of the annotation.

    +
    +
    Parameters:
    +

    t_annotation – The annotation.

    +
    +
    Returns:
    +

    The value of the annotation.

    +
    +
    +
    + +
    +
    +inline void set(const Annotation<ValueT> &t_annotation, ArgsT&&... t_args) const
    +

    Sets the value of the given annotation t_annotation associated to the object.

    +
    +
    Template Parameters:
    +
      +

    • ValueT – The value type of the annotation.

      • +

    • ArgsT – The parameter pack types for constructing the value of the annotation.

      • +
    +
    +
    Parameters:
    +
      +

    • t_annotation – The annotation.

      • +

    • t_args – The parameter pack arguments used to construct “in place” the value of the annotation.

      • +
    +
    +
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +template<unsigned int N = 1, unsigned int I = 0>
    static inline Vector<Ctr, N - I> make_vector(Env &t_env, const Dim<N> &t_dim, CtrType t_type, const std::string &t_name = "")
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class impl::Env
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/QuadExpr.html b/api/mixed-integer/modeling/QuadExpr.html new file mode 100644 index 000000000..1a8daecdc --- /dev/null +++ b/api/mixed-integer/modeling/QuadExpr.html @@ -0,0 +1,511 @@ + + + + + + + QuadExpr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    QuadExpr

    +
    +

    Doxygen

    +
    +
    +template<class KeyT = idol::Var, class ValueT = double>
    class QuadExpr : public idol::LinExpr<CommutativePair<idol::Var>, double>
    +
    +

    Public Types

    +
    +
    +using iterator = typename map_t::iterator
    +
    + +
    +
    +using const_iterator = typename map_t::const_iterator
    +
    + +
    +
    +

    Public Functions

    +
    +
    +QuadExpr() = default
    +
    + +
    +
    +inline QuadExpr(ValueT t_constant)
    +
    + +
    +
    +inline QuadExpr(const KeyT &t_key)
    +
    + +
    +
    +inline QuadExpr(LinExpr<KeyT, ValueT> t_expr)
    +
    + +
    +
    +inline QuadExpr(AffExpr<KeyT, ValueT> t_expr)
    +
    + +
    +
    +inline QuadExpr(const KeyT &t_key1, const KeyT &t_key2)
    +
    + +
    +
    +inline QuadExpr(const ValueT &t_factor, const KeyT &t_key1, const KeyT &t_key2)
    +
    + +
    +
    +inline QuadExpr(ValueT &&t_factor, const KeyT &t_key1, const KeyT &t_key2)
    +
    + +
    +
    +inline QuadExpr(const ValueT &t_factor, const KeyT &t_key)
    +
    + +
    +
    +inline QuadExpr(ValueT &&t_factor, const KeyT &t_key)
    +
    + +
    +
    +QuadExpr(const QuadExpr &t_src) = default
    +
    + +
    +
    +QuadExpr(QuadExpr&&) noexcept = default
    +
    + +
    +
    +QuadExpr &operator=(const QuadExpr &t_rhs) = default
    +
    + +
    +
    +QuadExpr &operator=(QuadExpr&&) noexcept = default
    +
    + +
    +
    +QuadExpr &operator+=(const QuadExpr &t_rhs)
    +
    + +
    +
    +QuadExpr &operator-=(const QuadExpr &t_rhs)
    +
    + +
    +
    +QuadExpr &operator*=(double t_rhs)
    +
    + +
    +
    +QuadExpr &operator/=(double t_rhs)
    +
    + +
    +
    +QuadExpr operator-() const
    +
    + +
    +
    +inline AffExpr<KeyT, ValueT> &affine()
    +
    + +
    +
    +inline const AffExpr<KeyT, ValueT> &affine() const
    +
    + +
    +
    +inline bool has_quadratic() const
    +
    + +
    +
    +inline bool empty_all() const
    +
    + +
    +
    +virtual bool is_zero(double t_tolerance) const override
    +
    + +
    +
    +void clear_all()
    +
    + +
    +
    +LinExpr &operator+=(const LinExpr<KeyT, ValueT> &t_rhs)
    +
    + +
    +
    +LinExpr &operator+=(const KeyT &t_rhs)
    +
    + +
    +
    +virtual SparseVector &operator+=(const SparseVector &t_vector)
    +
    + +
    +
    +LinExpr &operator-=(const LinExpr<KeyT, ValueT> &t_rhs)
    +
    + +
    +
    +LinExpr &operator-=(const KeyT &t_rhs)
    +
    + +
    +
    +virtual SparseVector &operator-=(const SparseVector &t_vector)
    +
    + +
    +
    +virtual SparseVector &operator*=(std::conditional_t<std::is_arithmetic_v<ValueT>, ValueT, double> t_scalar)
    +
    + +
    +
    +virtual SparseVector &operator/=(std::conditional_t<std::is_arithmetic_v<ValueT>, ValueT, double> t_scalar)
    +
    + +
    +
    +inline unsigned int size() const
    +
    + +
    +
    +inline bool empty() const
    +
    + +
    +
    +inline bool has_index(const IndexT &t_index) const
    +
    + +
    +
    +const ValueT &get(const IndexT &t_index1) const
    +
    + +
    +
    +void set(const IndexT &t_index, const ValueT &t_value)
    +
    + +
    +
    +inline void remove(const IndexT &t_index)
    +
    + +
    +
    +inline void clear()
    +
    + +
    +
    +inline void reserve(unsigned int t_capacity)
    +
    + +
    +
    +inline iterator begin()
    +
    + +
    +
    +inline const_iterator begin() const
    +
    + +
    +
    +inline iterator end()
    +
    + +
    +
    +inline const_iterator end() const
    +
    + +
    +
    +inline const_iterator cbegin() const
    +
    + +
    +
    +inline const_iterator cend() const
    +
    + +
    +
    +SparseVector &merge_without_conflict(const SparseVector &t_vec)
    +
    + +
    +
    +

    Public Static Attributes

    +
    +
    +static LinExpr<KeyT, ValueT> Zero = {}
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/TempCtr.html b/api/mixed-integer/modeling/TempCtr.html new file mode 100644 index 000000000..8c2ddd720 --- /dev/null +++ b/api/mixed-integer/modeling/TempCtr.html @@ -0,0 +1,380 @@ + + + + + + + TempCtr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    TempCtr

    +
    +

    Doxygen

    +
    +
    +class TempCtr
    +

    Temporary constraint class.

    +

    This class represents a constraint which has not been built yet by a Model. It contains all the arguments needed to create a real constraint as instantiated by the Ctr class. It is made of a row (see Row) and a type (see CtrType.rst.rst).

    +

    Typically, one creates a TempCtr by using the overloaded operators <=, >= and == between variable expressions (i.e., AffExpr) and constant terms (i.e., Constant).

    +

    Example 1: 

    ...
+model.add_ctr(x + y <= 1.);
+
    +
    + Example 2 (equivalent to Example 1): 
    ...
+model.add_ctr(TempCtr(Row(x + y, 1.), LessOrEqual));
+
    +
    +

    +
    +

    Public Functions

    +
    +
    +TempCtr() = default
    +

    Default constructor.

    +

    Creates an empty temporary constraint. The default type is LessOrEqual.

    +
    + +
    +
    +inline TempCtr(LinExpr<Var> &&t_lhs, CtrType t_type, double t_rhs)
    +

    Constructor.

    +

    Creates a new temporary constraint.

    +
    +
    Parameters:
    +
      +

    • t_row – The desired row.

      • +

    • t_type – The desired constraint type.

      • +
    +
    +
    +
    + +
    +
    +TempCtr(const TempCtr &t_src) = default
    +

    Copy constructor.

    +
    +
    Parameters:
    +

    t_src – The object to copy.

    +
    +
    +
    + +
    +
    +TempCtr(TempCtr &&t_src) noexcept = default
    +

    Move constructor.

    +
    +
    Parameters:
    +

    t_src – The object to move.

    +
    +
    +
    + +
    +
    +TempCtr &operator=(const TempCtr &t_src) = default
    +

    Copy-assignment operator.

    +
    +
    Parameters:
    +

    t_src – The object to copy.

    +
    +
    +
    + +
    +
    +TempCtr &operator=(TempCtr &&t_src) noexcept = default
    +

    Move-assignment operator.

    +
    +
    Parameters:
    +

    t_src – The object to move.

    +
    +
    +
    + +
    +
    +inline LinExpr<Var> &lhs()
    +
    + +
    +
    +inline const LinExpr<Var> &lhs() const
    +
    + +
    +
    +inline void set_lhs(LinExpr<Var> &&t_lhs)
    +
    + +
    +
    +inline CtrType type() const
    +

    Returns the temporary constraint type.

    +
    +
    Returns:
    +

    The temporary constraint type.

    +
    +
    +
    + +
    +
    +inline double rhs() const
    +
    + +
    +
    +inline double &rhs()
    +
    + +
    +
    +inline void set_rhs(double t_rhs)
    +
    + +
    +
    +inline void set_type(CtrType t_type)
    +

    Sets the type of the temporary constraint.

    +
    +
    Parameters:
    +

    t_type – the desired type.

    +
    +
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/TempQCtr.html b/api/mixed-integer/modeling/TempQCtr.html new file mode 100644 index 000000000..f4b688122 --- /dev/null +++ b/api/mixed-integer/modeling/TempQCtr.html @@ -0,0 +1,305 @@ + + + + + + + TempQCtr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    TempQCtr

    +
    +

    Doxygen

    +
    +
    +class TempQCtr
    +
    +

    Public Functions

    +
    +
    +TempQCtr() = default
    +
    + +
    +
    +inline TempQCtr(QuadExpr<Var> &&t_expr, CtrType t_type)
    +
    + +
    +
    +TempQCtr(const TempQCtr &t_src) = default
    +
    + +
    +
    +TempQCtr(TempQCtr&&) noexcept = default
    +
    + +
    +
    +TempQCtr &operator=(const TempQCtr &t_rhs) = default
    +
    + +
    +
    +TempQCtr &operator=(TempQCtr&&) noexcept = default
    +
    + +
    +
    +inline QuadExpr<Var> &expr()
    +
    + +
    +
    +inline const QuadExpr<Var> &expr() const
    +
    + +
    +
    +inline CtrType type() const
    +
    + +
    +
    +inline void set_expr(QuadExpr<Var> &&t_expr)
    +
    + +
    +
    +inline void set_type(CtrType t_type)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/TempVar.html b/api/mixed-integer/modeling/TempVar.html new file mode 100644 index 000000000..92080f32d --- /dev/null +++ b/api/mixed-integer/modeling/TempVar.html @@ -0,0 +1,424 @@ + + + + + + + TempVar + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    TempVar

    +
    +

    Doxygen

    +
    +
    +class TempVar
    +

    Temporary variable class.

    +

    This class represents a variable which has not been built yet by a Model. It contains all the arguments needed to create a real variable as instantiated by the Var class. It is made of a lower and an upper bound, a type (see VarType), and a column (see Column).

    +

    Example 1: 

    model.add_var(0., 1., Binary, 2.);
+// is the same as
+model.add_var(TempVar(0., 1., Binary, 2.));
+
    +
    +

    +
    +

    Public Functions

    +
    +
    +TempVar() = default
    +

    Default constructor.

    +

    Creates a new temporary variable. The default lower and upper bounds are 0 and Inf and the type is Continuous.

    +
    + +
    +
    +inline TempVar(double t_lb, double t_ub, VarType t_type, double t_obj, LinExpr<Ctr> &&t_column)
    +

    Constructor.

    +

    Creates a new temporary variable.

    +
    +
    Parameters:
    +
      +

    • t_lb – The desired lower bound.

      • +

    • t_ub – The desired upper bound.

      • +

    • t_type – The desired variable type.

      • +

    • t_column – The desired column.

      • +
    +
    +
    +
    + +
    +
    +TempVar(TempVar &&t_src) = default
    +

    Copy constructor.

    +
    +
    Parameters:
    +

    t_src – The object to copy.

    +
    +
    +
    + +
    +
    +inline TempVar(const TempVar &t_src)
    +

    Move constructor.

    +
    +
    Parameters:
    +

    t_src – The object to move.

    +
    +
    +
    + +
    +
    +TempVar &operator=(TempVar &&t_src) = default
    +

    Copy-assignment operator.

    +
    +
    Parameters:
    +

    t_src – The object to copy.

    +
    +
    +
    + +
    +
    +TempVar &operator=(const TempVar &t_src) = default
    +

    Move-assignment operator.

    +
    +
    Parameters:
    +

    t_src – The object to move.

    +
    +
    +
    + +
    +
    +inline const LinExpr<Ctr> &column() const
    +

    Returns the column of the temporary variable (see Column).

    +
    +
    Returns:
    +

    The column of the temporary variable.

    +
    +
    +
    + +
    +
    +inline LinExpr<Ctr> &column()
    +

    Returns the column of the temporary variable (see Column).

    +
    +
    Returns:
    +

    The column of the temporary variable.

    +
    +
    +
    + +
    +
    +inline double lb() const
    +

    Returns the lower bound of the temporary variable.

    +
    +
    Returns:
    +

    The lower bound of the temporary variable.

    +
    +
    +
    + +
    +
    +inline void set_lb(double t_lb)
    +

    Sets the lower bound of the temporary variable.

    +
    +
    Parameters:
    +

    t_lb – The desired lower bound of the temporary variable.

    +
    +
    +
    + +
    +
    +inline double ub() const
    +

    Returns the upper bound of the temporary variable.

    +
    +
    Returns:
    +

    The upper bound of the temporary variable.

    +
    +
    +
    + +
    +
    +inline void set_ub(double t_ub)
    +

    Sets the upper bound of the temporary variable.

    +
    +
    Parameters:
    +

    t_ub – The desired upper bound of the temporary variable.

    +
    +
    +
    + +
    +
    +inline VarType type() const
    +

    Returns the type of the temporary variable.

    +
    +
    Returns:
    +

    The type of the temporary variable.

    +
    +
    +
    + +
    +
    +inline void set_type(VarType t_type)
    +

    Sets the type of the temporary variable.

    +
    +
    Parameters:
    +

    t_type – The desired type of the temporary variable.

    +
    +
    +
    + +
    +
    +inline double obj() const
    +
    + +
    +
    +inline void set_obj(double t_obj)
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/modeling/Var.html b/api/mixed-integer/modeling/Var.html new file mode 100644 index 000000000..73ec7b288 --- /dev/null +++ b/api/mixed-integer/modeling/Var.html @@ -0,0 +1,455 @@ + + + + + + + Var + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Var

    +
    +

    Doxygen

    +
    +
    +class Var : public idol::Object<VarVersion, Var>
    +
    +

    Public Functions

    +
    +
    +Var(Env &t_env, double t_lb, double t_ub, VarType t_type, double t_obj = 0., std::string t_name = "")
    +

    Constructor.

    +

    Creates a new variable in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_lb – The lower bound (possibly -Inf) for the default version of the variable.

      • +

    • t_ub – The upper bound (possibly +Inf) for the default version of the variable.

      • +

    • t_type – The type for the default version of the variable.

      • +

    • t_name – The given name of the variable.

      • +
    +
    +
    +
    + +
    +
    +Var(Env &t_env, double t_lb, double t_ub, VarType t_type, double t_obj, LinExpr<Ctr, double> &&t_column, std::string t_name = "")
    +

    Constructor.

    +

    Creates a new variable in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_lb – The lower bound (possibly -Inf) for the default version of the variable.

      • +

    • t_ub – The upper bound (possibly +Inf) for the default version of the variable.

      • +

    • t_type – The type for the default version of the variable.

      • +

    • t_column – The column for the default version of the variable.

      • +

    • t_name – The given name of the variable.

      • +
    +
    +
    +
    + +
    +
    +Var(Env &t_env, double t_lb, double t_ub, VarType t_type, double t_obj, const LinExpr<Ctr, double> &t_column, std::string t_name = "")
    +

    Constructor.

    +

    Creates a new variable in the optimization environment.

    +

    If no name is given, a unique name in the environment is given.

    +
    +
    Parameters:
    +
      +

    • t_env – The optimization environment.

      • +

    • t_lb – The lower bound (possibly -Inf) for the default version of the variable.

      • +

    • t_ub – The upper bound (possibly +Inf) for the default version of the variable.

      • +

    • t_type – The type for the default version of the variable.

      • +

    • t_column – The column for the default version of the variable.

      • +

    • t_name – The given name of the variable.

      • +
    +
    +
    +
    + +
    +
    +Var(const Var&) = default
    +
    + +
    +
    +Var(Var&&) = default
    +
    + +
    +
    +Var &operator=(const Var&) = default
    +
    + +
    +
    +Var &operator=(Var&&) = default
    +
    + +
    +
    +unsigned int index(const Model &t_model) const
    +
    + +
    +
    +inline const std::string &name() const
    +

    Returns the name of the optimization object.

    +
    +
    Returns:
    +

    The name of the optimization object.

    +
    +
    +
    + +
    +
    +inline unsigned int id() const
    +

    Returns the id of the optimization object.

    +
    +
    Returns:
    +

    The id of the optimization object.

    +
    +
    +
    + +
    +
    +inline bool is_in(const Model &t_model) const
    +

    Returns true if the optimization object is part of the model t_model, false otherwise.

    +
    +
    Parameters:
    +

    t_model – The model.

    +
    +
    Returns:
    +

    True if the optimization object is part of the model t_model, false otherwise.

    +
    +
    +
    + +
    +
    +inline const ValueT &get(const Annotation<ValueT> &t_annotation) const
    +

    Returns the value of the given annotation t_annotation associated to the object.

    +

    If no value is found, the default value of the annotation is returned. If no default value was set, an exception is thrown.

    +
    +
    Template Parameters:
    +

    ValueT – The value type of the annotation.

    +
    +
    Parameters:
    +

    t_annotation – The annotation.

    +
    +
    Returns:
    +

    The value of the annotation.

    +
    +
    +
    + +
    +
    +inline void set(const Annotation<ValueT> &t_annotation, ArgsT&&... t_args) const
    +

    Sets the value of the given annotation t_annotation associated to the object.

    +
    +
    Template Parameters:
    +
      +

    • ValueT – The value type of the annotation.

      • +

    • ArgsT – The parameter pack types for constructing the value of the annotation.

      • +
    +
    +
    Parameters:
    +
      +

    • t_annotation – The annotation.

      • +

    • t_args – The parameter pack arguments used to construct “in place” the value of the annotation.

      • +
    +
    +
    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +template<unsigned int N = 1, unsigned int I = 0>
    static inline Vector<Var, N - I> make_vector(Env &t_env, const Dim<N> &t_dim, double t_lb, double t_ub, VarType t_type, double t_obj, const std::string &t_name = "")
    +

    Creates a (nested) vector of variables.

    +

    Example:

    +

    Env env;
+
+auto x = Var::make_vector(env, Dim<2>(m, n), 0., 1., Continuous, "x");
+
+std::cout << x[1][4].name() << std::endl; // "x_1_4"
+
    +
    +

    +
    +
    Template Parameters:
    +
      +

    • N – The dimension of the (nested) vector.

      • +

    • I – Used for recursion.

      • +
    +
    +
    Parameters:
    +
      +

    • t_env – The environment to store the variables.

      • +

    • t_dim – The number of elements in each dimension.

      • +

    • t_lb – The lower bound.

      • +

    • t_ub – The upper bound.

      • +

    • t_type – The type of the variables.

      • +

    • t_name – The given name of the variables.

      • +
    +
    +
    Returns:
    +

    A (nested) vector of variables.

    +
    +
    +
    + +
    +
    +

    Friends

    +
    +
    +friend class impl::Env
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/padm/Optimizers_PADM.html b/api/mixed-integer/padm/Optimizers_PADM.html new file mode 100644 index 000000000..6839ca1d0 --- /dev/null +++ b/api/mixed-integer/padm/Optimizers_PADM.html @@ -0,0 +1,528 @@ + + + + + + + Optimizers::PADM + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Optimizers::PADM

    +
    +

    Doxygen

    +
    +
    +class PADM : public idol::Algorithm
    +
    +

    Public Functions

    +
    +
    +PADM(const Model &t_model, ADM::Formulation t_formulation, std::vector<idol::ADM::SubProblem> &&t_sub_problem_specs, PenaltyUpdate *t_penalty_update, SolutionStatus t_feasible_solution_status, Plots::Manager *t_plot_manager)
    +
    + +
    +
    +inline virtual std::string name() const override
    +
    + +
    +
    +virtual double get_var_primal(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_reduced_cost(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_var_ray(const Var &t_var) const override
    +
    + +
    +
    +virtual double get_ctr_dual(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual double get_ctr_farkas(const Ctr &t_ctr) const override
    +
    + +
    +
    +virtual unsigned int get_n_solutions() const override
    +
    + +
    +
    +virtual unsigned int get_solution_index() const override
    +
    + +
    +
    +unsigned int get_outer_loop_iteration_count() const
    +
    + +
    +
    +unsigned int get_inner_loop_iteration_count() const
    +
    + +
    +
    +ADM::SubProblem &sub_problem_spec(unsigned int t_sub_problem_id)
    +
    + +
    +
    +virtual SolutionStatus get_status() const override
    +
    + +
    +
    +virtual SolutionReason get_reason() const override
    +
    + +
    +
    +virtual double get_best_obj() const override
    +
    + +
    +
    +virtual double get_best_bound() const override
    +
    + +
    +
    +virtual double get_relative_gap() const override
    +
    + +
    +
    +virtual double get_absolute_gap() const override
    +
    + +
    +
    +inline virtual const ::idol::Model &parent() const
    +
    + +
    +
    +inline bool get_param_logs() const
    +
    + +
    +
    +inline virtual void set_param_logs(bool t_value)
    +
    + +
    +
    +inline double get_param_time_limit() const
    +
    + +
    +
    +inline virtual void set_param_time_limit(double t_time_limit)
    +
    + +
    +
    +inline unsigned int get_param_thread_limit() const
    +
    + +
    +
    +inline virtual void set_param_threads(unsigned int t_threads)
    +
    + +
    +
    +double get_param_best_obj_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_obj_stop(double t_best_obj_stop)
    +
    + +
    +
    +double get_param_best_bound_stop() const
    +
    + +
    +
    +inline virtual void set_param_best_bound_stop(double t_best_bound_stop)
    +
    + +
    +
    +inline double get_tol_mip_relative_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_relative_gap(double t_tol_mip_relative_gap)
    +
    + +
    +
    +inline double get_tol_mip_absolute_gap() const
    +
    + +
    +
    +inline virtual void set_tol_mip_absolute_gap(double t_mip_tol_absolute_gap)
    +
    + +
    +
    +inline double get_tol_feasibility() const
    +
    + +
    +
    +inline virtual void set_tol_feasibility(double t_tol_feasibility)
    +
    + +
    +
    +inline double get_tol_optimality() const
    +
    + +
    +
    +inline virtual void set_tol_optimality(double t_tol_optimality)
    +
    + +
    +
    +inline double get_tol_integer() const
    +
    + +
    +
    +inline virtual void set_tol_integer(double t_tol_integer)
    +
    + +
    +
    +inline unsigned int get_param_iteration_limit() const
    +
    + +
    +
    +inline void set_param_iteration_limit(unsigned int t_iteration_limit)
    +
    + +
    +
    +inline bool get_param_presolve() const
    +
    + +
    +
    +inline virtual void set_param_presolve(bool t_value)
    +
    + +
    +
    +inline bool get_param_infeasible_or_unbounded_info() const
    +
    + +
    +
    +inline virtual void set_param_infeasible_or_unbounded_info(bool t_value)
    +
    + +
    +
    +inline const Timer &time() const
    +
    + +
    +
    +double get_remaining_time() const
    +
    + +
    +
    +inline bool is_terminated() const
    +
    + +
    +
    +virtual void terminate()
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    +
    +class IterationPlot
    +
    +

    Public Functions

    +
    +
    +explicit IterationPlot(Plots::Manager &t_manager)
    +
    + +
    +
    +void update(unsigned int t_outer_loop_iteration, unsigned int t_inner_loop_iteration, const std::vector<double> &t_objective_values, const std::vector<double> &t_infeasibilities)
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/mixed-integer/padm/PADM.html b/api/mixed-integer/padm/PADM.html new file mode 100644 index 000000000..9f3f2c57b --- /dev/null +++ b/api/mixed-integer/padm/PADM.html @@ -0,0 +1,600 @@ + + + + + + + PADM + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    PADM

    +
    +

    Doxygen

    +
    +
    +class PADM : public idol::OptimizerFactoryWithDefaultParameters<PADM>
    +
    +

    Public Functions

    +
    +
    +explicit PADM(Annotation<unsigned int> t_decomposition)
    +
    + +
    +
    +PADM(Annotation<unsigned int> t_decomposition, Annotation<double> t_penalized_constraints)
    +
    + +
    +
    +PADM(const PADM &t_src)
    +
    + +
    +
    +PADM(PADM&&) = default
    +
    + +
    +
    +PADM &operator=(const PADM&) = delete
    +
    + +
    +
    +PADM &operator=(PADM&&) = default
    +
    + +
    +
    +PADM &with_default_sub_problem_spec(ADM::SubProblem t_sub_problem)
    +
    + +
    +
    +PADM &with_sub_problem_spec(unsigned int t_id, ADM::SubProblem t_sub_problem)
    +
    + +
    +
    +PADM &with_rescaling_threshold(double t_threshold)
    +
    + +
    +
    +PADM &with_penalty_update(const PenaltyUpdate &t_penalty_update)
    +
    + +
    +
    +PADM &with_feasible_solution_status(SolutionStatus t_status)
    +
    + +
    +
    +PADM &with_iteration_plot(Plots::Manager &t_manager)
    +
    + +
    +
    +virtual Optimizer *operator()(const Model &t_model) const override
    +

    Creates and returns a new optimizer to solve the model given as parameter.

    +
    +
    Parameters:
    +

    t_model – The model which the optimizer will solve

    +
    +
    Returns:
    +

    A new optimizer for the model

    +
    +
    +
    + +
    +
    +virtual OptimizerFactory *clone() const override
    +

    Creates and return a copy of the optimizer factory. This is used for polymorphism.

    +
    +
    Returns:
    +

    A copied object of the current object (i.e., *this)

    +
    +
    +
    + +
    +
    +PADM &with_logs(bool t_value)
    +

    Sets the log_master level and color for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_logs(true);
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_log_level – the log_master level

      • +

    • t_log_color – the output color

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_time_limit(double t_time_limit)
    +

    Sets the time limit for the optimizer

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_time_limit(3600);
+
    +
    +

    +
    +
    Parameters:
    +

    t_time_limit – the time limit (in seconds)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_thread_limit(unsigned int t_max_n_threads)
    +

    Sets the maximum number of threads which the optimizer can use

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_thread_limit(5);
+
    +
    +

    +
    +
    Parameters:
    +

    t_max_n_threads – the number of threads which can be used

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_iteration_limit(unsigned int t_iteration_count_limit)
    +

    Sets the maximum number of iterations which the optimizer go through

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_iteration_limit(200);
+
    +
    +

    +
    +
    Parameters:
    +

    t_iteration_count_limit – the maximum number of iterations

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_best_bound_stop(double t_best_bound_stop)
    +

    Sets a threshold on the best bound for stopping the optimizer. When the optimizer have found a best bound which is greater than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_obj = 0.;
+auto algorithm = GLPK()
+                     .with_best_bound_stop(my_known_best_obj);
+
    +
    +

    +
    +
    Parameters:
    +

    t_best_bound_stop – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_best_obj_stop(double t_user_best_obj)
    +

    Sets a threshold on the best objective value for stopping the optimizer. When the optimizer have found a best objective value which is less than this threshold, the optimizer stops.

    +

    Example: 

    const double my_known_best_bound = 0;
+auto algorithm = GLPK()
+                     .with_best_obj_stop(my_known_best_bound);
+
    +
    +

    +
    +
    Parameters:
    +

    t_user_best_obj – the threshold

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_relative_gap_tolerance(double t_relative_gap_tolerance)
    +

    Sets the relative gap tolerance for the optimizer. When the optimizer proves that the relative optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_relative_gap_tolerance(.05); // sets a gap tolerance of 5%
+
    +
    +

    +
    +
    Parameters:
    +

    t_relative_gap_tolerance – the relative gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_absolute_gap_tolerance(double t_absolute_gap_tolerance)
    +

    Sets the absolute gap tolerance for the optimizer. When the optimizer proves that the absolute optimality gap is less than this threshold, the optimizer stops.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_absolute_gap_tolerance(1e-4);
+
    +
    +

    +
    +
    Parameters:
    +

    t_absolute_gap_tolerance – the absolute gap tolerance

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_presolve(bool t_value)
    +

    Sets the get_param_presolve activation for the optimizer.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_presolve(false); // turns off get_param_presolve phase
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level for the optimizer’s get_param_presolve (0 for disabling, 1 for enabling)

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &with_infeasible_or_unbounded_info(bool t_value)
    +

    Sets the behaviour of the optimizer when a model is shown to be infeasible or unbounded. When set to true, the optimizer is forced to prove feasibility or unboundedness by providing a certificate.

    +

    Example: 

    auto algorithm = GLPK()
+                     .with_infeasible_or_unbounded_info(true);
+
    +
    +

    +
    +
    Parameters:
    +

    t_value – the activation level

    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &conditional(bool t_conditional_value, const std::function<void(PADM&)> &t_if)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve, [](auto& x){ x.with_presolve(true); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, nothing happens.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +PADM &conditional(bool t_conditional_value, const std::function<void(PADM&)> &t_if, const std::function<void(PADM&)> &t_else)
    +

    Executes the lambda function given as second parameter if and only if its first argument is true. This function can be used to build different optimizer factories depending on some external variable.

    +

    Example: 

    for (const bool use_presolve : {true, false}) {
+     auto algorithm = GLPK()
+                         .conditional(use_presolve,
+                                         [](auto& x){ x.with_presolve(true); },
+                                         [](auto& x){ x.with_presolve(false); })
+      model.use(algorithm);
+      model.optimize();
+}
+
    +
    +

    +
    +
    Parameters:
    +
      +

    • t_conditional_value – if true, the t_if lambda function is executed, if false, the t_else lambda function is.

      • +

    • t_if – lambda function to execute in case t_conditional_value is true

      • +

    • t_else – lambda function to execute in case t_conditional_value is false

      • +
    +
    +
    Returns:
    +

    the optimizer factory itself

    +
    +
    +
    + +
    +
    +template<class T>
    inline T &as()
    +
    + +
    +
    +template<class T>
    inline const T &as() const
    +
    + +
    +
    +template<class T>
    inline bool is() const
    +
    + +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/robust/index.html b/api/robust/index.html new file mode 100644 index 000000000..295843768 --- /dev/null +++ b/api/robust/index.html @@ -0,0 +1,245 @@ + + + + + + + Robust Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Robust Optimization

    +
    +

    Modeling

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/robust/modeling/Description.html b/api/robust/modeling/Description.html new file mode 100644 index 000000000..d82a65eda --- /dev/null +++ b/api/robust/modeling/Description.html @@ -0,0 +1,363 @@ + + + + + + + Robust::Description + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Robust::Description

    +
    +

    Doxygen

    +
    +
    +class Description
    +
    +

    Public Functions

    +
    +
    +inline explicit Description(const Model &t_uncertainty_set)
    +
    + +
    +
    +const Annotation<unsigned int> &stage_annotation() const
    +
    + +
    +
    +void set_stage(const Var &t_var, unsigned int t_stage)
    +
    + +
    +
    +unsigned int stage(const Var &t_var) const
    +
    + +
    +
    +unsigned int stage(const Ctr &t_var) const
    +
    + +
    +
    +inline const Model &uncertainty_set() const
    +
    + +
    +
    +inline auto uncertain_mat_coeffs() const
    +
    + +
    +
    +inline auto uncertain_rhs() const
    +
    + +
    +
    +inline auto uncertain_obj() const
    +
    + +
    +
    +const LinExpr<Var> &uncertain_mat_coeff(const Ctr &t_ctr, const Var &t_var) const
    +
    + +
    +
    +const LinExpr<Var, LinExpr<Var>> &uncertain_mat_coeffs(const Ctr &t_ctr) const
    +
    + +
    +
    +const LinExpr<Var> &uncertain_rhs(const Ctr &t_ctr) const
    +
    + +
    +
    +const LinExpr<Var> &uncertain_obj(const Var &t_var) const
    +
    + +
    +
    +inline void set_uncertain_mat_coeff(const Ctr &t_ctr, const Var &t_var, const LinExpr<Var> &t_coeff)
    +
    + +
    +
    +inline void set_uncertain_rhs(const Ctr &t_ctr, const LinExpr<Var> &t_rhs)
    +
    + +
    +
    +inline void set_uncertain_obj(const Var &t_var, const LinExpr<Var> &t_obj)
    +
    + +
    +
    +inline void set_uncertain_obj(LinExpr<Var, LinExpr<Var>> t_obj)
    +
    + +
    +
    +inline void set_uncertain_rhs(LinExpr<Ctr, LinExpr<Var>> t_rhs)
    +
    + +
    +
    +
    +class View
    +
    +

    Public Functions

    +
    +
    +View(const Model &t_deterministic_model, const Description &t_description)
    +
    + +
    +
    +inline const Description &description() const
    +
    + +
    +
    +inline const Model &deterministic_model() const
    +
    + +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/types/index.html b/api/types/index.html new file mode 100644 index 000000000..c4fab616d --- /dev/null +++ b/api/types/index.html @@ -0,0 +1,228 @@ + + + + + + + Type List + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Type List

    +
    +

    Mixed-Integer Programming

    +
    + +
    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/types/universal-callbacks/CallbackEvent.html b/api/types/universal-callbacks/CallbackEvent.html new file mode 100644 index 000000000..6a41033a0 --- /dev/null +++ b/api/types/universal-callbacks/CallbackEvent.html @@ -0,0 +1,248 @@ + + + + + + + Events + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Events

    +
    +
    +enum idol::CallbackEvent
    +

    CallbackEvent is an enumerated type used to indicate events during a branch-and-bound tree execution.

    +

    It is typically used inside of a Callback to influence or modify the behaviour of the algorithm at execution time.

    +

    Values:

    +
    +
    +enumerator NodeLoaded
    +

    Occurs when a node is about to be solved

    +
    + +
    +
    +enumerator IncumbentSolution
    +

    Occurs when an incumbent solution has been found

    +
    + +
    +
    +enumerator InvalidSolution
    +

    Occurs when a solution of the relaxation is not valid (e.g., not integer)

    +
    + +
    +
    +enumerator PrunedSolution
    +
    + +
    + +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/api/types/universal-callbacks/index.html b/api/types/universal-callbacks/index.html new file mode 100644 index 000000000..4580c9a6d --- /dev/null +++ b/api/types/universal-callbacks/index.html @@ -0,0 +1,222 @@ + + + + + + + Universal Callbacks + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Universal Callbacks

    +
    + +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/benchmark/index.html b/benchmark/index.html new file mode 100644 index 000000000..ad1b1d9bd --- /dev/null +++ b/benchmark/index.html @@ -0,0 +1,249 @@ + + + + + + + Benchmark + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Benchmark

    +
    +

    Warning

    +

    This page is under construction.

    +
    +
    +

    Branch-and-Price for the Generalized Assignment Problem

    +../_images/ecdf-gap.png +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/developer_guide/build-the-doc.html b/developer_guide/build-the-doc.html new file mode 100644 index 000000000..fe62fac26 --- /dev/null +++ b/developer_guide/build-the-doc.html @@ -0,0 +1,282 @@ + + + + + + + Build the Documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Build the Documentation

    +

    This page explains how to build the documentation on a local machine.

    +
    +

    Dependencies

    +
    +

    Description

    +

    The documentation is built using doxygen and a bunch of other tools, in particular:

    +
      +

    • doxygen the C++ documentation generator;

      • +

    • Sphinx the python documentation generator;

      • +

    • sphinx-rtd-theme a Sphinx theme used to render the +HTML version of the documentation;

      • +

    • sphinx-sitemap a Sphinx extension +to generate multi-version and multi-language sitemaps.org compliant sitemaps for the HTML version +of a Sphinx documentation;

      • +

    • sphinx-copybutton a Sphinx extension which +automatically adds buttons on code-blocks environments to copy its content;

      • +

    • Breathe the Sphinx plugin for integrating doxygen outputs into Sphinx.

      • +
    +

    For a detailed description on how these tools interact, please refer to this article.

    +
    +
    +

    Installation guide (Ubuntu)

    +
    sudo apt-get install doxygen # installs the last version of doxygen
+
+sudo apt-get install python3-sphinx # installs the last version of Sphinx
+
+sudo apt-get install python3-breathe # installs the last version of Breathe
+
+pip3 install sphinx-sitemap sphinx-rtd-theme sphinx-copybutton # installs theme and extensions
+
    +
    +
    +
    +
    +

    Build instructions

    +

    By default, CMake automatically creates a doc target. All you have to do to build the documentation website +is to build this target. For instance, inside a build directory, the following command can be used.

    +
    cmake .. && make doc
+
    +
    +

    Note that you do not need to use make and use the following generic command.

    +
    cmake --build . --target doc
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/developer_guide/index.html b/developer_guide/index.html new file mode 100644 index 000000000..5dac46e5b --- /dev/null +++ b/developer_guide/index.html @@ -0,0 +1,275 @@ + + + + + + + Developers + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Developers

    +
    +

    Unit Tests and Integration

    +

    idol is tested using Catch2. Currently, the level of testing is not sufficient, but we are working on it.

    +

    Here is a grid plot of the code coverage:

    +https://codecov.io/gh/hlefebvr/idol/graphs/tree.svg?token=BWMH5522QP +

    Each block represents a single file in the project. The size and color of each block is represented by the number of statements and the coverage, respectively. (see codecov)

    +

    For more information on how to run the tests, please refer to the Unit and Integration Tests page.

    +
    +
    +

    Building the Documentation

    +

    The documentation is built using doxygen and a bunch of other tools. For more information, please refer to the Build the Documentation page.

    +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/developer_guide/tests.html b/developer_guide/tests.html new file mode 100644 index 000000000..9d2937218 --- /dev/null +++ b/developer_guide/tests.html @@ -0,0 +1,303 @@ + + + + + + + Unit and Integration Tests + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Unit and Integration Tests

    +

    This page explains how to build the unit and integration tests on a local machine.

    +
    +

    Dependencies

    +

    Tests are managed by the C++ unit testing framework Catch2.

    +

    When CMake is told to create test targets, it will automatically look for an installation of Catch2 on your +machine. If it cannot be found, CMake will attempt to download Catch2 from its GitHub repository.

    +
    +

    Installation guide (Ubuntu)

    +
    git clone https://github.com/catchorg/Catch2.git # Clone Catch2 repository
+
+cd Catch2 # go inside the new directory
+
+cmake -Bbuild -H. -DBUILD_TESTING=OFF # Create install target
+
+sudo cmake --build build/ --target install # Build and install
+
    +
    +
    +
    +
    +

    Build instructions

    +

    By default, CMake will not create test targets nor look for Catch2. To tell CMake to generate them, you +need to set the CMake option BUILD_TESTS to YES.

    +
    +

    Example

    +

    The following will tell CMake to create targets for tests.

    +
    cmake -DBUILD_TESTS=YES ..
+
    +
    +

    For instance, we can now build all the existing tests

    +
    make tests
+
    +
    +

    and run them.

    +
    ./tests/tests
+
    +
    +
    +
    +
    +

    Code coverage options

    +

    Code coverage is done via gcov.

    +

    If you want to active code coverage options, you shall set the CMake option WITH_TEST_COVERAGE to YES. +Note that this only has an effect when BUILD_TESTS is also set to YES.

    +
    +

    Example

    +

    The following command will tell CMake to generate targets for tests with code coverage options.

    +
    cmake -DBUILD_TESTS=YES -DWITH_CODE_COVERAGE=YES ..
+
    +
    +

    Then, you should build and run the tests.

    +
    make tests && ./tests/tests
+
    +
    +

    Once you are there, you may generate a report to a file called coverage.info by using gcov.

    +
    lcov --directory . --capture --output-file coverage.info
+
    +
    +
    +

    Also note that this forces g++ to be used for compiling.

    +
    +

    Tip

    +

    Code coverage reports are also automatically generated at every push action on idol’s GitHub repository and +are available on codecov.

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/bilevel-kkt.html b/examples/bilevel-kkt.html new file mode 100644 index 000000000..64c711a05 --- /dev/null +++ b/examples/bilevel-kkt.html @@ -0,0 +1,342 @@ + + + + + + + Solving an optimistic LP-LP bilevel problem with KKT reformulation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving an optimistic LP-LP bilevel problem with KKT reformulation

    +
    +

    Problem Definition

    +

    This example is taken from [8] and is an LP-LP bilevel problem.

    +

    The problem is formulated as follows:

    +
    +\[\begin{split}\begin{align} + \min_{x, y} \quad & x + 6 y \\ + \text{s.t.} \quad & -x + 5y \le 12.5, \\ + & x \ge 0, \\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & -y \\ + \text{s.t.} \quad & 2 x - y \ge 0, \\ + & -x - y \ge -6, \\ + & -x + 6 y \ge -3, \\ + & x + 3 y \ge 3. + \end{array} +\end{align}\end{split}\]
    +

    In this example, we will reformulate the bilevel problem as a single-level problem using the KKT conditions. +The resulting problem will be solved by Gurobi as an NLP. Note that it is also possible to provide valid big-Ms to +reformulate this problem as an MILP. Check out our tutorials to learn more.

    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 30.08.24.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/bilevel/modeling/Description.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+#include "idol/bilevel/modeling/read_from_file.h"
+#include "idol/mixed-integer/modeling/models/KKT.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+#include "idol/mixed-integer/modeling/models/KKT.h"
+#include "idol/bilevel/optimizers/KKT/KKT.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    /*
+        This example is taken from Kleinert, T. (2021). “Algorithms for Mixed-Integer Bilevel Problems with Convex Followers.” PhD thesis.
+        min x + 6 y
+        s.t.
+
+        -x + 5 y <= 12.5,
+
+        y in argmin { -y :
+            2 x - y >= 0,
+            -x - y >= -6,
+            -x + 6 y >= -3,
+            x + 3 y >= 3.
+        }
+
+        x >= 0.
+
+     */
+
+    Env env;
+
+    // Define High Point Relaxation
+    Model high_point_relaxation(env);
+
+    auto x = high_point_relaxation.add_var(0, Inf, Continuous, 0., "x");
+    auto y = high_point_relaxation.add_var(-Inf, Inf, Continuous, 0., "y");
+
+    high_point_relaxation.set_obj_expr(x + 6 * y);
+    auto follower_c1 = high_point_relaxation.add_ctr(2 * x - y >= 0, "f1");
+    auto follower_c2 = high_point_relaxation.add_ctr(-x - y >= -6, "f2");
+    auto follower_c3 = high_point_relaxation.add_ctr(-x + 6 * y >= -3, "f3");
+    auto follower_c4 = high_point_relaxation.add_ctr(x + 3 * y >= 3, "f4");
+    high_point_relaxation.add_ctr(-x + 5 * y <= 12.5);
+
+    // Prepare bilevel description
+    Bilevel::Description description(env);
+    description.set_lower_level_obj(-y);
+    description.make_lower_level(y);
+    description.make_lower_level(follower_c1);
+    description.make_lower_level(follower_c2);
+    description.make_lower_level(follower_c3);
+    description.make_lower_level(follower_c4);
+    
+    auto single_level = Bilevel::KKT::make_model(high_point_relaxation, description);
+    single_level.use(Gurobi());
+    single_level.optimize();
+
+    /**
+     * Alternatively, you could also do
+     *  high_point_relaxation.use(Bilevel::KKT().with_single_level_optimizer(Gurobi()));
+     *  high_point_relaxation.optimize();
+     * Or even,
+     *  high_point_relaxation.use(Bilevel::KKT() + Gurobi());
+     */
+
+    single_level.write("kkt.lp");
+
+    std::cout << save_primal(single_level) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/bilevel-mibs.html b/examples/bilevel-mibs.html new file mode 100644 index 000000000..cbfa165e4 --- /dev/null +++ b/examples/bilevel-mibs.html @@ -0,0 +1,327 @@ + + + + + + + Solving an optimistic MILP-MILP bilevel problem with coin-or/MibS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving an optimistic MILP-MILP bilevel problem with coin-or/MibS

    +
    +

    Problem Definition

    +

    This example is taken from [10] and is a bilevel problem where the upper level is a mixed-integer linear program (MILP) and the lower level is a mixed-integer linear program (MILP).

    +

    The problem is formulated as follows:

    +
    +\[\begin{split}\begin{align} + \min_{x, y} \quad & -x + -10 y \\ + \text{s.t.} \quad & x \in \mathbb Z_{\ge 0 },\\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & y \\ + \text{s.t.} \quad & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_{\ge 0}. + \end{array} +\end{align}\end{split}\]
    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 07.02.24.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/bilevel/optimizers/wrappers/MibS/MibS.h"
+#include "idol/bilevel/modeling/Description.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    /*
+     This example is taken from "The Mixed Integer Linear Bilevel Programming Problem" (Moore and Bard, 1990).
+
+        min -1 x + -10 y
+        s.t.
+
+        y in argmin { y :
+            -25 x + 20 y <= 30,
+            1 x + 2 y <= 10,
+            2 x + -1 y <= 15,
+            2 x + 10 y >= 15,
+            y >= 0 and integer.
+        }
+        x >= 0 and integer.
+
+     */
+
+    Env env;
+
+    // Define High Point Relaxation
+    Model high_point_relaxation(env);
+
+    auto x = high_point_relaxation.add_var(0, Inf, Integer, -1, "x");
+    auto y = high_point_relaxation.add_var(0, Inf, Integer, -10, "y");
+
+    auto follower_c1 = high_point_relaxation.add_ctr(-25 * x + 20 * y <= 30);
+    auto follower_c2 = high_point_relaxation.add_ctr(x + 2 * y <= 10);
+    auto follower_c3 = high_point_relaxation.add_ctr(2 * x - y <= 15);
+    auto follower_c4 = high_point_relaxation.add_ctr(2 * x + 10 * y >= 15);
+
+    // Prepare bilevel description
+    Bilevel::Description description(env);
+    description.set_lower_level_obj(y);
+    description.make_lower_level(y);
+    description.make_lower_level(follower_c1);
+    description.make_lower_level(follower_c2);
+    description.make_lower_level(follower_c3);
+    description.make_lower_level(follower_c4);
+
+    // Use coin-or/MibS as external solver
+    high_point_relaxation.use(
+                Bilevel::MibS(description)
+                    .with_logs(true)
+    );
+
+    // Optimize and print solution
+    high_point_relaxation.optimize();
+
+    std::cout << save_primal(high_point_relaxation) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/bilevel-pessimistic.html b/examples/bilevel-pessimistic.html new file mode 100644 index 000000000..441d6523c --- /dev/null +++ b/examples/bilevel-pessimistic.html @@ -0,0 +1,357 @@ + + + + + + + Solving a pessimistic bilevel problem using an optimistic reformulation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a pessimistic bilevel problem using an optimistic reformulation

    +
    +

    Problem Definition

    +

    This example is taken from [16] (example 1) and is an LP-LP bilevel problem.

    +
    +\[\begin{split}\begin{align} + \min_{x} \quad & -8 x_1 - 6x_2 + \max_{ y\in S(x) } - 25 y_1 - 30 y_2 + 2 y_3 + 16 y_4 \\ + \text{s.t.} \quad & x_1 + x_2 \le 10, \\ + & x_1, x_2 \ge 0, +\end{align}\end{split}\]
    +

    where \(S(x)\) is defined as

    +
    +\[\begin{split}\begin{align} + S(x) := \underset{y}{\text{arg min}} \ & -10 y_1 - 10 y_2 - 10 y_3 - 10 y_4 \\ + \text{s.t.} \ & y_1 + y_2 + y_3 + y_4 \le 10 - x_1 - x_2, \\ + & -y_1 + y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & y_2 + y_4 \le 4 x_2, \\ + & y_1, y_2, y_3, y_4 \ge 0. +\end{align}\end{split}\]
    +

    In this example, we will reformulate this pessimistic bilevel problem as an optimistic one. Then, we will solve it +using its KKT reformulation. The resulting problem will be solved by Gurobi as an MILP.

    +
    +

    Hint

    +

    Here, the optimistic reformulation reads as follows.

    +
    +\[\begin{split} \begin{align} + \min_{x, \bar y, y} \quad & -8 x_1 - 6x_2 - 25 y_1 - 30 y_2 + 2 y_3 + 16 y_4 \\ + \text{s.t.} \quad & x_1 + x_2 \le 10, \\ + & x_1, x_2 \ge 0, \\ + & \bar y_1 + \bar y_2 + \bar y_3 + \bar y_4 \le 10 - x_1 - x_2, \\ + & -\bar y_1 + \bar y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & \bar y_2 + \bar y_4 \le 4 x_2, \\ + & \bar y_1, \bar y_2, \bar y_3, \bar y_4 \ge 0, \\ + & y \in \tilde S(x, \bar y), +\end{align}\end{split}\]
    +

    in which \(\tilde S(x)\) is defined as

    +
    +\[\begin{split}\begin{align} + S(x) := \underset{y}{\text{arg min}} \quad & 25 y_1 + 30 y_2 - 2 y_3 - 16 y_4 \\ + \text{s.t.} \quad & y_1 + y_2 + y_3 + y_4 \le 10 - x_1 - x_2, \\ + & -y_1 + y_4 \le 0.8 x_1 + 0.8 x_2, \\ + & y_2 + y_4 \le 4 x_2, \\ + & -10 y_1 - 10 y_2 - 10 y_3 - 10 y_4 \le -10 \bar y_1 - 10 \bar y_2 - 10 \bar y_3 - 10 \bar y_4, \\ + & y_1, y_2, y_3, y_4 \ge 0. +\end{align}\end{split}\]
    +
    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 17.12.24.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/bilevel/modeling/Description.h"
+#include "idol/bilevel/optimizers/PessimisticAsOptimistic/PessimisticAsOptimistic.h"
+#include "idol/bilevel/optimizers/KKT/KKT.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    /*
+     This example is taken from "A Practical Scheme to Compute Pessimistic Bilevel Optimization Problem" (Bo Zeng, 2025).
+     See https://optimization-online.org/wp-content/uploads/2015/09/5090.pdf
+
+        min -8 x_1 - 6x_2 - 25 y_1 - 30 y_2 + 2 y_3 + 16 y_4
+        s.t.
+
+        x_1 + x_2 <= 10,
+        x_1, x_2 >= 0,
+
+        y in argmin { -10 y_1 - 10 y_2 - 10 y_3 - 10 y_4 :
+            y_1 + y_2 + y_3 + y_4 <= 10 - x_1 - x_2,
+            -y_1 + y_4 <= 0.8 x_1 + 0.8 x_2,
+            y_2 + y_4 <= 4 x_2,
+            y_1, y_2, y_3, y_4 >= 0
+        }
+
+     */
+
+    Env env;
+
+    // Define High Point Relaxation
+    Model high_point_relaxation(env);
+
+    auto x = high_point_relaxation.add_vars(Dim<1>(3), 0, Inf, Continuous, 0, "x");
+    auto y = high_point_relaxation.add_vars(Dim<1>(4), 0, Inf, Continuous, 0, "y");
+
+    auto leader_c = high_point_relaxation.add_ctr(x[0] + x[1] <= 10, "leader_c");
+    auto follower_c1 = high_point_relaxation.add_ctr(y[0] + y[1] + y[2] + y[3] <= 10 - x[0] - x[1], "follower_c1");
+    auto follower_c2 = high_point_relaxation.add_ctr(-y[0] + y[3] <= 0.8 * x[0] + 0.8 * x[1], "follower_c2");
+    auto follower_c3 = high_point_relaxation.add_ctr(y[1] + y[3] <= 4 * x[1], "follower_c3");
+
+    high_point_relaxation.set_obj_expr(-8 * x[0] - 6 * x[1] - 25 * y[0] - 30 * y[1] + 2 * y[2] + 16 * y[3]);
+
+    // Prepare bilevel description
+    Bilevel::Description description(env);
+    description.set_lower_level_obj(-10 * y[0] - 10 * y[1] - 10 * y[2] - 10 * y[3]);
+    description.make_lower_level<1>(y);
+    description.make_lower_level(follower_c1);
+    description.make_lower_level(follower_c2);
+    description.make_lower_level(follower_c3);
+
+    auto [opt_model, opt_description] = Bilevel::PessimisticAsOptimistic::make_model(high_point_relaxation, description);
+    Annotation<double> big_M(env, "big_M", 1e4); // By default, we will set our big-M value to 1e4
+
+    opt_model.use(Bilevel::KKT(opt_description).with_big_M(big_M) + Gurobi());
+
+    // Optimize and print solution
+    opt_model.optimize();
+
+    std::cout << save_primal(opt_model) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/facility-location-problem.html b/examples/facility-location-problem.html new file mode 100644 index 000000000..2c9e59660 --- /dev/null +++ b/examples/facility-location-problem.html @@ -0,0 +1,387 @@ + + + + + + + Solving a facility location problem with a custom branch-and-bound + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a facility location problem with a custom branch-and-bound

    +
    +

    Problem Definition

    +

    We consider the capacitated Facility Location Problem (FLP). +Given a set of potential facility locations \(V_1\) and a set of customers \(V_2\), the goal is to select +a subset of facility location to activate in order to serve all customers’ demand, while minimizing the total cost.

    +

    Each facility \(i\in V_1\) has an opening cost \(f_i\) and a maximum capacity \(q_i\). +Each customer \(j\in V_2\) has a demand \(d_j\). +The unitary cost for serving customer \(j\in V_2\) from facility \(i\in V_1\) is \(t_{ij}\).

    +

    We model the capacitated FLP with the MILP:

    +
    +\[\begin{split}\begin{align*} + \min_{x,y} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j y_{ij} \le q_i, && i\in V_1, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. +\end{align*}\end{split}\]
    +
    +
    +

    Instance

    +

    We will use an instance stored in a file called facility.data.txt. This file reads

    +
    10	20
+109.6	131.484
+169.498	103.513
+24.7946	41.8319
+150.331	156.535
+140.651	128.462
+68.8231	66.0825
+5.40097	33.6793
+123.19	113.974
+118.503	152.262
+27.5682	125.587
+36.1992
+5.60365
+10.0339
+20.1965
+17.4686
+35.8237
+14.8866
+2.75196
+36.7471
+2.76135
+12.0892
+16.2641
+11.3815
+8.96618
+32.1548
+13.7501
+0.631599
+26.9407
+36.4762
+10.0098
+0.674345	0.377274	0.60077	0.725902	0.347025	0.648906	0.635155	0.607522	0.333549	0.300607	0.416598	0.628605	0.753687	0.644812	0.405533	0.152511	0.424802	0.261078	0.50283	0.403443
+0.79483	0.0798539	0.347963	0.756363	0.654002	0.484362	0.663717	0.820894	0.220568	0.548021	0.218845	0.779403	0.804299	0.507375	0.592223	0.172742	0.63654	0.0894973	0.819295	0.712606
+0.988408	0.473435	0.741449	1.02582	0.420089	0.859221	0.932609	0.913111	0.206479	0.606641	0.592807	0.943148	1.05883	0.871605	0.719628	0.296455	0.735305	0.405338	0.70923	0.472351
+0.801213	0.930165	1.12413	0.970236	0.281743	1.11036	0.911725	0.579372	0.840547	0.467774	0.937797	0.721997	0.961574	1.08599	0.57822	0.70739	0.533045	0.812734	0.148052	0.238144
+0.033511	0.742563	0.729705	0.21527	0.807152	0.579068	0.209073	0.232984	0.91811	0.384516	0.620859	0.0675881	0.187979	0.528276	0.248045	0.699975	0.263439	0.677736	0.632054	0.831136
+0.379508	0.394834	0.402656	0.338167	0.703938	0.315728	0.243857	0.475284	0.607753	0.336413	0.270847	0.38184	0.381389	0.285442	0.271919	0.405371	0.331478	0.346229	0.681973	0.748633
+1.01954	0.586318	0.852622	1.08059	0.340762	0.955962	0.989606	0.914744	0.331927	0.616543	0.693984	0.966318	1.10785	0.963435	0.742256	0.385068	0.74801	0.505968	0.654321	0.385256
+0.124851	0.647767	0.637432	0.198938	0.766693	0.495492	0.15157	0.278676	0.831333	0.339767	0.525301	0.137635	0.200255	0.446836	0.203461	0.614955	0.238989	0.585824	0.629149	0.796432
+0.822042	0.611747	0.850139	0.920143	0.113758	0.898665	0.836445	0.683577	0.462689	0.406345	0.66767	0.759121	0.93636	0.891583	0.542633	0.376275	0.534339	0.501362	0.400407	0.172095
+0.728693	0.27883	0.523355	0.749647	0.439242	0.602651	0.655937	0.692852	0.235195	0.391798	0.348472	0.692708	0.785082	0.607712	0.47688	0.0436219	0.506139	0.16976	0.61561	0.497567
+
    +
    +

    On the first line, the number of facilities and the numbers of customers are specified. +Then, for each facility, the opening cost and the capacity are given. +For each customer, the demand is given. +Finally, the cost of serving each customer from each facility is given.

    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 06/04/23.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/mixed-integer/problems/facility-location-problem/FLP_Instance.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/BranchAndBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/PseudoCost.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestEstimate.h"
+#include "idol/mixed-integer/optimizers/wrappers/HiGHS/HiGHS.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "idol/mixed-integer/optimizers/callbacks/ReducedCostFixing.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    // Read instance
+    const auto instance = Problems::FLP::read_instance_1991_Cornuejols_et_al("facility.data.txt");
+    const unsigned int n_customers = instance.n_customers();
+    const unsigned int n_facilities = instance.n_facilities();
+
+    // Make model
+
+    Model model(env);
+
+    auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, 0., "x");
+    auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., 1., Binary, 0., "y");
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        model.add_ctr(idol_Sum(j, Range(n_customers), instance.demand(j) * y[i][j]) <= instance.capacity(i));
+    }
+
+    for (unsigned int j = 0 ; j < n_customers ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) == 1);
+    }
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        for (unsigned int j = 0 ; j < n_customers ; ++j) {
+            model.add_ctr(y[i][j] <= x[i]);
+        }
+    }
+
+    model.set_obj_expr(idol_Sum(i, Range(n_facilities),
+                                instance.fixed_cost(i) * x[i]
+                                + idol_Sum(j, Range(n_customers),
+                                             instance.per_unit_transportation_cost(i, j) *
+                                             instance.demand(j) *
+                                             y[i][j]
+                                         )
+                                 )
+                         );
+
+    // Set backend options
+    model.use(
+            BranchAndBound()
+                    .with_node_optimizer(Gurobi::ContinuousRelaxation())
+                    .with_branching_rule(PseudoCost())
+                    .with_node_selection_rule(BestEstimate())
+                    .add_callback(ReducedCostFixing())
+                    .with_logs(true)
+    );
+
+    model.optimize();
+
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/generalized-assignment-problem-bap.html b/examples/generalized-assignment-problem-bap.html new file mode 100644 index 000000000..dab46dc6b --- /dev/null +++ b/examples/generalized-assignment-problem-bap.html @@ -0,0 +1,361 @@ + + + + + + + Solving a generalized assignment problem by column generation and branch-and-price + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a generalized assignment problem by column generation and branch-and-price

    +
    +

    Problem Definition

    +

    Given a set of \(m\) agents and \(n\) jobs, the goal is to assign each job to exactly one agent in such a +way that the total cost is minimized, while respecting the capacity constraints of each agent.

    +

    Each agent \(i\in\{1,\dotsc,m\}\) has a capacity \(C_i\). +Each job \(j\in\{1,\dotsc,n\}\) has a resource consumption \(r_{ij}\) and a cost \(c_{ij}\) when assigned to agent \(i\).

    +

    We model the GAP with the following binary linear program:

    +
    +\[\begin{split}\begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij} \le C_i, && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in \{0,1\}, && i=1,\dotsc,m, j=1,\dotsc,n. +\end{align*}\end{split}\]
    +
    +
    +

    Decomposition

    +

    In this example, we use a Dantzig-Wolfe decomposition to break down the problem into a master problem and as many subproblems as agents. +The master problem coordinates the assignment of jobs to agents, while the subproblems handle the capacity constraints for each agent individually.

    +
      +

    1. Master Problem: The master problem is responsible for ensuring that each job is assigned to exactly one agent. It maintains the overall objective of minimizing the total cost.

      2. +

    2. Subproblems: Each subproblem corresponds to an agent and ensures that the agent’s capacity constraints are respected. The subproblems are solved independently and their solutions are used to update the master problem.

      3. +
    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 13/03/23.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/mixed-integer/problems/generalized-assignment-problem/GAP_Instance.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/WorstBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/BranchAndBound.h"
+#include "idol/mixed-integer/optimizers/callbacks/heuristics/IntegerMaster.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/DantzigWolfeDecomposition.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/infeasibility-strategies/FarkasPricing.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/stabilization/Neame.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/logs/Info.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+#include "idol/mixed-integer/optimizers/wrappers/Mosek/Mosek.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/infeasibility-strategies/ArtificialCosts.h"
+#include "idol/mixed-integer/optimizers/callbacks/ReducedCostFixing.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    const auto instance = Problems::GAP::read_instance("assignment-bap.data.txt");
+
+    const unsigned int n_agents = instance.n_agents();
+    const unsigned int n_jobs = instance.n_jobs();
+
+    // Create optimization environment
+    Env env;
+
+    // Create model
+    Model model(env);
+
+    // Create decomposition annotation
+    Annotation decomposition(env, "decomposition", MasterId);
+
+    // Create assignment variables (x_ij binaries)
+    auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, 0., "x");
+
+    // Create knapsack constraints (i.e., capacity constraints)
+    for (unsigned int i = 0 ; i < n_agents ; ++i) {
+        auto capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+
+        capacity.set(decomposition, i); // Assign constraint to i-th subproblem
+    }
+
+    // Create assignment constraints
+    for (unsigned int j = 0 ; j < n_jobs ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j));
+    }
+
+    // Set the objective function
+    model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j])));
+
+    // Build algorithms
+    const auto column_generation = DantzigWolfeDecomposition(decomposition)
+            .with_master_optimizer(Gurobi::ContinuousRelaxation().with_logs(false))
+            .with_default_sub_problem_spec(
+                    DantzigWolfe::SubProblem()
+                            .add_optimizer(Gurobi().with_logs(false))
+                            .with_column_pool_clean_up(1500, .75)
+            )
+            .with_logger(Logs::DantzigWolfe::Info().with_frequency_in_seconds(.00000001))
+            .with_dual_price_smoothing_stabilization(DantzigWolfe::Neame(.3))
+            .with_infeasibility_strategy(DantzigWolfe::FarkasPricing())
+            .with_hard_branching(true)
+            .with_logs(true);
+
+    const auto branch_and_bound = BranchAndBound()
+            .with_subtree_depth(0)
+            .with_branching_rule(MostInfeasible())
+            .with_node_selection_rule(WorstBound())
+            .add_callback(Heuristics::IntegerMaster().with_optimizer(Gurobi().with_logs(false)))
+            .with_logger(Logs::BranchAndBound::Info<DefaultNodeInfo>().with_node_logs(true).with_frequency_in_seconds(.00000001))
+            .with_logs(true);
+
+    const auto branch_and_price = branch_and_bound + column_generation;
+
+    model.use(branch_and_price);
+    model.optimize();
+
+    // Set optimizer
+    model.use(branch_and_price);
+
+    // Solve
+    model.optimize();
+
+    // Print solution
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/generalized-assignment-problem-penalty-bap.html b/examples/generalized-assignment-problem-penalty-bap.html new file mode 100644 index 000000000..72da10191 --- /dev/null +++ b/examples/generalized-assignment-problem-penalty-bap.html @@ -0,0 +1,362 @@ + + + + + + + Combining branch-and-price, column generation, and a penalty method for the generalized assignment problem + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Combining branch-and-price, column generation, and a penalty method for the generalized assignment problem

    +
    +

    Problem Definition

    +

    We consider the Generalized Assignment Problem (GAP) already studied in the branch-and-price example.

    +

    In this example, we solve the continuous relaxation of the GAP using a penalty method and column generation. +Then possibly branch on the integer variables to solve the mixed-integer problem.

    +

    First, we consider the continuous relaxation of the GAP:

    +
    +\[\begin{split}\begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij}, \le C_i && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in [0,1], && i=1,\dotsc,m, j=1,\dotsc,n. +\end{align*}\end{split}\]
    +

    Then, we introduce penalty parameters \(\rho_j\) to penalize the constraints \(\sum_{i=1}^m x_{ij} = 1\) in the objective function.

    +
    +\[\begin{split}\begin{align*} + \min_{x} \ & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} + \sum_{j=1}^n \rho_j \left| \sum_{i=1}^m x_{ij} - 1 \right| \\ + \text{s.t.} & \sum_{j=1}^n r_{ij} x_{ij} \le C_i && i=1,\dotsc,m \\ + & x_{ij} \in [0,1] && i=1,\dotsc,m, j=1,\dotsc,n. +\end{align*}\end{split}\]
    +

    Throughout the optimization process, we update the penalty parameters \(\rho_j\) iteratively to enforce the feasibility of the solution.

    +

    Finally, we solve the continuous relaxation of the GAP using column generation to generate new columns (variables) and improve the objective function. +That is, we iteratively solve the master problem and the subproblems to generate new columns and update the master problem.

    +
    +
    +

    Implementation with idol

    +
    //
+// Created by henri on 13/03/23.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/mixed-integer/problems/generalized-assignment-problem/GAP_Instance.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/WorstBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/BranchAndBound.h"
+#include "idol/mixed-integer/optimizers/callbacks/heuristics/IntegerMaster.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/DantzigWolfeDecomposition.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/infeasibility-strategies/FarkasPricing.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/stabilization/Neame.h"
+#include "idol/mixed-integer/optimizers/dantzig-wolfe/logs/Info.h"
+#include "idol/mixed-integer/optimizers/padm/PenaltyMethod.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    const auto instance = Problems::GAP::read_instance("assignment-penalty-bap.data.txt");
+
+    const unsigned int n_agents = instance.n_agents();
+    const unsigned int n_jobs = instance.n_jobs();
+
+    // Create optimization environment
+    Env env;
+
+    // Create model
+    Model model(env);
+
+    // Create decomposition annotation
+    Annotation decomposition(env, "decomposition", MasterId);
+
+    // Create penalized constraints annotation
+    Annotation<double> initial_penalty_parameters(env, "initial_penalty_parameters", -1); // By default, constraints are not penalized
+
+    // Create assignment variables (x_ij binaries)
+    auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, 0., "x");
+
+    // Create knapsack constraints (i.e., capacity constraints)
+    for (unsigned int i = 0 ; i < n_agents ; ++i) {
+        auto capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+
+        capacity.set(decomposition, i); // Assign constraint to i-th subproblem
+    }
+
+    // Create assignment constraints
+    for (unsigned int j = 0 ; j < n_jobs ; ++j) {
+        auto assignment = model.add_ctr(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j));
+
+        assignment.set(initial_penalty_parameters, 1e2); // With an initial penalty value of 1e2
+    }
+
+    // Set the objective function
+    model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j])));
+
+    const auto column_generation = DantzigWolfeDecomposition(decomposition)
+            .with_master_optimizer(GLPK::ContinuousRelaxation().with_logs(false))
+            .with_default_sub_problem_spec(
+                    DantzigWolfe::SubProblem()
+                            .add_optimizer(GLPK().with_logs(false))
+                            .with_column_pool_clean_up(1500, .75)
+            )
+            .with_logger(Logs::DantzigWolfe::Info().with_frequency_in_seconds(.00000001))
+            .with_dual_price_smoothing_stabilization(DantzigWolfe::Neame(.3))
+            .with_infeasibility_strategy(DantzigWolfe::FarkasPricing())
+            .with_hard_branching(true)
+            .with_logs(true);
+
+
+    const auto penalty_method = PenaltyMethod(initial_penalty_parameters)
+            .with_penalty_update(PenaltyUpdates::Multiplicative(2))
+            .with_rescaling_threshold(1e3)
+            .with_feasible_solution_status(Optimal);
+
+    const auto branch_and_bound = BranchAndBound()
+            .with_subtree_depth(0)
+            .with_branching_rule(MostInfeasible())
+            .with_node_selection_rule(WorstBound())
+            //.add_callback(Heuristics::IntegerMaster().with_osi_interface(HiGHS().with_logs(false)))
+            .with_logs(true);
+
+    // Set optimizer
+    model.use(branch_and_bound + (penalty_method + column_generation));
+
+    // Solve
+    model.optimize();
+
+    // Print solution
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/index.html b/examples/index.html new file mode 100644 index 000000000..b7520261f --- /dev/null +++ b/examples/index.html @@ -0,0 +1,276 @@ + + + + + + + Examples + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Examples

    +
    +

    Mixed-Integer Optimization

    +
    + +
    +
    +
    +

    Bilevel Optimization

    +
    + +
    +
    +
    +

    Robust Optimization

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/knapsack-problem.html b/examples/knapsack-problem.html new file mode 100644 index 000000000..30bdb4a3e --- /dev/null +++ b/examples/knapsack-problem.html @@ -0,0 +1,312 @@ + + + + + + + Solving a knapsack problem with HiGHS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a knapsack problem with HiGHS

    +
    +

    Problem Definition

    +

    Given a set of \(n\) items, the goal is to select of subset of items to be put in a knapsack of limited capacity. +Each item has a weight (the amount of space it takes in the knapsack) and a profit (the value of the item). +The goal is to maximize the total profit of the items in the knapsack, while not exceeding the capacity.

    +

    For each item \(j\in\{1,\dotsc,n\}\), we let \(w_j\) denote its weight and \(p_j\) be its profit. +The capacity of the knapsack is noted \(C\).

    +

    The knapsack problem can be formulated as the following binary linear problem:

    +
    +\[\begin{split}\begin{align*} + \max_{x} \quad & \sum_{j=1}^n p_j x_j \\ + \text{s.t.} \quad & \sum_{j=1}^n w_j x_j \le C, \\ + & x \in \{0,1\}^n. +\end{align*}\end{split}\]
    +
    +
    +

    Instance

    +

    We will use an instance stored in a file called knapsack.data.txt. This file reads

    +
    5
+40 50 100 95 30
+2 3.14 1.98 5 3
+10
+
    +
    +

    The first line contains the number of items \(n\). +Then, the following line contains the profits of each item, \(p_j\). +The third line contains the weights of each item, \(w_j\). +Finally, the last line contains the capacity of the knapsack, \(C\).

    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 06/04/23.
+//
+#include <iostream>
+#include "idol/mixed-integer/problems/knapsack-problem/KP_Instance.h"
+#include "idol/modeling.h"
+#include "idol/mixed-integer/optimizers/wrappers/HiGHS/HiGHS.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    const auto instance = Problems::KP::read_instance("knapsack.data.txt");
+
+    const auto n_items = instance.n_items();
+
+    Env env;
+
+    // Create model
+    Model model(env);
+
+    auto x = model.add_vars(Dim<1>(n_items), 0, 1, Binary, 0., "x");
+
+    model.add_ctr(idol_Sum(j, Range(n_items), instance.weight(j) * x[j]) <= instance.capacity());
+
+    model.set_obj_expr(idol_Sum(j, Range(n_items), -instance.profit(j) * x[j]));
+
+    // Set optimizer
+    model.use(HiGHS());
+
+    // Solve
+    model.optimize();
+
+    std::cout << "Objective value = " << model.get_best_obj() << std::endl;
+
+    std::cout << "Solution:\n";
+    std::cout << save_primal(model) << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/robust-adr.html b/examples/robust-adr.html new file mode 100644 index 000000000..c93f079f1 --- /dev/null +++ b/examples/robust-adr.html @@ -0,0 +1,373 @@ + + + + + + + Using affine decision rules to solve a two-stage facility location problem with facility disruption + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using affine decision rules to solve a two-stage facility location problem with facility disruption

    +
    +

    Problem Definition

    +

    We consider a facility location problem with facility disruption. +Given a set of potential facility locations \(V_1\) and a set of customers \(V_2\), the goal is to select a subset of facility locations +to activate in order to serve all customers’ demand, while minimizing the total cost. +This version considers random disruptions of the opened facilities making them unusable.

    +

    Note that there is also an example for the deterministic version of the FLP using Column Generation.

    +

    Each facility \(i\in V_1\) has an opening cost \(f_i\) and a maximum capacity \(q_i\). +Each customer \(j\in V_2\) has a demand \(d_j\). +The unitary cost for serving customer \(j\in V_2\) from facility \(i\in V_1\) is \(t_{ij}\). +The maximum number of facilities that can be disrupted is noted \(\Gamma\).

    +

    The two-stage robust facility location problem can be formulated as

    +
    +\[\begin{align} + \min_{ x\in \{0,1\}^{|V_1|} } \quad & \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \min_{y\in Y(x,\xi)} \quad \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\}, +\end{align}\]
    +

    in which \(\Xi := \left\{ \xi\in\{0,1\}^{|V_1|} : e^\top\xi \le \Gamma \right\}\) and \(Y(x,\xi)\) is the feasible set of the second-stage problem defined as

    +
    +\[\begin{split}\begin{align} + & \sum_{j\in V_2} d_j y_{ij} \le q_i, && i\in V_1,\\ + & \sum_{i\in V_1} y_{ij} \ge 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & y_{ij} \le 1 - \xi_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. +\end{align}\end{split}\]
    +

    In this example, we will approximate the robust problem using affine decision rules and solve it using Gurobi. +To this end, we will restrict the adjustable decisions to be affine functions of the uncertain parameters, i.e., \(y(\xi) = \bar y + Y\xi\).

    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 28.11.24.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/mixed-integer/problems/facility-location-problem/FLP_Instance.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/BranchAndBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/PseudoCost.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestEstimate.h"
+#include "idol/mixed-integer/optimizers/wrappers/HiGHS/HiGHS.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "idol/mixed-integer/optimizers/callbacks/ReducedCostFixing.h"
+#include "idol/robust/modeling/Description.h"
+#include "idol/robust/optimizers/deterministic/Deterministic.h"
+#include "idol/robust/optimizers/affine-decision-rule/AffineDecisionRule.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    // Read instance
+    const auto instance = Problems::FLP::read_instance_1991_Cornuejols_et_al("adr-facility-location.data.txt");
+    const unsigned int n_customers = instance.n_customers();
+    const unsigned int n_facilities = instance.n_facilities();
+
+    // Uncertainty set
+    Model uncertainty_set(env);
+    const double Gamma = .2;
+    const auto xi = uncertainty_set.add_vars(Dim<2>(n_facilities, n_customers), 0., 1., Continuous, 0., "xi");
+    uncertainty_set.add_ctr(idol_Sum(i, Range(n_facilities), idol_Sum(j, Range(n_customers), xi[i][j])) <= Gamma);
+
+    // Make model
+    Model model(env);
+    Robust::Description description(uncertainty_set);
+
+    auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, 0., "x");
+    auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., 1., Continuous, 0., "y");
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        model.add_ctr(idol_Sum(j, Range(n_customers), instance.demand(j) * y[i][j]) <= instance.capacity(i));
+    }
+
+    for (unsigned int j = 0 ; j < n_customers ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) >= 1);
+    }
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        for (unsigned int j = 0 ; j < n_customers ; ++j) {
+            model.add_ctr(y[i][j] <= x[i]);
+        }
+    }
+
+    model.set_obj_expr(idol_Sum(i, Range(n_facilities),
+                                instance.fixed_cost(i) * x[i]
+                                + idol_Sum(j, Range(n_customers),
+                                           instance.per_unit_transportation_cost(i, j) *
+                                           instance.demand(j) *
+                                           y[i][j]
+                                )
+                       )
+    );
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        for (unsigned int j = 0; j < n_customers; ++j) {
+            const auto c = model.add_ctr(y[i][j] <= 1);
+            description.set_uncertain_rhs(c, -xi[i][j]); // models y_ij <= 1 - xi_j
+            description.set_stage(y[i][j], 1); // models y_ij as a second-stage variable
+        }
+    }
+
+    model.use(Gurobi());
+    model.optimize();
+    std::cout << "Deterministic Problem has value: " << model.get_best_obj() << std::endl;
+
+    /*
+     * Alternatively, you could also do
+     * const auto adr_result = Robust::AffineDecisionRule::make_model(model, description);
+     * std::cout << Robust::Description::View(adr_result.model, description) << std::endl;
+     */
+
+    model.use(
+            Robust::AffineDecisionRule(description)
+                    .with_deterministic_optimizer(Gurobi().with_logs(true))
+    );
+    model.optimize();
+    std::cout << "Affine Decision Rule Problem has value: " << model.get_best_obj() << std::endl;
+
+    model.use(
+            Robust::Deterministic(description)
+                    .with_deterministic_optimizer(Gurobi())
+    );
+    model.optimize();
+    std::cout << "Robust Problem has value: " << model.get_best_obj() << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/robust-determistic.html b/examples/robust-determistic.html new file mode 100644 index 000000000..833687fbd --- /dev/null +++ b/examples/robust-determistic.html @@ -0,0 +1,383 @@ + + + + + + + Solving a robust facility location problem by its deterministic equivalent + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a robust facility location problem by its deterministic equivalent

    +
    +

    Problem Definition

    +

    We consider a facility location problem with uncertain demand. +Given a set of potential facility locations \(V_1\) and a set of customers \(V_2\), the goal is to select a subset of facility locations +to activate in order to serve all customers’ demand, while minimizing the total cost. +This version introduces uncertainty in the customers’ demands.

    +

    Note that there is also an example for the deterministic version of the FLP using Column Generation.

    +

    Each facility \(i\in V_1\) has an opening cost \(f_i\) and a maximum capacity \(q_i\). +Each customer \(j\in V_2\) has a demand \(d_j\). +The unitary cost for serving customer \(j\in V_2\) from facility \(i\in V_1\) is \(t_{ij}\). +The uncertainty in customer demands is controlled by a parameter \(\Gamma\).

    +

    In this robust variant, we consider that the demands are uncertain and can be expressed as \(d_j(\xi) = d_j(1 + 0.2 \xi_j)\) +with \(\xi\) being an unknown vector taken in the uncertainty set

    +
    +\[\Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}.\]
    +

    The goal is to minimize the total cost of opening facilities and serving customers, considering the worst-case demand scenario.

    +

    The robust version can be formulated as

    +
    +\[\begin{split}\begin{align*} + \min_{x,y} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j(\xi) y_{ij} \le q_i, && i\in V_1, \quad \text{for all }\xi\in\Xi, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. +\end{align*}\end{split}\]
    +

    In this example, we will reformulate this robust facility location problem as a deterministic one. Then, we will solve it using Gurobi.

    +
    +

    Hint

    +

    Here, the deterministic reformulation reads as follows.

    +
    +\[\begin{split}\begin{align*} + \min_{x,y,u.v} \quad & \sum_{i\in V_1} f_i x_i + \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \\ + \text{s.t.} \quad & \sum_{j\in V_2} d_j y_{ij} + \Gamma u + \sum_{j\in V_2} v_j \le q_i, && i\in V_1, \\ + & u + v_j \ge 0.2 d_j y_j, && j\in V_2, \\ + & \sum_{i\in V_1} y_{ij} = 1, && j\in V_2, \\ + & u, v_j \ge 0, && j\in V_2, \\ + & y_{ij} \le x_i && i\in V_1, j\in V_2, \\ + & x_i \in \{0,1\}, && i\in V_1, \\ + & y_{ij} \in \{0,1\}, && i\in V_1, j\in V_2. +\end{align*}\end{split}\]
    +
    +
    +
    +

    Implementation

    +
    //
+// Created by henri on 06/04/23.
+//
+#include <iostream>
+#include "idol/modeling.h"
+#include "idol/mixed-integer/problems/facility-location-problem/FLP_Instance.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/BranchAndBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/PseudoCost.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestEstimate.h"
+#include "idol/mixed-integer/optimizers/wrappers/HiGHS/HiGHS.h"
+#include "idol/mixed-integer/optimizers/wrappers/GLPK/GLPK.h"
+#include "idol/mixed-integer/optimizers/wrappers/Gurobi/Gurobi.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/node-selection-rules/factories/BestBound.h"
+#include "idol/mixed-integer/optimizers/branch-and-bound/branching-rules/factories/MostInfeasible.h"
+#include "idol/mixed-integer/optimizers/callbacks/ReducedCostFixing.h"
+#include "idol/robust/modeling/Description.h"
+#include "idol/robust/optimizers/deterministic/Deterministic.h"
+
+using namespace idol;
+
+int main(int t_argc, const char** t_argv) {
+
+    Env env;
+
+    // Read instance
+    const auto instance = Problems::FLP::read_instance_1991_Cornuejols_et_al("robust-facility-location.data.txt");
+    const unsigned int n_customers = instance.n_customers();
+    const unsigned int n_facilities = instance.n_facilities();
+
+    // Uncertainty set
+    Model uncertainty_set(env);
+    const double Gamma = 1;
+    const auto xi = uncertainty_set.add_vars(Dim<1>(n_customers), 0., 1., Continuous, 0., "xi");
+    uncertainty_set.add_ctr(idol_Sum(i, Range(n_customers), xi[i]) <= Gamma);
+
+    // Make model
+    Model model(env);
+    Robust::Description description(uncertainty_set);
+
+    auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, 0., "x");
+    auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., 1., Continuous, 0., "y");
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+
+        const auto c = model.add_ctr(idol_Sum(j, Range(n_customers), instance.demand(j) * y[i][j]) <= instance.capacity(i));
+
+        for (unsigned int j = 0 ; j < n_customers ; ++j) {
+            description.set_uncertain_mat_coeff(c, y[i][j], 0.2 * instance.demand(j) * xi[j]);
+        }
+
+    }
+
+    for (unsigned int j = 0 ; j < n_customers ; ++j) {
+        model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) == 1);
+    }
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        for (unsigned int j = 0 ; j < n_customers ; ++j) {
+            model.add_ctr(y[i][j] <= x[i]);
+        }
+    }
+
+    model.set_obj_expr(idol_Sum(i, Range(n_facilities),
+                                instance.fixed_cost(i) * x[i]
+                                + idol_Sum(j, Range(n_customers),
+                                           instance.per_unit_transportation_cost(i, j) *
+                                           instance.demand(j) *
+                                           y[i][j]
+                                )
+                       )
+    );
+
+    for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+        for (unsigned int j = 0; j < n_customers; ++j) {
+            description.set_uncertain_obj(y[i][j], 0.2 * instance.per_unit_transportation_cost(i, j) * instance.demand(j) * xi[j]);
+        }
+    }
+
+    model.use(Gurobi());
+    model.optimize();
+    std::cout << "Deterministic Problem has value: " << model.get_best_obj() << std::endl;
+
+    /*
+     * Alternatively, you could also do
+     * const auto deterministic_model = Robust::Deterministic::make_model(model, description);
+     * std::cout << Robust::Description::View(model, description) << std::endl;
+     */
+
+    model.use(
+                Robust::Deterministic(description)
+                    .with_deterministic_optimizer(Gurobi().with_logs(false))
+            );
+    model.optimize();
+    std::cout << "Robust Problem has value: " << model.get_best_obj() << std::endl;
+
+    return 0;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/examples/two-stage-robust-facility-location-problem.html b/examples/two-stage-robust-facility-location-problem.html new file mode 100644 index 000000000..4b48300dc --- /dev/null +++ b/examples/two-stage-robust-facility-location-problem.html @@ -0,0 +1,248 @@ + + + + + + + Two-Stage Robust Facility Location Problem (CCG) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Two-Stage Robust Facility Location Problem (CCG)

    +
    +

    Problem Description

    +

    We consider a robust version of the capacitated Facility Location Problem (FLP). +Given a set of potential facility locations \(V_1\) and a set of customers \(V_2\), the goal is to select a subset of facility locations +to activate in order to serve all customers’ demand, while minimizing the total cost. +This version introduces uncertainty in the customers’ demands.

    +

    Note that there is also an example for the deterministic version of the FLP using Column Generation.

    +

    Each facility \(i\in V_1\) has an opening cost \(f_i\) and a maximum capacity \(q_i\). +Each customer \(j\in V_2\) has a demand \(d_j\). +The unitary cost for serving customer \(j\in V_2\) from facility \(i\in V_1\) is \(t_{ij}\). +The uncertainty in customer demands is controlled by a parameter \(\Gamma\).

    +

    In this robust variant, we consider that the demands are uncertain and can be expressed as \(d_j(\xi) = d_j(1 + p\xi_j)\) +with \(p\) being the maximum increase in demand and \(\xi\) being an unknown vector taken in the uncertainty set

    +
    +\[\Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}.\]
    +

    We model the two-stage robust FLP as

    +
    +\[\min_{x\in \{0,1\}^{|V_1|}} \ \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \ \min_{y\in Y(x,\xi)} \ \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\}\]
    +

    where \(Y(x,\xi)\) is the set of feasible solutions for the second stage problem, given the first stage solution \(x\) and the realization \(\xi\) of the uncertain demand vector. +It is defined as the set of vectors \(y\in \mathbb{R}^{|V_1|\times|V_2|}\) that satisfy the following constraints

    +
    +\[\begin{split}\begin{align*} + & \sum_{i\in V_1} y_{ij} = d_j(\xi) && j\in V_2, \\ + & \sum_{j\in V_2} y_{ij} \le q_i x_i && i\in V_1, \\ + & y_{ij} \ge 0 && i\in V_1, j\in V_2. +\end{align*}\end{split}\]
    +
    +
    +

    Implementation

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/faq/gap.html b/faq/gap.html new file mode 100644 index 000000000..5ac561c4f --- /dev/null +++ b/faq/gap.html @@ -0,0 +1,250 @@ + + + + + + + How is the Optimality Gap Computed? + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    How is the Optimality Gap Computed?

    +

    To assess global optimality, we use two different optimality gaps.

    +

    The relative optimality gap is computed as

    +
    +\[\begin{equation} + \gamma_{\text{rel}} := \frac{ UB - LB }{ 10^{-10} + |UB| }. +\end{equation}\]
    +

    The absolute optimality gap is computed as

    +
    +\[\begin{equation} + \gamma_{\text{abs}} := UB - LB. +\end{equation}\]
    +

    See also Tolerances.

    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/faq/index.html b/faq/index.html new file mode 100644 index 000000000..17619d5f3 --- /dev/null +++ b/faq/index.html @@ -0,0 +1,248 @@ + + + + + + + FAQ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    FAQ

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/faq/mosek-and-eigen.html b/faq/mosek-and-eigen.html new file mode 100644 index 000000000..7b0249a4a --- /dev/null +++ b/faq/mosek-and-eigen.html @@ -0,0 +1,289 @@ + + + + + + + Why is Eigen Necessary to Solve QCQPs with Mosek? + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Why is Eigen Necessary to Solve QCQPs with Mosek?

    +
    +

    In Short

    +

    The interface of idol is based on quadratic expressions like

    +
    +\[\sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i.\]
    +

    The C++ interface of Mosek, instead, is based on “conic expressions” like

    +
    +\[(x_0, \textbf{Fx}) \in \mathcal Q^n,\]
    +

    where \(\mathcal Q^n\) denotes the second-order cone and \(F\) is some matrix related to \(Q^i\).

    +

    In order to make the conversion between the Mosek interface and +the idol interface (for instance, computing the matrix \(F\)), +one needs to compute an eigen value decomposition. +This is automatically done by idol using Eigen. +This is why Eigen is necessary if one wants to use Mosek with idol to solve QPs or QCQPs.

    +
    +
    +

    Detailed Answer

    +

    Consider the quadratic expression

    +
    +\[\sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^ix_jx_k \le b_i.\]
    +

    It can be written as

    +
    +\[a_{(i)}^\top x + x^\top Q^i x \le b_i.\]
    +

    The first task is to compute an eigen value decomposition of \(Q^i\), i.e., +to find matrices \(L\) and \(D\) such that \(Q^i = L D L^\top\) +and \(D\) is a diagonal matrix containing the eigen values of \(Q^i\).

    +

    If there are more than two negative eigen values, the constraint is not convex and an exeception is thrown.

    +

    Otherwise, we compute \(F\) and \(N\) so that \(x^\top Q^i x = \lVert Fx \rVert_2^2 + x^\top N x\). +This is done by setting \(F = \sqrt{D^+} L^\top\) where \(D^+\) is \(D\) with the negative eigen values replaced by zero, +and \(N = L D^- L^\top\).

    +

    Hence, we have that the constraint is expressed as

    +
    +\[\lVert Fx \rVert_2^2 + x^\top N x \le b_i - a_{(i)}^\top x.\]
    +

    If \(N = 0\), it can be written as

    +
    +\[\begin{split}\begin{align} + & \lVert Fx \rVert_2^2 \le b_i - a_{(i)}^\top x \\ + \iff & (.5, b_i - a_{(i)}^\top x, Fx) \in\mathcal Q^{n+2}_r, +\end{align}\end{split}\]
    +

    where \(\mathcal Q^{n+2}_r\) denotes the rotated second-order cone.

    +

    Otherwise, if \(N\) has one non-zero entry, say \(n_{ij}\). +Then, it must be that \(a_{(i)} = 0\) and \(b_i \le 0\) for the constraint to be +converted by idol. Under this assumption, the constraint can be written as

    +
    +\[\begin{split}\begin{align} + & \lVert Fx \rVert_2^2 + \sqrt{-b_i}^2 \le n_{ij} x_i x_j \\ + \iff & (.5 n_{i,j} x_i, x_j, Fx, \sqrt{-b_i}) \in\mathcal Q^{n+1}_r, +\end{align}\end{split}\]
    +

    where it is assumed that \(n_{i,j} x_{i}x_{j} \ge 0\) holds +(for now, a warning is printed to enlight this expectation).

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/genindex.html b/genindex.html new file mode 100644 index 000000000..6732d9608 --- /dev/null +++ b/genindex.html @@ -0,0 +1,2483 @@ + + + + + + + Index + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + + +

    Index

    + +
    + I + +
    +

    I

    + + + +
    + + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 000000000..4d7360de2 --- /dev/null +++ b/index.html @@ -0,0 +1,369 @@ + + + + + + + idol, a C++ Framework for Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    + +

    A C++ Framework for Optimization

    + +

    + Start solving optimization problems now. +

    + + + Get started now +   + To installation guidelines + + +
    +

    What is idol?

    +

    idol is a C++ framework for mathematical optimization and complex decision-making problems. +It is designed to help you build new algorithms for solving complex optimization problems. +The main philosophy behind idol is interoperability and ease of use. +Hence, any algorithm can be seamlessly combined with any other algorithm to create a new one. +For instance, you can combine a Branch-and-Bound algorithm with a Column Generation algorithm to create a Branch-and-Price algorithm.

    +
    const auto branch_and_price = branch_and_bound + column_generation;
+model.use(branch_and_price);
+model.optimize();
+
    +
    +

    idol offers a variety of tools to tackle many different kinds of optimization problems:

    +
    +
    +

    Getting Started with idol

    +

    New to idol? Be sure to have a look at our tutorials. If you want to get a fast hands-on +start, have a look at our local installation guideline. It is the easiest installation process +one could think of: it automatically downloads the latest version of idol, and installs it locally in a sub-folder of your CMake project. +It’s really a mater of seconds before you can start using idol.

    +
    +

    Example

    +

    Idol has a user-friendly interface which should look natural to people working in optimization. For instance, +here is how one solves a Knapsack Problem using the Gurobi solver.

    +
    using namespace idol;
+
+const unsigned int n_items = 5;
+const double[] profit = { 40., 50., 100., 95., 30., };
+const double[] weight = { 2., 3.14, 1.98, 5., 3., };
+const double capacity = 10.;
+
+Env env;
+
+Model model(env);
+
+const auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, 0., "x");
+
+model.add_ctr(idol_Sum(j, Range(n_items), weight[j] * x[j]) <= capacity);
+
+model.set_obj_expr(idol_Sum(j, Range(n_items), -profit[j] * x[j]);
+
+model.use(Gurobi());
+
+model.optimize();
+
    +
    +
    +
    +
    +

    Is this a MIP Solver?

    +

    idol is not a MIP solver in itself. In fact, it typically needs to call external +solvers as a sub-routine of more complex algorithms such as Branch-and-Price.

    +

    The idea is to work hand in hand with existing well-engineered optimization +software to enhance their possibilities. By doing so, we aim at solving larger and more complex problems than what is currently possible.

    +

    Still, idol can be used to solve your favourite MILP, MIQP, or MIQCQP through the +many external solvers it interfaces with. +A clear advantage of using idol to solve these problems is that it offers a unified and common interface to every solver. +Thus, you can write your code once and test it with different solvers. +The following solvers are currently supported by idol:

    + +
    +
    +

    Table of Contents

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/installation/global-installation/index.html b/installation/global-installation/index.html new file mode 100644 index 000000000..e2e67b77c --- /dev/null +++ b/installation/global-installation/index.html @@ -0,0 +1,311 @@ + + + + + + + Global Installation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Global Installation

    +

    This page is dedicated to the local installation of idol. It is thought for more advanced users who want to install +idol globally on their computer (e.g., in /usr/lib). +If you simply want to “try out” idol, we advise you to opt for a local installation. +The installation process is managed by the CMake build system. You will therefore need to have it +installed on your computer.

    +

    The installation process follows the classical CMake build process configure, build, install.

    +
    +

    Configure

    +

    The first step is to create a build directory. +This is where the library will be compiled before being it is installed (i.e., copied) on your system.

    +
    mkdir build
+cd build
+
    +
    +

    Then, you should call CMake to configure the build process. +It is at this time that we let CMake look for the necessary dependencies such as, e.g., external optimization solvers. +By default, running CMake without options will cause idol to be built without any external solver. Note that options +should be specified as follows:

    +
    cmake -D<YOUR_CMAKE_OPTION>=<YOUR_VALUE> ..
+
    +
    +

    A list of all possible options can be found on the complete list of options.

    +
    +

    Example for Gurobi

    +

    Here is an example of a possible CMake command which will create the necessary targets for configuring idol to interface Gurobi.

    +
    cmake -DUSE_GUROBI=YES ..
+
    +
    +

    Note that this example assumes that your environment variable GUROBI_HOME has been correctly configured +(see this official Gurobi page).

    +

    If you want to specify the path to the Gurobi installation folder, you can use the GUROBI_DIR option.

    +
    cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir ..
+
    +
    +
    +
    +
    +

    Build

    +

    Now that the build process has been configured, we can build idol by running the following command.

    +
    make idol
+
    +
    +

    This will compile the idol C++ library, and make it ready to be installed (i.e., copied) on your computer.

    +

    If you encounter any error at this stage, please, do not hesitate to contact us on our GitHub page.

    +
    +
    +

    Install

    +

    To install idol on your computer, run the following command.

    +
    sudo make install
+
    +
    +
    +

    Hint

    +

    Here, you need superuser rights to install idol globally. If you want to install idol in a specific folder, +you may also use the CMAKE_INSTALL_PREFIX CMake option to change the destination folder.

    +
    cmake -CMAKE_INSTALL_PREFIX=/my/custom/installation/folder <YOUR_OTHER_CMAKE_OPTIONS...> ..
+make install
+
    +
    +
    +
    +
    +

    And Then?

    +

    That’s it! idol is now installed on your computer. You can now use it in your C++ projects. To do so, you will need to +link your project against the idol library. See the related pages for more information.

    +
    + +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/installation/global-installation/linking.html b/installation/global-installation/linking.html new file mode 100644 index 000000000..ca8fc24d9 --- /dev/null +++ b/installation/global-installation/linking.html @@ -0,0 +1,277 @@ + + + + + + + Linking Your C++ Project + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Linking Your C++ Project

    +

    If you have installed idol globally, you can link your C++ project with idol using CMake. +Note that if idol was locally installed, you should refer to the local installation guideline, +this page is only for global installation.

    +

    Idol is built with and for CMake (even though it is still possible to link using Makefile or pure gcc, clang, …).

    +

    Here is a minimal CMakeLists.txt which creates a new executable target linked with idol.

    +
    cmake_minimum_required(VERSION 3.22)
+project(my_project)
+
+set(CMAKE_CXX_STANDARD 17)
+
+add_executable(my_target main.cpp)
+
+find_package(idol REQUIRED) ## Here, we search for the installed library idol
+
+target_link_library(my_target PUBLIC idol) ## Here, we ask CMake to link with idol
+
    +
    +

    Note that you do not need to link with any external solver if idol was already linked with one.

    +

    The following main.cpp is then a minimal example.

    +
    #include <iostream>
+#include <idol/modeling.h>
+
+int main(int t_argc, const char** t_argv) {
+
+    using namespace idol;
+
+    Env env;
+
+    Model model(env);
+
+    const auto x = model.add_var(0., 1., Binary, "x");
+
+    // ...
+
+    return 0;
+}
+
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/installation/index.html b/installation/index.html new file mode 100644 index 000000000..83bf94d69 --- /dev/null +++ b/installation/index.html @@ -0,0 +1,265 @@ + + + + + + + Installation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Installation

    +

    You are here on the installation guidelines. This page will guide through the installation process of idol.

    +

    There are two ways to install idol: a local installation (easy to use) and a global installation (for more advanced users).

    +
    +

    Local Installation

    +

    A local installation lets CMake automatically download and install idol in a sub-folder of your CMake project. This is the easiest way to get started.

    +
    +
    +

    Global Installation

    +

    A global installation installs idol globally on your computer (e.g., in /usr/lib).

    +
    +
    +
    +
    +

    Options (External Solvers, etc.)

    +

    No matter which installation method you choose, you can customize the installation by setting a set of parameters accordingly. +This is particularly useful if you want to install idol with some external solver such as Gurobi. +Please refer to the complete list of options for more information.

    +
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/installation/local_installation.html b/installation/local_installation.html new file mode 100644 index 000000000..708cdfd6a --- /dev/null +++ b/installation/local_installation.html @@ -0,0 +1,301 @@ + + + + + + + Local Installation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Local Installation

    +

    This page is dedicated to the local installation of idol. This is the easiest way to get your project working with +idol without installing it globally on your computer. +If you want to install idol globally, please read our global installation guide.

    +

    The idea behind local installation is to let CMake download and manage the installation of idol in a sub-folder of your +project. This is done by using the CMake FetchContent_* directives.

    +

    We provide here a minimal CMakeLists.txt.

    +
    cmake_minimum_required(VERSION 3.23)
+project(my_project)
+
+set(CMAKE_CXX_STANDARD 17)
+
+include(FetchContent)
+
+# Define your idol CMake options here
+set(USE_GUROBI YES) # For instance, here, we specify that Gurobi will be used by idol
+
+# Tell CMake which version of idol you want to use
+FetchContent_Declare(
+        idol
+        GIT_REPOSITORY https://github.com/hlefebvr/idol.git
+        GIT_TAG        origin/main
+)
+
+# Ask CMake to download idol and install it to a sub-folder
+FetchContent_MakeAvailable(idol)
+
+# Normal executable definition
+add_executable(my_target main.cpp)
+
+# Link your CMake target with idol as classically done
+target_link_libraries(my_target PUBLIC idol)
+
    +
    +

    By default, CMake will download the latest version of idol. However, you can also explicitly specify the desired version +of idol by setting the GIT_TAG variable in the FetchContent_Declare function to the specific +version, e.g., v0.2.4-alpha.

    +
    +

    Hint

    +

    As you can see in the above example, some options must be set to tell CMake to look for external solvers. Here, we +specify that Gurobi will be used by idol. You can, of course, add other solvers such as Mosek or GLPK.

    +

    This is done with the set CMake function. For instance, to set the option MY_OPTION to the +value MY_VALUE. You should add set(MY_OPTION MY_VALUE) to your CMakeLists.txt file.

    +

    A list of all possible options can be found on the complete list of options.

    +
    +

    Then, here is a starting main.cpp.

    +
    #include <iostream>
+#include <idol/modeling.h>
+
+int main(int t_argc, const char** t_argv) {
+
+    using namespace idol;
+
+    Env env;
+
+    Model model(env);
+
+    const auto x = model.add_var(0., 1., Binary, 0., "x");
+
+    // ...
+
+    return 0;
+}
+
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/installation/options.html b/installation/options.html new file mode 100644 index 000000000..3414b2117 --- /dev/null +++ b/installation/options.html @@ -0,0 +1,438 @@ + + + + + + + List of CMake Options + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    List of CMake Options

    +

    This page contains a list of all CMake options that can be used to configure idol. In particular, this is useful to +link idol with external solvers.

    + +
    +

    Linking with External Solvers

    +
    +

    Gurobi (Commercial Solver)

    +

    To link with Gurobi, you will need to pass the USE_GUROBI CMake option with value YES.

    +

    By default, CMake will look for Gurobi inside the folder indicated by the environment variable GUROBI_HOME +(see this official Gurobi page). +Note that it is also possible to pass the CMake option GUROBI_DIR=/path/to/gurobi/install/dir in order to specify +another directory to look for Gurobi.

    +
    +

    Example

    +

    The following will create an install target which will install idol with Gurobi.

    +
    cmake -DUSE_GUROBI=YES -DGUROBI_DIR=/path/to/gurobi/install/dir ..
+
    +
    +

    If you are doing a local installation, then the same can be achieved as follows.

    +
    set(USE_GUROBI YES)
+set(GUROBI_DIR /path/to/gurobi/install/dir)
+
    +
    +
    +
    +
    +

    Mosek (Commercial Solver)

    +

    To link with Mosek, you will need to pass the USE_MOSEK CMake option with value YES.

    +

    By default, CMake will look for Mosek inside the folder indicated by the environment variable MOSEK_HOME. +Note that it is also possible to pass the CMake option MOSEK_DIR=/path/to/mosek/install/dir in order to specify +another directory to look for Mosek.

    +

    Note that MOSEK_HOME (or equivalently MOSEK_DIR) should point to the Mosek installation folder where +folders h and bin can be found. For instance, MOSEK_HOME=~/mosek/10.0/tools/platform/linux64x86.

    +
    +

    Example

    +

    The following will create an install target which will install idol with Mosek.

    +
    cmake -DUSE_MOSEK=YES -DMOSEK_DIR=/path/to/mosek/install/dir ..
+
    +
    +

    If you are doing a local installation, then the same can be achieved as follows.

    +
    set(USE_MOSEK YES)
+set(MOSEK_DIR /path/to/mosek/install/dir)
+
    +
    +
    +
    +

    Attention

    +

    If you intend to use Mosek for solving QPs or SOCPs, please read this.

    +
    +
    +
    +

    GLPK (Open-Source Solver)

    +

    To link with GLPK, you will need to pass the USE_GLPK CMake option with value YES.

    +

    By default, CMake will look for GLPK inside the folder indicated by the environment variable GLPK_HOME as well +as in the default installation folders /usr/include and /usr/lib. +Note that it is also possible to pass the CMake option GLPK_DIR=/path/to/glpk/install/dir in order to specify +another directory to look for GLPK.

    +
    +

    Example

    +

    The following will create an install target which will install idol with GLPK.

    +
    cmake -DUSE_GLPK=YES -DGLPK_DIR=/path/to/glpk/install/dir ..
+
    +
    +

    If you are doing a local installation, then the same can be achieved as follows.

    +
    set(USE_GLPK YES)
+set(GLPK_DIR /path/to/glpk/install/dir)
+
    +
    +
    +
    +
    +

    HiGHS (Open-Source Solver)

    +

    To link with GLPK, you will need to pass the USE_HIGHS CMake option with value YES.

    +

    By default, CMake will look for HIGHS inside the default installation folders /usr/include and /usr/lib. +Note that it is also possible to pass the CMake option HIGHS_DIR=/path/to/highs/install/dir in order to specify +another directory to look for GLPK.

    +
    +

    Example

    +

    The following will create an install target which will install idol with GLPK.

    +
    cmake -DUSE_HIGHS=YES -DHIGHS_DIR=/path/to/glpk/install/dir ..
+
    +
    +

    If you are doing a local installation, then the same can be achieved as follows.

    +
    set(USE_HIGHS YES)
+set(HIGHS_DIR /path/to/glpk/install/dir)
+
    +
    +
    +
    +
    +

    coin-or (Open-Source Solvers)

    +

    idol can be linked with some of the coin-or libraries. +Hereafter, we give a list of such libraries. For all the USE_* options, you will need to define the environment +variable COIN_OR_HOME or to set the CMake option COIN_OR_DIR. It must point to the dist directory +of coin-or.

    +
    +

    Example

    +

    The following will prepare CMake for linking against coin-or libraries.

    +
    cmake -DCOIN_OR_DIR=/path/to/coin_or/dist <OTHER_OPTIONS_GO_HERE> ..
+
    +
    +

    If you are doing a local installation, then the same can be achieved as follows.

    +
    set(COIN_OR_DIR /path/to/coin_or/dist)
+
    +
    +
    +

    We now give the list of options which can be used in relation with coin-or libraries.

    +
      +

    • USE_OSI=YES: use the Osi solver.

      • +

    • USE_SYMPHONY=YES: use the Symphony solver (can only be used through Osi).

      • +

    • USE_CBC=YES: use the Cbc solver (can only be used through Osi).

      • +

    • USE_CLP=YES: use the Clp solver (can only be used through Osi).

      • +

    • USE_CPLEX=YES: use the Cplex solver (can only be used through Osi).

      • +

    • USE_MIBS=YES: use the MibS solver (will automatically search for Alps, Bcps, Blis, and Cgl).

      • +
    +
    +
    +
    +

    Building Examples

    +

    Examples : can be found at the root level of the idol repository, inside the directory examples.

    +

    By default, CMake will not generate targets to build these example. To tell CMake to generate these, you +need to set the CMake option BUILD_EXAMPLE to YES.

    +
    +

    Example

    +

    The following will tell CMake to create targets for examples.

    +
    cmake -DBUILD_EXAMPLES=YES ..
+
    +
    +

    For instance, we can now build the Knapsack Problem example,

    +
    make example_knapsack
+
    +
    +

    and run it.

    +
    cd examples && ./example_knapsack
+
    +
    +
    +
    +
    +

    Other optional dependencies

    +
    +

    Using martinus/robin-hood-hashing hash map

    +

    Internally, idol uses unordered maps (also called hash maps). +Unfortunately, the default std implementation is not the best choice when +it comes to performance. To avoid this, if found relevant, users can tell idol to use the hash-map implementation of +martinus/robin-hood-hashing. It’s actually a header-only library, so +all you have to do is to tell CMake where the robin_hood.hpp file is. This is done through the CMake option +ROBINHOOD_DIR=/path/to/robin_hood/folder together with USE_ROBINHOOD=YES.

    +

    Note that, if ROBINHOOD_DIR is not specified, robin_hood.hpp is searched for in /usr/include, +/usr/include/robin_hood/, /usr/local/include/, /usr/local/include/robin_hood/ and in the path +stored in the environment variable ROBINHOOD_HOME.

    +
    +

    Example

    +

    The following will create an install target which will install idol with martinus’s robin_hood hash map +implementation.

    +
    cmake -DUSE_ROBINHOOD=YES -DROBINHOOD_DIR=/path/to/robin_hood/folder ..
+
    +
    +
    +
    +
    +

    Using Eigen

    +

    Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. +It is internally used by idol for some of its functionalities. In particular, this is necessary for solving QPs and SOCPs +with the Mosek solver.

    +

    Since Eigen is a header-only library, all you have to do is to tell CMake where the Eigen folder is. This is done +through the CMake option EIGEN_DIR=/path/to/eigen/folder together with USE_EIGEN=YES.

    +
    +

    Example

    +

    The following will create an install target which will install idol with Eigen.

    +
    cmake -DUSE_EIGEN=YES -DEIGEN_DIR=/path/to/eigen/folder ..
+
    +
    +
    +
    +
    +
    +

    Building Unit and Integration Tests

    +

    To build tests for idol, please refer to this developer page.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
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HcmV?d00001 diff --git a/references.html b/references.html new file mode 100644 index 000000000..f1359641e --- /dev/null +++ b/references.html @@ -0,0 +1,305 @@ + + + + + + + References + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    References

    +

    This page contains references to the literature used in the documentation.

    +
    +
    +
    +[1] +

    Tobias Achterberg, Thorsten Koch, and Alexander Martin. Branching rules revisited. Operations Research Letters, 33(1):42–54, 2005. doi:https://doi.org/10.1016/j.orl.2004.04.002.

    +
    +
    +[2] +

    Josette Ayoub and Michael Poss. Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Computational Management Science, 13(2):219–239, 2016. doi:10.1007/s10287-016-0249-2.

    +
    +
    +[3] +

    Daniel Baena, Jordi Castro, and Antonio Frangioni. Stabilized benders methods for large-scale combinatorial optimization, with application to data privacy. Management Science, 66(7):3051–3068, 2020. doi:10.1287/mnsc.2019.3341.

    +
    +
    +[4] +

    Timo Berthold. Primal heuristics for mixed integer programs. Master's thesis, Technische Universität Berlin, 2006.

    +
    +
    +[5] +

    George B. Dantzig and Philip Wolfe. The decomposition algorithm for linear programs. Econometrica, 29(4):767, 1961. doi:10.2307/1911818.

    +
    +
    +[6] +

    Elizabeth D. Dolan and Jorge J. Moré. Benchmarking optimization software with performance profiles. Mathematical Programming, 91(2):201–213, 2002. doi:10.1007/s101070100263.

    +
    +
    +[7] +

    J. J. H. Forrest, J. P. H. Hirst, and J. A. Tomlin. Practical solution of large mixed integer programming problems with umpire. Management Science, 20(5):736–773, 1974. doi:10.1287/mnsc.20.5.736.

    +
    +
    +[8] +

    Thomas Kleinert. Algorithms for Mixed-Integer Bilevel Problems with Convex Followers. PhD thesis, Universität Trier, 2021. URL: https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/383.

    +
    +
    +[9] +

    J. T. Linderoth and M. W. P. Savelsbergh. A computational study of search strategies for mixed integer programming. INFORMS Journal on Computing, 11(2):173–187, 1999. doi:10.1287/ijoc.11.2.173.

    +
    +
    +[10] +

    James T. Moore and Jonathan F. Bard. The mixed integer linear bilevel programming problem. Operations Research, 38(5):911–921, 1990. doi:10.1287/opre.38.5.911.

    +
    +
    +[11] +

    A. Pessoa, R. Sadykov, E. Uchoa, and F. Vanderbeck. Automation and combination of linear-programming based stabilization techniques in column generation. INFORMS Journal on Computing, 30(2):339–360, 2018. doi:10.1287/ijoc.2017.0784.

    +
    +
    +[12] +

    Johannes Thürauf, Thomas Kleinert, Ivana Ljubić, Ted Ralphs, and Martin Schmidt. Bobilib: bilevel optimization (benchmark) instance library. Technical Report, Universität Trier, Quantagonia, ESSEC Business School, Lehigh University, 2024. URL: https://optimization-online.org/?p=27063.

    +
    +
    +[13] +

    Eduardo Uchoa, Artur Pessoa, and Lorenza Moreno. Optimizing with Column Generation: advanced branch-cut-and-price algorithms. Technical Report L-2024-3, Cadernos do LOGIS-UFF, Universidade Federal Fluminense, Engenharia de Produção, 2024. URL: https://optimizingwithcolumngeneration.github.io.

    +
    +
    +[14] +

    François Vanderbeck. Implementing Mixed Integer Column Generation, pages 331–358. Springer US, Boston, MA, 2005. doi:10.1007/0-387-25486-2_12.

    +
    +
    +[15] +

    Laurence Wolsey. Integer Programming. Wiley, 2020. doi:10.1002/9781119606475.

    +
    +
    +[16] +

    Bo Zeng. A practical scheme to compute the pessimistic bilevel optimization problem. INFORMS Journal on Computing, 2020. doi:10.1287/ijoc.2019.0927.

    +
    +
    +[17] +

    Bo Zeng and Long Zhao. Solving two-stage robust optimization problems using a column-and-constraint generation method. Operations Research Letters, 41(5):457–461, 2013. doi:10.1016/j.orl.2013.05.003.

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    + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 000000000..b0f542a6a --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"alltitles": {"A First Example": [[144, "a-first-example"]], "A Two-Stage Robust Facility Location Problem": [[155, "a-two-stage-robust-facility-location-problem"]], "API": [[17, null]], "About stage annotations": [[155, null]], "Accessing Constraints": [[133, "accessing-constraints"]], "Accessing Variables": [[139, "accessing-variables"]], "Accessing the Objective Function": [[138, "accessing-the-objective-function"]], "Accessing the Solution": [[145, "accessing-the-solution"]], "Adding User Cuts and Lazy Constraints": [[146, null]], "Adding User Cuts and Lazy Constraints [TODO]": [[123, null]], "Adding an Objective Function": [[138, "adding-an-objective-function"]], "Adjustable Robust Optimization (Two-stage)": [[154, null]], "AffExpr": [[69, null]], "AffExpr: Affine Expressions": [[135, "affexpr-affine-expressions"]], "An Example of Lazy Cut Constraints: Benders Optimality Cuts": [[146, "an-example-of-lazy-cut-constraints-benders-optimality-cuts"]], "An Example of User Cuts: Knapsack Cover Inequalities": [[146, "an-example-of-user-cuts-knapsack-cover-inequalities"]], "An Example: Knapsack Cover Cuts": [[142, "an-example-knapsack-cover-cuts"]], "And Then?": [[105, "and-then"]], "Annotation": [[65, null]], "Assigning Stages": [[155, "assigning-stages"]], "Assumption": [[151, null]], "Automatic Reformulation": [[125, "automatic-reformulation"]], "Basic Idea": [[150, "basic-idea"]], "Benchmark": [[86, null]], "BestBound": [[27, null]], "BestEstimate": [[28, null]], "Bilevel Optimization": [[2, null], [11, "bilevel-optimization"], [17, "bilevel-optimization"], [96, "bilevel-optimization"], [112, null], [117, "bilevel-optimization"]], "Bilevel::Description": [[3, null]], "Bilevel::KKT": [[4, null]], "Bilevel::MibS": [[0, null]], "Bilevel::Mibs": [[8, null]], 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"abov": [108, 129], "absolut": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 64, 80, 101, 145], "absolute_gap": 64, "acceler": 127, "access": [12, 19, 65, 68, 104, 111, 117, 132, 135, 136, 143, 144], "accord": [18, 19], "accordingli": [107, 139, 144], "account": [64, 112], "achiev": 109, "achterberg": 110, "action": 89, "activ": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 89, 93, 98, 99, 100, 151, 155], "actual": [18, 109, 129, 133, 135, 142], "ad": [12, 14, 18, 19, 117, 131, 132, 133, 135, 139, 142, 143, 150], "add": [12, 14, 18, 19, 71, 87, 108, 125, 127, 133, 136, 137, 142, 143, 144, 145, 146, 151], "add_callback": [0, 8, 18, 49, 51, 53, 93, 94, 95, 142, 146], "add_ctr": [71, 75, 90, 91, 92, 93, 94, 95, 97, 98, 99, 104, 113, 115, 125, 133, 142, 144, 146, 155], "add_execut": [106, 108], "add_lazy_cut": [12, 19], "add_local_variable_branch": 19, "add_optim": [94, 95, 125, 129, 131], "add_phas": [37, 129], "add_qctr": 71, "add_user_cut": [12, 19, 142], "add_var": [70, 71, 77, 90, 91, 92, 93, 94, 95, 97, 98, 99, 104, 106, 108, 113, 115, 125, 133, 140, 142, 144, 145, 146, 155], "add_vector": 71, "addit": [12, 64, 65, 125, 139, 145], "addition": [129, 151, 155], "adjust": [98, 104, 110, 117, 147], "adm": [79, 80], "adr": 98, "adr_result": 98, "advanc": [12, 19, 105, 107, 110, 125, 140, 142, 145, 146, 155], "advanced_interfac": 19, "advantag": [19, 104, 111], "advis": [18, 68, 105, 134], "affect": 139, "affexpr": [3, 17, 61, 74, 75, 133], "affin": [74, 96], "affinedecisionrul": 98, "after": [129, 144, 150], "again": [137, 139], "against": [14, 105, 109, 114], "agent": [94, 125], "ahead": 129, "aim": 104, "alexand": 110, "algebra": 109, "algorithm": [0, 4, 5, 6, 7, 8, 12, 18, 19, 41, 44, 48, 49, 50, 51, 56, 57, 58, 59, 60, 65, 79, 80, 84, 90, 94, 104, 109, 110, 117, 129, 132, 144, 146, 147, 149, 151, 154], "align": [14, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 103, 112, 113, 115, 116, 125, 132, 137, 142, 146, 150, 151, 155], "all": [14, 64, 68, 75, 77, 87, 89, 93, 98, 99, 100, 104, 105, 108, 109, 112, 115, 125, 129, 132, 136, 142, 146, 150, 155], "allow": [127, 129, 140, 146], "along": 18, "alow": 150, "alp": 109, "alpha": 108, "alreadi": [95, 106, 114, 116, 131, 143, 150, 152], "also": [12, 14, 18, 41, 56, 64, 68, 89, 90, 98, 99, 100, 101, 105, 108, 109, 113, 114, 115, 131, 134, 136, 137, 138, 139, 142, 144, 146, 150, 152, 155], "altern": [17, 90, 98, 99, 138, 139], "alwai": [64, 129, 144, 145, 146, 150], "among": 129, "amount": [64, 97], "an": [12, 14, 18, 19, 56, 64, 65, 66, 68, 73, 75, 77, 78, 84, 89, 93, 94, 95, 96, 97, 98, 99, 100, 103, 105, 109, 111, 113, 114, 115, 116, 117, 122, 125, 127, 129, 132, 133, 134, 135, 136, 137, 139, 140, 143, 144, 150, 151, 152, 155], "angular": 127, "ani": [56, 104, 105, 106, 114, 116, 129, 133, 135, 139, 142, 150, 155], "annot": [3, 4, 5, 17, 41, 61, 66, 68, 73, 78, 80, 82, 92, 94, 95, 113, 115, 125, 129, 131], "anoth": [109, 113, 125, 129, 144], "anticip": 146, "antonio": 110, "anywher": 65, "apart": 64, "api": 104, "appli": [125, 129], "applic": [110, 112, 146, 151], "approach": [113, 129, 150], "appropri": [139, 140], "approxim": [98, 129], "apt": 87, "ar": [12, 14, 18, 19, 41, 43, 65, 68, 77, 88, 89, 93, 94, 95, 99, 100, 103, 104, 107, 109, 111, 112, 115, 117, 125, 127, 129, 131, 132, 133, 134, 135, 136, 137, 139, 140, 142, 144, 146, 150, 151, 152, 155], "arg": [90, 91, 92, 113, 115], "argmax": [129, 150], "argmin": [90, 91, 92], "argst": [65, 66, 67, 73, 78], "argument": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 65, 66, 73, 75, 77, 78, 80, 114, 115, 125, 129, 133, 139, 144, 145, 151, 152], "aris": [14, 144], "around": 112, "arrai": [67, 90, 91, 115], "articl": 87, "artificialcost": [17, 61, 94], "artur": 110, "ask": [12, 106, 108], "aspect": [129, 150], "assembl": 144, "assess": 101, "assign": [75, 77, 96, 125, 127, 129, 131, 152, 154], "assignment_": [94, 95, 125], "associ": [14, 65, 66, 73, 78, 113, 125, 133, 139], "assum": [14, 103, 105, 111, 112, 114, 116, 129, 131, 143, 144, 152, 155], "assumpt": [103, 150, 152], "attach": [114, 137, 152, 155], "attempt": [89, 129], "attribut": [69, 70, 74, 133, 139], "author": 116, "auto": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 66, 68, 70, 78, 80, 82, 90, 91, 92, 93, 94, 95, 97, 98, 99, 104, 106, 108, 111, 113, 114, 115, 116, 125, 129, 131, 133, 135, 137, 139, 140, 142, 144, 145, 146, 155], "autom": 110, "automat": [14, 18, 87, 89, 103, 104, 107, 109, 113, 116, 131, 139], "aux": 111, "aux_filenam": 111, "avail": [12, 89, 115, 125, 133, 139, 145], "avoid": [18, 109, 129], "ax": 113, "ayoub": 110, "b": [110, 113], "b_i": [103, 132, 137], "back": 151, "backend": 93, "badli": 129, "baena": 110, "bap": [94, 95, 125], "bar": [92, 98, 112, 116, 125, 151], "bard": [91, 110], "base": [103, 110, 117, 122, 127, 129, 132, 146, 155], "basic": [136, 143], "bbuild": 89, "bcp": 109, "becaus": [113, 129, 146], "becom": 150, "been": [12, 14, 56, 75, 77, 84, 105, 114, 125, 129, 138, 139, 145, 150], "befor": [104, 105, 125, 129], "begin": [14, 19, 70, 72, 74, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 103, 112, 113, 115, 116, 125, 127, 132, 137, 142, 146, 150, 151, 155], "behavior": [12, 68], "behaviour": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 84], "behind": [104, 108], "being": [12, 18, 19, 99, 100, 105, 125, 131, 144, 155], "belong": [137, 139], "below": 129, "benchmark": [104, 110], "bender": [14, 110, 151], "benders_cut": 146, "berlin": 110, "berthold": 110, "best": [0, 4, 7, 8, 12, 18, 19, 28, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 109, 131, 138, 139, 144, 145], "best_bound": [12, 19, 40, 42, 44], "best_obj": [12, 19, 40, 42, 44], "bestbound": [18, 32, 93, 98, 99, 129, 131, 144], "bestestim": [32, 93, 98, 99], "between": [75, 103, 133, 146, 150], "bewar": 129, "big": [90, 92, 113], "big_m": [92, 113], "bilevel": [104, 110, 113, 151, 152], "bin": 109, "binari": [63, 77, 93, 94, 95, 97, 98, 99, 104, 106, 108, 113, 125, 139, 142, 144, 145, 146, 151, 155], "blanco": 146, "bli": 109, "block": [12, 19, 87, 88, 127], "bo": [92, 110], "bobilib": [110, 112, 117], "book": 127, "bool": [0, 3, 4, 5, 6, 7, 8, 18, 21, 41, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 64, 65, 66, 69, 70, 71, 72, 73, 74, 78, 79, 80], "boston": 110, "both": [71, 129, 146, 150, 152], "bound": [0, 4, 7, 8, 12, 14, 17, 18, 19, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 77, 78, 80, 84, 94, 95, 96, 98, 99, 104, 113, 117, 127, 129, 131, 132, 138, 139, 144, 145], "box": 12, "branch": [12, 17, 18, 19, 65, 84, 96, 98, 99, 104, 110, 117, 125, 132, 144, 146, 151], "branch_and_bound": [94, 95, 104, 129, 131, 144], "branch_and_pric": [94, 104, 129], "branchandbound": [12, 17, 19, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 43, 61, 93, 94, 95, 98, 99, 129, 131, 142, 144], "branchandboundcallback": [12, 17, 18, 20, 21, 43, 61], "branchandboundcallbackfactori": [17, 18, 19, 21, 43, 61], "branching_rul": [129, 144], "branchingrul": [33, 34, 35, 36, 37, 38], "branchingrulefactori": 18, "branchingrulefactoryt": 18, "breadthfirst": 32, "break": [94, 112], "breath": 87, "build": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 94, 104], "build_exampl": 109, "build_test": 89, "built": [75, 77, 87, 88, 105, 106], "bunch": [87, 88], "burden": 129, "busi": 110, "button": 87, "c": [14, 87, 89, 97, 98, 99, 103, 104, 105, 109, 113, 129, 132, 135, 137, 142, 146], "c_": [94, 95, 125], "c_0": [132, 135, 137], "c_1": 135, "c_i": [94, 95, 125], "caderno": 110, "call": [12, 18, 19, 65, 89, 93, 97, 104, 105, 109, 111, 113, 115, 125, 129, 131, 133, 137, 139, 142, 144, 145, 146, 150, 151, 152, 155], "callack": 142, "callback": [11, 13, 14, 15, 18, 19, 23, 24, 25, 53, 83, 84, 93, 94, 95, 98, 99, 117, 132, 143, 146], "callbackasbranchandboundcallback": [19, 20], "callbackev": [12, 19, 84, 142], "callbackfactori": [0, 8, 11, 12, 14, 15, 16, 18, 23, 24, 25, 49, 51, 142, 146], "callbacki": 12, "can": [0, 4, 7, 8, 12, 14, 18, 19, 41, 43, 48, 49, 50, 51, 56, 57, 58, 59, 60, 64, 65, 68, 80, 87, 89, 97, 98, 99, 100, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 125, 127, 129, 131, 133, 134, 135, 136, 137, 138, 139, 140, 142, 144, 145, 146, 150, 151, 152, 155], "candid": 129, "cannot": [1, 9, 12, 19, 54, 55, 89, 142, 144], "capac": [93, 94, 95, 97, 98, 99, 100, 104, 125, 142, 145, 146, 155], "capacit": [93, 100], "capacity_": [94, 95, 125], "caption": 151, "captur": 89, "carefulli": 129, "case": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 99, 112, 115, 125, 129, 132, 139, 140, 142, 144, 145, 146, 150, 152, 155], "cast": 140, "castro": 110, "catch2": [88, 89], "catchorg": 89, "categori": 129, "caus": [105, 144], "cbc": [17, 61, 109], "cbegin": [70, 72, 74], "ccg": [150, 151, 152], "ccgsepar": [151, 152], "ccgstabil": 151, "cd": [89, 105, 109], "cdot": [132, 137], "cend": [70, 72, 74], "center": 151, "certain": 12, "certif": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 133, 145], "cgl": 109, "chang": [19, 64, 105, 139], "chapter7": 125, "char": [90, 91, 92, 93, 94, 95, 97, 98, 99, 106, 108], "character": 64, "check": [14, 19, 65, 90, 133, 139, 140, 142, 146, 150, 155], "child": [12, 18, 129, 142], "children": 18, "choic": 109, "choos": [107, 112, 129], "circumv": 112, "clang": 106, "class": [0, 1, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 129, 132, 133, 134, 135, 136, 137, 138, 142, 144, 145, 146, 150, 151], "classic": [105, 108, 112, 115, 146, 150, 155], "clear": [69, 70, 72, 74, 104, 150], "clear_al": 74, "clearli": [129, 150], "clone": [0, 4, 7, 8, 12, 13, 14, 15, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 56, 57, 58, 59, 60, 71, 80, 89, 142], "close": 64, "closer": 64, "closest": [64, 129], "clp": [56, 109], "cmake": [87, 89, 104, 105, 106, 107, 108], "cmake_cxx_standard": [106, 108], "cmake_install_prefix": 105, "cmake_minimum_requir": [106, 108], "cmakelist": [106, 108], "code": [65, 68, 87, 88, 104, 113, 114, 115, 116, 129, 133, 134, 135, 137, 139, 140, 142, 144, 145, 151, 155], "codecov": [88, 89], "coeffici": 139, "coefficient_for_x_in_constraint": 133, "coefficient_for_y_in_constraint": 133, "coin": [17, 61, 96, 104, 112, 117], "coin_or": 109, "coin_or_dir": 109, "coin_or_hom": 109, "collect": 117, "color": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 88], "column": [77, 78, 96, 98, 99, 100, 104, 110, 117, 129, 131, 132, 139, 147, 150, 154, 155], "column_gener": [94, 95, 104, 125, 129, 131], "columnandconstraintgener": [151, 152], "columngener": 44, "columnori": 71, "com": [89, 108], "combin": [96, 104, 110, 114, 127, 129, 131], "combinatori": 110, "come": 109, "command": [87, 89, 105], "common": [12, 104, 113, 129, 133, 139, 140, 150], "commun": 152, "commutativepair": 74, "compact": [133, 139, 150], "compar": [64, 129], "compat": 104, "compil": [89, 105, 114], "complementar": 113, "complet": [105, 107, 108, 125, 147, 150, 151, 152, 154], "complex": [104, 144], "compliant": [12, 87], "complic": 146, "compon": 136, "comput": [64, 92, 102, 103, 105, 107, 108, 110, 129, 150], "computation": 129, "compute_smoothed_dual_solut": [45, 46], "concept": [117, 132, 136, 143, 145, 150], "condit": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 90, 113], "conditional_t": [70, 72, 74], "cone": 103, "configur": 109, "conic": 103, "consid": [14, 64, 93, 95, 98, 99, 100, 103, 112, 113, 114, 115, 116, 129, 144, 145, 146, 150, 152, 155], "consist": [12, 19, 70, 155], "const": [0, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 90, 91, 92, 93, 94, 95, 97, 98, 99, 104, 106, 108, 114, 125, 129, 131, 133, 135, 137, 139, 142, 144, 145, 146, 155], "const_iter": [70, 72, 74], "constant": [69, 75, 135, 146], "constexpr": 64, "constiteratorforward": 71, "constraint": [12, 14, 64, 65, 66, 75, 94, 95, 100, 103, 104, 110, 113, 115, 116, 117, 125, 127, 129, 131, 132, 134, 135, 136, 139, 142, 143, 144, 145, 147, 151, 154, 155], "constraint1": 139, "constraint1_coefficient_for_x": 139, "constraint2": 139, "constraint2_coefficient_for_x": 139, "constraint_1_4": 66, "construct": [66, 73, 78, 86, 147, 148], "constructor": [18, 66, 68, 75, 77, 78, 125, 133, 137, 138, 139, 142], "consumpt": [94, 125], "contact": 105, "contain": [18, 75, 77, 97, 103, 109, 110, 111, 125, 127, 135, 155], "content": [87, 92, 132], "context": 129, "continu": [18, 63, 70, 77, 78, 90, 92, 95, 98, 99, 113, 125, 131, 132, 133, 139, 140, 142, 144, 145, 146, 155], "continuous_relax": 144, "continuousrelax": [18, 19, 48, 49, 50, 51, 56, 57, 58, 59, 60, 93, 94, 95, 125, 129, 131, 144], "contrari": 152, "control": [12, 68, 99, 100, 134, 151, 155], "conveni": [129, 139], "convent": [150, 155], "converg": [12, 127, 152], "convers": 103, "convert": [18, 103], "convex": [90, 103, 110], "cooper": 112, "coordin": 94, "copi": [0, 4, 7, 8, 12, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 71, 75, 77, 80, 87, 105, 142], "copybutton": 87, "correctli": 105, "correspond": [19, 94, 113, 125, 133, 139, 145, 146], "cost": [64, 93, 94, 95, 98, 99, 100, 125, 139, 155], "could": [90, 98, 99, 104, 113, 139, 140, 145], "coupl": [116, 154], "cours": [108, 114], "cout": [12, 19, 65, 66, 71, 78, 90, 91, 92, 93, 94, 95, 97, 98, 99, 114, 116, 135, 137, 139, 142, 145, 152], "cover": 143, "cover_cut": 146, "coverag": 88, "cplex": [17, 61, 104, 109], "cpp": [106, 108], "creat": [0, 4, 7, 8, 18, 19, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 65, 66, 68, 70, 75, 77, 78, 80, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 104, 105, 106, 109, 111, 114, 115, 116, 117, 129, 132, 134, 135, 136, 138, 143, 144, 145, 146, 155], "create_osi_solver_interfac": [56, 57, 58, 59, 60], "creation": 144, "crtp": 18, "crucial": [125, 129], "ctr": [3, 5, 6, 17, 52, 53, 61, 65, 68, 71, 73, 75, 77, 78, 79, 82, 125, 133, 135, 137, 139, 145, 155], "ctrtype": [17, 19, 61, 64, 66, 71, 73, 75, 76], "ctrversion": 66, "cup": 151, "current": [0, 4, 7, 8, 12, 14, 18, 19, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 64, 80, 88, 104, 112, 129, 144, 146], "custom": [12, 18, 96, 98, 99, 100, 105, 107, 155], "cut": [12, 14, 17, 19, 20, 61, 110, 117, 127, 132, 143], "cutsepar": [12, 14, 15], "cx": 113, "cycl": 145, "d": [103, 105, 110, 113, 132, 137], "d_j": [93, 98, 99, 100, 155], "daniel": 110, "dantzig": [41, 94, 95, 110, 117, 127, 131, 132], "dantzigwolf": [17, 41, 44, 47, 61, 94, 95, 125, 129, 131], "dantzigwolfedecomposit": [17, 40, 42, 43, 61, 94, 95, 125, 129, 131], "data": [64, 93, 94, 95, 97, 98, 99, 110, 125, 132, 137, 152, 155], "dbuild_exampl": 109, "dbuild_test": 89, "dcoin_or_dir": 109, "de": [110, 135], "deal": [132, 145], "death": [68, 134], "decid": 129, "decis": [96, 104, 112, 125, 129, 132, 133, 137, 138, 139, 150, 151], "declar": [64, 129], "decltyp": 64, "declval": 64, "decompos": 129, "decomposit": [14, 41, 65, 95, 103, 110, 127, 129, 131, 146, 151], "dedic": [56, 105, 108, 142, 146, 150], "default": [12, 13, 14, 18, 19, 20, 23, 24, 25, 33, 34, 35, 36, 37, 38, 41, 43, 48, 49, 50, 51, 56, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 87, 89, 92, 95, 105, 108, 109, 113, 115, 125, 129, 142, 146, 151, 155], "default_valu": 65, "defaultnodeinfo": [18, 21, 43, 94], "defin": [12, 64, 90, 91, 92, 98, 100, 108, 109, 112, 129, 131, 137, 138, 142, 146, 150, 154], "definit": [12, 14, 108, 154], "degre": 18, "dei": 125, "deigen_dir": 109, "delet": [0, 8, 18, 43, 48, 49, 50, 51, 56, 71, 80], "delta": 151, "delta_j": 129, "demand": [93, 98, 99, 100, 155], "demonstr": 117, "denot": [14, 97, 103, 112, 125, 129, 150], "depend": [0, 4, 7, 8, 18, 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78, 87, 94, 95, 105, 109, 117, 125, 132, 136, 137, 139, 155], "equal": [18, 62, 64, 125, 129], "equalto": 133, "equat": 101, "equival": [75, 96, 109, 115, 133, 139, 150, 155], "error": [105, 140], "essec": 110, "essenti": [14, 68], "estim": [28, 129], "evalu": [129, 155], "even": [90, 106, 139], "event": [12, 19, 83, 85, 142], "eventu": 68, "everi": [12, 18, 68, 89, 104, 125, 134, 136, 142], "exactli": [94, 125, 151], "exampl": [0, 4, 7, 8, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 66, 75, 77, 78, 80, 90, 91, 92, 94, 95, 98, 99, 100, 106, 108, 113, 125, 129, 136, 137, 138, 139, 147, 152, 154], "example_knapsack": 109, "exceed": 97, "except": [66, 73, 78, 140, 144, 155], "execept": 103, "execut": [0, 4, 7, 8, 12, 18, 19, 40, 41, 42, 44, 48, 49, 50, 51, 56, 57, 58, 59, 60, 68, 80, 84, 106, 108, 134, 146], "exist": [12, 14, 19, 89, 104, 112, 116, 136, 150, 152], "expect": [103, 125], "expens": 129, "explain": [87, 89, 129], "explicit": [0, 3, 4, 7, 8, 14, 15, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 41, 43, 45, 46, 52, 53, 67, 71, 72, 79, 80, 82], "explicitli": [108, 133, 139, 146, 150], "exploit": [18, 104, 127], "explor": [12, 18, 19, 127], "exponenti": 125, "exportbranchandboundtreetocsv": [19, 20], "expos": 140, "expr": [76, 135], "express": [70, 75, 99, 100, 103, 117, 132, 133, 136, 138, 146, 155], "extend": [116, 127, 145], "extens": 87, "extern": [0, 4, 7, 8, 11, 17, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 64, 80, 91, 104, 105, 106, 108, 111, 117, 132, 137, 143], "extra": 139, "f": [103, 110, 112, 113, 116, 150, 151], "f1": 90, "f2": 90, "f3": 90, "f4": 90, "f_i": [93, 98, 99, 100, 155], "facil": [96, 147, 154], "fact": [104, 146], "factor": 151, "factori": [0, 4, 7, 8, 12, 18, 41, 44, 48, 49, 50, 51, 56, 57, 58, 59, 60, 80, 93, 94, 95, 98, 99, 114, 125, 131, 140, 142, 144, 145, 146], "fail": 145, "fall": 129, "fals": [0, 4, 7, 8, 18, 41, 48, 49, 50, 51, 56, 57, 58, 59, 60, 65, 66, 71, 73, 78, 80, 94, 95, 99], "familiar": [18, 115, 145, 155], "faq": 104, 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sek.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/external-solvers/Osi.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/external-solvers/Osi/OsiCbc.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/external-solvers/Osi/OsiClp.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/external-solvers/Osi/OsiCplex.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/external-solvers/Osi/OsiSymphony.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/index.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/misc/CtrType.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/misc/VarType.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/misc/tolerances.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Annotation.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Ctr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Dim.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Env.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Expr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/LinExpr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Model.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Point.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/QCtr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/QuadExpr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/TempCtr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/TempQCtr.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/TempVar.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/modeling/Var.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/padm/Optimizers_PADM.htmlhttps://hlefebvr.github.io/idol/en/api/mixed-integer/padm/PADM.htmlhttps://hlefebvr.github.io/idol/en/api/robust/index.htmlhttps://hlefebvr.github.io/idol/en/api/robust/modeling/Description.htmlhttps://hlefebvr.github.io/idol/en/api/types/index.htmlhttps://hlefebvr.github.io/idol/en/api/types/universal-callbacks/CallbackEvent.htmlhttps://hlefebvr.github.io/idol/en/api/types/universal-callbacks/index.htmlhttps://hlefebvr.github.io/idol/en/benchmark/index.htmlhttps://hlefebvr.github.io/idol/en/developer_guide/build-the-doc.htmlhttps://hlefebvr.github.io/idol/en/developer_guide/index.htmlhttps://hlefebvr.github.io/idol/en/developer_guide/tests.htmlhttps://hlefebvr.github.io/idol/en/examples/bilevel-kkt.htmlhttps://hlefebvr.github.io/idol/en/examples/bilevel-mibs.htmlhttps://hlefebvr.github.io/idol/en/examples/bilevel-pessimistic.htmlhttps://hlefebvr.github.io/idol/en/examples/facility-location-problem.htmlhttps://hlefebvr.github.io/idol/en/examples/generalized-assignment-problem-bap.htmlhttps://hlefebvr.github.io/idol/en/examples/generalized-assignment-problem-penalty-bap.htmlhttps://hlefebvr.github.io/idol/en/examples/index.htmlhttps://hlefebvr.github.io/idol/en/examples/knapsack-problem.htmlhttps://hlefebvr.github.io/idol/en/examples/robust-adr.htmlhttps://hlefebvr.github.io/idol/en/examples/robust-determistic.htmlhttps://hlefebvr.github.io/idol/en/examples/two-stage-robust-facility-location-problem.htmlhttps://hlefebvr.github.io/idol/en/faq/gap.htmlhttps://hlefebvr.github.io/idol/en/faq/index.htmlhttps://hlefebvr.github.io/idol/en/faq/mosek-and-eigen.htmlhttps://hlefebvr.github.io/idol/en/index.htmlhttps://hlefebvr.github.io/idol/en/installation/global-installation/index.htmlhttps://hlefebvr.github.io/idol/en/installation/global-installation/linking.htmlhttps://hlefebvr.github.io/idol/en/installation/index.htmlhttps://hlefebvr.github.io/idol/en/installation/local_installation.htmlhttps://hlefebvr.github.io/idol/en/installation/options.htmlhttps://hlefebvr.github.io/idol/en/references.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/files.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/index.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/kkt.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/mibs.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/modeling.htmlhttps://hlefebvr.github.io/idol/en/tutorials/bilevel-optimization/pessimistic.htmlhttps://hlefebvr.github.io/idol/en/tutorials/index.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/create-callback.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/create-node.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/index.htmlhttps://hlefebvr.github.io/idol/en/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.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\ No newline at end of file diff --git a/tutorials/bilevel-optimization/files.html b/tutorials/bilevel-optimization/files.html new file mode 100644 index 000000000..e05f4d999 --- /dev/null +++ b/tutorials/bilevel-optimization/files.html @@ -0,0 +1,293 @@ + + + + + + + Reading and Writing Bilevel Instances (BOBILib) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Reading and Writing Bilevel Instances (BOBILib)

    +

    BOBILib is a library of instances for bilevel optimization problems. +In this tutorial, we will show how to read and write bilevel instances in the format which is used by BOBILib. +The advantage is twofold. First, we can easily access a large number of bilevel instances. +Second, we can easily share our bilevel instances with others.

    +

    Let’s get started!

    + +
    +

    The Format

    +

    The instances in BOBILib are stored in two files:

    +
      +

    • An .mps or .lp file containing the high-point relaxation of the bilevel problem,

      • +

    • An .aux file containing the description of the lower-level problem.

      • +
    +

    For more details, we refer to the report [12].

    +
    +
    +

    Implementation

    +
    +

    Reading Instances

    +

    Reading a BOBILib instance is straightforward. We can use the Bilevel::read_from_file function. +However, it requires an underlying solver to parse the .mps file. Here, we will use Gurobi.

    +
    Env env;
+auto [model, description] =
+    Bilevel::read_from_file<Gurobi>(env, aux_filename);
+
    +
    +

    The function returns a pair made by the high-point relaxation model and the description of the lower-level problem.

    +
    +
    +

    Writing Instances

    +

    Assume that you have a bilevel model model and a description description for the lower-level problem. +Writing this problem to file can be done by a single call to Bilevel::write_to_file. +Here, no external solver is necessary.

    +
    /*
+    the following creates two files:
+    - instance-filename.mps
+    - instance-filename.aux
+*/
+Bilevel::write_to_file(model, description, "instance-filename");
+
    +
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/bilevel-optimization/index.html b/tutorials/bilevel-optimization/index.html new file mode 100644 index 000000000..e9d181a86 --- /dev/null +++ b/tutorials/bilevel-optimization/index.html @@ -0,0 +1,289 @@ + + + + + + + Bilevel Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Bilevel Optimization

    +

    Bilevel optimization is a field of mathematical optimization in which two optimization problems are intertwined: the +upper-level and the lower-level problem. The upper-level problem minimizes a given objective function taking into account +the solution to the lower-level problem, which is parameterized by the upper-level’s decision. Such problems have many +applications in, e.g., economics where it is used to model non-cooperative games.

    +

    A classic model for a bilevel problem is as follows.

    +
    +(1)\[\begin{split}\begin{align} + \text{''}\min_{x}\text{''} \quad & F(x,y) \\ + \text{s.t.} \quad & G(x,y) \ge 0, \\ + & x\in X, \\ + & y\in S(x), +\end{align}\end{split}\]
    +

    in which \(S(x)\) denotes the solution set of the lower-level problem, which is parameterized by the upper-level decision +\(x\). The lower-level problem is defined as

    +
    +\[\begin{split}\begin{align} + \min_{y} \quad & f(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y. +\end{align}\end{split}\]
    +

    Note that the quotes around the \(\min\) operator in (1) is here to highlight that the problem is +ill-defined in its current form. Indeed, in case multiple solutions to the lower-level problem exist, the upper-level problem +has to somehow “choose” one of them. To circumvent this, we typically consider the optimistic setting, where the lower-level +is assumed to pick the solution in favor of the upper-level problem, in order to break ties.

    +

    Optimistic bilevel problems can be modeled as:

    +
    +\[\begin{split}\begin{align} + \min_{x,y} \quad & F(x,y) \\ + \text{s.t.} \quad & G(x,y) \ge 0, \\ + & x\in X, \\ + & y\in S(x), +\end{align}\end{split}\]
    +

    Note that there exists other notions such as pessimistic bilevel problems. There, the lower-level problem is assumed to pick +the worst solution for the upper-level problem. This can be modeled as follows.

    +
    +\[\begin{split}\begin{align} + \min_{x} \quad & \max_{ y\in S(x) } \ F(x,y) \\ + \text{s.t.} \quad & G(x,\bar y) \ge 0, \quad \text{for all } \bar y\in S(x), \\ + & x\in X, \\ + & S(x) \neq \emptyset. + \end{align}\end{split}\]
    +

    Pessimisitc bilevel problems are less studied in the literature.

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/bilevel-optimization/kkt.html b/tutorials/bilevel-optimization/kkt.html new file mode 100644 index 000000000..7abfbf995 --- /dev/null +++ b/tutorials/bilevel-optimization/kkt.html @@ -0,0 +1,408 @@ + + + + + + + Deriving Single-level Reformulations + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Deriving Single-level Reformulations

    +

    A standard technique for solving LP-LP bilevel problems is to reformulate the problem as a single-level problem. +This can be done in several ways. In this tutorial, we will show how we can use idol to derive the +Karush-Kuhn-Tucker (KKT) reformulation and the strong-duality reformulation of a bilevel problem.

    +

    Let’s get started!

    + +
    +

    Problem Formulation

    +

    Consider the following bilevel optimization problem:

    +
    +\[\begin{split}\begin{align} + \min_{x,y} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & y \in \text{arg min} \{ f^\top y : Dy \ge b - Cx \}. +\end{align}\end{split}\]
    +

    In order to solve problem (1) with a standard optimization solver, we need to reformulate it as a single-level optimization problem. +This can be automatically done by idol using the KKT reformulation or the strong-duality reformulation.

    +

    For this tutorial, we will work on the following code snippet:

    +
    Env env;
+
+Model high_point_relaxation(env);
+
+auto x = high_point_relaxation.add_var(0, Inf, Continuous, 0., "x");
+auto y = high_point_relaxation.add_var(-Inf, Inf, Continuous, 0., "y");
+
+high_point_relaxation.set_obj_expr(x + 6 * y);
+auto lower_c1 = high_point_relaxation.add_ctr(2 * x - y >= 0);
+auto lower_c2 = high_point_relaxation.add_ctr(-x - y >= -6);
+auto lower_c3 = high_point_relaxation.add_ctr(-x + 6 * y >= -3);
+auto lower_c4 = high_point_relaxation.add_ctr(x + 3 * y >= 3);
+high_point_relaxation.add_ctr(-x + 5 * y <= 12.5);
+
+Bilevel::Description description(env);
+description.set_lower_level_obj(-y);
+description.make_lower_level(y);
+description.make_lower_level(lower_c1);
+description.make_lower_level(lower_c2);
+description.make_lower_level(lower_c3);
+description.make_lower_level(lower_c4);
+
    +
    +

    Here, a bilevel problem is modeled with idol. The high point relaxation is stored in high_point_relaxation, while +the lower-level problem is described using the Bilevel::Description object description.

    +
    +
    +

    The KKT Reformulation

    +

    The KKT reformulation of a bilevel problem is obtained by replacing the lower-level problem with its KKT optimality conditions. +The KKT reformulation of the bilevel problem is as follows:

    +
    +(1)\[\begin{split}\begin{align} + \min_{x,y,\lambda} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & Dy \ge b - Cx, \\ + & D^\top \lambda = f, \; \lambda \ge 0, \\ + & \lambda^\top (b - Cx - Dy) = 0. +\end{align}\end{split}\]
    +
    +

    Getting the Reformulated Model

    +

    With idol, it is possible to generate the KKT reformulation of the bilevel problem using the Bilevel::KKT::make_model function.

    +

    For instance, one could do the following.

    +
    auto single_level_model = Bilevel::KKT::make_model(
+    high_point_relaxation, description
+    );
+
    +
    +

    Then, one can solve the single-level model using a standard optimization solver. Here, we use Gurobi.

    +
    single_level.use(Gurobi());
+single_level.optimize();
+
    +
    +

    Note that the KKT reformulation (1), and thus single_level, is a nonlinear problem because of the complementarity constraint. +Hence, we use the nonlinear solving features of Gurobi here.

    +

    A common approach to handle the complementarity constraints is to linearize them by introducing binary variables. +This can also be done in idol. To do this, we will need to provide some valid bounds on the dual variables. +This is done by annotating the lower-level problem constraints. The constraints associated with the variables +bounds can also have their big-M values by annotating the corresponding variable.

    +

    In the following code, we will simply use a default value for the big-M values of \(10^{4}\).

    +
    Annotation<double> big_M(env, "big_M", 1e4);
+auto single_level_model = Bilevel::KKT::make_model(
+        high_point_relaxation, description, big_M
+        );
+
    +
    +

    The returned model is now a mixed-integer linear program that can be solved using a standard optimization solver.

    +

    Now, say that constraint lower_c1 is known to have a dual variable bounded by, say, 10. One could do the following.

    +
    Annotation<double> big_M(env, "big_M", 1e4);
+lower_c1.set(big_M, 10);
+
+auto single_level_model = Bilevel::KKT::make_model(
+        high_point_relaxation, description, big_M
+        );
+
    +
    +
    +
    +

    Solving the KKT Reformulation directly

    +

    In the previous section, we showed how to generate the KKT reformulation of a bilevel problem. +However, idol also provides a function to solve the KKT reformulation directly. +This can be done by using the Bilevel::KKT optimizer.

    +

    Here is a code snippet that shows how to solve the KKT reformulation directly.

    +
    high_point_relaxation.use(Bilevel::KKT(description) + Gurobi());
+
    +
    +

    Note that big-M values can also be provided to the Bilevel::KKT optimizer. Here is an example.

    +
    high_point_relaxation.use(
+    Bilevel::KKT(description)
+        .with_single_level_optimizer(Gurobi())
+        .with_big_M(big_M)
+);
+
    +
    +

    Calling the optimize method on the model will solve the KKT reformulation of the bilevel problem.

    +
    +
    +
    +

    The Strong-duality Reformulation

    +

    Another single-level reformulation is the so-called strong-duality reformulation which reads

    +
    +\[\begin{split}\begin{align} + \min_{x,y,\lambda} \quad & c^\top x + d^\top y \\ + \text{s.t.} \quad & Ax + By \ge a, \\ + & Dy \ge b - Cx, \\ + & D^\top \lambda = f, \; \lambda \ge 0, \\ + & f^\top y \le (b - Cx)^\top \lambda. +\end{align}\end{split}\]
    +
    +

    Getting the Reformulated Model

    +

    The strong-duality reformulation can be obtained using the Bilevel::StrongDuality::make_model function. +This function works similarly to the Bilevel::KKT::make_model function. +Here is an example.

    +
    auto single_level_model = Bilevel::StrongDuality::make_model(
+    high_point_relaxation, description
+    );
+single_level_model.use(Gurobi());
+single_level_model.optimize();
+
    +
    +

    Note that here, the strong-duality reformulation is a nonlinear problem because of the dual objective function. +Hence, we use the nonlinear solving features of Gurobi here.

    +
    +
    +

    Solving the Strong-duality Reformulation directly

    +

    Similarly to the KKT reformulation, idol also provides a function to solve the strong-duality reformulation directly. +This can be done by using the Bilevel::StrongDuality optimizer as follows.

    +
    high_point_relaxation.use(
+    Bilevel::StrongDuality(description) + Gurobi()
+);
+high_point_relaxation.optimize();
+
    +
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/bilevel-optimization/mibs.html b/tutorials/bilevel-optimization/mibs.html new file mode 100644 index 000000000..b700b8d2a --- /dev/null +++ b/tutorials/bilevel-optimization/mibs.html @@ -0,0 +1,296 @@ + + + + + + + Solving Mixed-Integer Bilevel Problems with coin-or/MibS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving Mixed-Integer Bilevel Problems with coin-or/MibS

    +

    MibS is an optimization solver for mixed-integer bilevel problems; for more information, please refer to the MibS website. +Idol seamlessly interfaces with MibS to solve bilevel problems.

    +

    We will see that solving bilevel problems with MibS is very similar to solving any optimization problem in idol.

    + +
    +

    Setup

    +

    We will assume that you have your bilevel problem already modeled in idol. In particular, we consider that you have +two variables:

    +
      +

    1. high_point_relaxation which is a Model representing the high-point relaxation of your bilevel problem.

      2. +

    2. description which is a Bilevel:Description object representing the bilevel problem. If you do not know what this is or how to create it, please refer to the previous tutorial.

      3. +
    +
    +
    +

    Using MibS

    +

    To solve your bilevel problem, you can use the MibS optimizer factory as follows:

    +
    high_point_relaxation.use(Bilevel::MibS(description));
+
+high_point_relaxation.optimize();
+
+std::cout << save_primal(high_point_relaxation) << std::endl;
+
    +
    +

    Notice how the MibS optimizer factory is attached to the high-point relaxation model and that the bilevel description +is passed as an argument.

    +

    The rest of the code is the same as with any other solver.

    +
    +

    Hint

    +

    To use MibS, you need to have the MibS library installed on your system and idol linked against it. +You can download MibS from here.

    +

    Then, idol should be compiled with the options USE_MIBS=YES, USE_CLP=YES.

    +
    +
    +
    +

    Using CPLEX for Feasibility Check

    +

    Note that it is also possible to use MibS in combination with CPLEX for the feasibility check. This can be done as follows:

    +
    const auto mibs = Bilevel::MibS(description)
+                    .with_cplex_for_feasibility(true)
+                    .with_time_limit(3600)
+                    .with_logs(true);
+
+high_point_relaxation.use(mibs);
+
+high_point_relaxation.optimize();
+
+std::cout << save_primal(high_point_relaxation) << std::endl;
+
    +
    +

    Off course, MibS must have been installed with CPLEX for this to work.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/bilevel-optimization/modeling.html b/tutorials/bilevel-optimization/modeling.html new file mode 100644 index 000000000..d81719f76 --- /dev/null +++ b/tutorials/bilevel-optimization/modeling.html @@ -0,0 +1,354 @@ + + + + + + + Modeling a Bilevel Problem + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Modeling a Bilevel Problem

    +

    In this tutorial, we will see how to model a bilevel problem in idol.

    +

    To follow this tutorial, you should be familiar with bilevel optimization and modeling optimization problems in idol. +If this is not the case, we recommend you to read the tutorial on MIP modeling.

    + +
    +

    Problem Definition and Main Steps

    +

    We consider the optimistic bilevel problem

    +
    +\[\begin{split}\begin{align} + \min_{x, y} \quad & -x + -10 y \\ + \text{s.t.} \quad & x \in \mathbb Z_{\ge 0} \\ + & y\in + \begin{array}[t]{rl} + \displaystyle \underset{y}{\text{arg min}} \quad & y \\ + \text{s.t.} \quad & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_{\ge 0}. + \end{array} +\end{align}\end{split}\]
    +

    This is an ILP-ILP bilevel problem which is taken from [10] (Example 1).

    +

    To model this problem in idol, there are three main steps:

    +
      +

    1. Define the high-point relaxation (HPR) model,

      2. +

    2. Describe which variables and constraints are part of the lower-level problem,

      3. +

    3. Define the lower-level objective function.

      4. +
    +
    +
    +

    Modeling the High-Point Relaxation

    +

    The HPR can be modeled in the same way as a classical optimization problem. +If you are not familiar with modeling optimization problems in idol, +we recommend you to read the tutorial on MIP modeling.

    +

    In our example, the HPR reads

    +
    +\[\begin{split}\begin{align} + \min_{x, y} \ & -x + -10 y \\ + \text{s.t.} \ & x \in \mathbb Z_+ \\ + & -25 x + 20 y \leq 30, \\ + & x + 2 y \leq 10, \\ + & 2 x - y \leq 15, \\ + & 2 x + 10 y \geq 15, \\ + & y \geq 0, \\ + & y \in \mathbb Z_+. +\end{align}\end{split}\]
    +

    Here is the code to model the HPR of the bilevel problem.

    +
    Env env;
+Model high_point_relaxation(env);
+
+auto x = high_point_relaxation.add_var(0, Inf, Integer, 0, "x");
+auto y = high_point_relaxation.add_var(0, Inf, Integer, 0, "y");
+
+high_point_relaxation.set_obj_expr(-x - 10 * y);
+auto lower_c1 = high_point_relaxation.add_ctr(-25*x + 20*y <= 30);
+auto lower_c2 = high_point_relaxation.add_ctr(x + 2 * y <= 10);
+auto lower_c3 = high_point_relaxation.add_ctr(2 * x - y <= 15);
+auto lower_c4 = high_point_relaxation.add_ctr(2 * x + 10 * y >= 15);
+
    +
    +
    +
    +

    Describing the Lower-Level Problem

    +

    To describe the lower-level problem, we need to specify which variables and constraints are part of it. +This is done by creating an object of type Bilevel::Description and calling the methods make_lower_level.

    +
    Bilevel::Description description(env);
+description.make_lower_level(y);
+description.make_lower_level(lower_c1);
+description.make_lower_level(lower_c2);
+description.make_lower_level(lower_c3);
+description.make_lower_level(lower_c4);
+
    +
    +

    Note that this does nothing more but to create a new Annotation<unsigned int> to indicate variables and constraints that are part of the lower-level problem. +These annotations are used by the bilevel solvers to identify the lower-level problem. +In particular, all variables and constraints that are not annotated as lower-level variables or constraints are considered as upper-level variables or constraints, respectively. +Upper-level variables and constraints have an annotation which is set to MasterId by default.

    +

    Also note that it is possible to create and use your own annotation. For instance, the following code is equivalent to the previous one.

    +
    Annotation<unsigned int> lower_level(env, MasterId, "lower_level");
+
+y.set(lower_level, 0);
+lower_c1.set(lower_level, 0);
+lower_c2.set(lower_level, 0);
+lower_c3.set(lower_level, 0);
+lower_c4.set(lower_level, 0);
+
+
+Bilevel::Description description(lower_level);
+
    +
    +
    +
    +

    Defining the Lower-Level Objective Function

    +

    Finally, we need to define the lower-level objective function. +This is done by calling the method set_lower_level_obj on the object of type Bilevel::Description. +A QuadExpr object is passed as argument to this method.

    +
    description.set_lower_level_obj(y);
+
    +
    +
    +
    +

    Complete Example

    +

    A complete example is available here and uses the MibS solver.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/bilevel-optimization/pessimistic.html b/tutorials/bilevel-optimization/pessimistic.html new file mode 100644 index 000000000..dcbfa415a --- /dev/null +++ b/tutorials/bilevel-optimization/pessimistic.html @@ -0,0 +1,318 @@ + + + + + + + From Pessimistic Bilevel Optimization to Optimistic Bilevel Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    From Pessimistic Bilevel Optimization to Optimistic Bilevel Optimization

    +

    Most of the litereature on bilevel optimization focuses on the optimistic setting, where the lower-level problem is assumed to +pick the solution in favor of the upper-level problem. +However, there exists other notions such as pessimistic bilevel problems.

    +

    A pessimistic problem reads as follows:

    +
    +(1)\[\begin{split}\begin{align} + \min_{x} \quad & \max_{ y\in S(x) } \ F(x,y) \\ + \text{s.t.} \quad & x\in X, \\ + & S(x) \neq \emptyset, + \end{align}\end{split}\]
    +

    with \(S(x)\) the solution set of

    +
    +\[\begin{split}\begin{align} + \min_{y} \quad & f(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y. +\end{align}\end{split}\]
    +

    In this tutorial, we will show how a pessimistic bilevel problem can be automatically transformed into an optimistic bilevel problem. +This transformation is due to [16].

    +
    +

    Hint

    +

    Here, (1) does not have coupling constraints for simplicity. +However, the transformation can be extended to bilevel problems with coupling constraints.

    +
    + +
    +

    The Equivalent Optimistic Problem

    +

    In [16], the authors show that the pessimistic bilevel problem (1) is equivalent to the following optimistic bilevel problem:

    +
    +(2)\[\begin{split}\begin{align} + \min_{x,\bar y} \quad & F(x,y) \\ + \text{s.t.} \quad & x\in X, \ \bar y\in Y, \\ + & g(x,\bar y) \ge 0, \\ + & y\in \tilde S(x, \bar y), +\end{align}\end{split}\]
    +

    in which \(\tilde S(x, \bar y)\) is the solution set of

    +
    +\[\begin{split}\begin{align} + \min_y \quad & -F(x,y) \\ + \text{s.t.} \quad & g(x,y) \ge 0, \\ + & y\in Y, \\ + & f(x,y) \le f(x, \bar y). +\end{align}\end{split}\]
    +

    Note that (2) is an optimistic bilevel problem.

    +
    +
    +

    Implementation

    +

    Deriving the equivalent optimistic bilevel problem from a pessimistic bilevel problem can be done easily in idol.

    +

    To this end, let us assume that you have your bilevel problem already modeled in idol. In particular, let us consider that you have +two variables:

    +
      +

    1. high_point_relaxation which is a Model representing the high-point relaxation of your bilevel problem.

      2. +

    2. description which is a Bilevel:Description object representing the bilevel problem. If you do not know what this is or how to create it, please refer to the previous tutorial.

      3. +
    +

    Then, you can derive the equivalent optimistic bilevel problem as follows:

    +
    auto [opt_model, opt_description] =
+    Bilevel::PessimisticAsOptimistic::make_model(
+                                        high_point_relaxation,
+                                        description
+                                );
+
    +
    +

    Here, opt_model is the high-point relaxation of (2) and opt_description is the bilevel description of (2).

    +

    The rest of the code is the same as with any other solver. For instance, you can solve the optimistic bilevel problem with MibS as follows:

    +
    opt_model.use(Bilevel::MibS(opt_description));
+
+opt_model.optimize();
+
+std::cout << save_primal(opt_model) << std::endl;
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/index.html b/tutorials/index.html new file mode 100644 index 000000000..6731873cc --- /dev/null +++ b/tutorials/index.html @@ -0,0 +1,318 @@ + + + + + + + Tutorials + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Tutorials

    +

    On this page, you will find a collection of tutorials that demonstrate how to use idol to solve various optimization problems. +The tutorials are organized by topic.

    +
    +

    Mixed-Integer Optimization

    +
    + +
    +
    +
    +

    Bilevel Optimization

    +
    + +
    +
    +
    +

    Robust Optimization

    +
    + +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.html b/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.html new file mode 100644 index 000000000..47ba45f2c --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/create-branching-rule.html @@ -0,0 +1,221 @@ + + + + + + + Creating Your Own Branching Rule (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Creating Your Own Branching Rule (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/create-callback.html b/tutorials/mixed-integer-programming/branch-and-bound/create-callback.html new file mode 100644 index 000000000..5ade8545a --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/create-callback.html @@ -0,0 +1,221 @@ + + + + + + + Create Your Own Callback (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Create Your Own Callback (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.html b/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.html new file mode 100644 index 000000000..d7cb0888d --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/create-node-selection-rule.html @@ -0,0 +1,221 @@ + + + + + + + Creating Your Own Node Selection Rule (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Creating Your Own Node Selection Rule (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/create-node.html b/tutorials/mixed-integer-programming/branch-and-bound/create-node.html new file mode 100644 index 000000000..dc97130c7 --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/create-node.html @@ -0,0 +1,221 @@ + + + + + + + Creating Your Own Node Class (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Creating Your Own Node Class (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/index.html b/tutorials/mixed-integer-programming/branch-and-bound/index.html new file mode 100644 index 000000000..88f1c14de --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/index.html @@ -0,0 +1,248 @@ + + + + + + + Branch-and-Bound Algorithm + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Branch-and-Bound Algorithm

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.html b/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.html new file mode 100644 index 000000000..da6ac4cf4 --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/user-cuts-lazy-constraints.html @@ -0,0 +1,221 @@ + + + + + + + Adding User Cuts and Lazy Constraints [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Adding User Cuts and Lazy Constraints [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.html b/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.html new file mode 100644 index 000000000..d85c18a32 --- /dev/null +++ b/tutorials/mixed-integer-programming/branch-and-bound/write-branch-and-bound.html @@ -0,0 +1,245 @@ + + + + + + + Writing an LP-based Branch-and-Bound [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Writing an LP-based Branch-and-Bound [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.html b/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.html new file mode 100644 index 000000000..f27b34427 --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/dantzig-wolfe.html @@ -0,0 +1,432 @@ + + + + + + + Solving A Dantzig-Wolfe Reformulation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving A Dantzig-Wolfe Reformulation

    +

    In this tutorial, we will see how to implement a column generation algorithm to solve a continuous relaxation of the Generalized Assignment Problem (GAP). +This relaxation is obtained by relaxing the Dantzig-Wolfe reformulation of the GAP.

    +
    +

    Hint

    +

    This tutorial regards the advanced topic of Column Generation and Dantzig-Wolfe decomposition. +Rudimentary notions in the following subjects are recommended:

    + +
    +

    A complete example which includes branching is available here.

    + +
    +

    Problem Definition

    +

    Given a set of \(m\) agents and \(n\) jobs, the goal is to assign each job to exactly one agent in such a +way that the total cost is minimized, while respecting the capacity constraints of each agent.

    +

    Each agent \(i\in\{1,\dotsc,m\}\) has a capacity \(C_i\). +Each job \(j\in\{1,\dotsc,n\}\) has a resource consumption \(r_{ij}\) and a cost \(c_{ij}\) when assigned to agent \(i\).

    +
    +

    The Natural Formulation

    +

    We model the GAP with the following binary linear program:

    +
    +\[\begin{split}\begin{align*} + \min_{x} \quad & \sum_{i=1}^m \sum_{j=1}^n c_{ij} x_{ij} \\ + \text{s.t.} \quad & \sum_{j=1}^n r_{ij} x_{ij} \le C_i, && i=1,\dotsc,m, \\ + & \sum_{i=1}^m x_{ij} = 1, && j=1,\dotsc,n, \\ + & x_{ij} \in \{0,1\}, && i=1,\dotsc,m, j=1,\dotsc,n. +\end{align*}\end{split}\]
    +

    Here, variable \(x_{ij}\) encodes the assignment decision and equals 1 if and only if task \(j\) is assigned to +agent \(i\).

    +
    +
    +

    The Dantzig-Wolfe Reformulation

    +

    Let us enumerate the list of all feasible assignments, i.e., let

    +
    +\[\{\bar x^e_{ij} \}_{e\in E} = \left\{ x \in \{ 0,1 \}^{mn} : \sum_{j=1}^n r_{ij}x_{ij} \le C_i \quad i=1,...,m \right\},\]
    +

    in which \(E\) denotes a list for their indices.

    +

    The Dantzig-Wolfe reformulation of GAP reads

    +
    +(1)\[\begin{split}\min_{\lambda} \quad & \sum_{e\in E} \lambda_e\left( \sum_{i=1}^m\sum_{j=1}^n c_{ij}\bar x_{ij}^e \right) \\ +\textrm{s.t.} \quad & \sum_{e\in E} \lambda_e \left( \sum_{i=1}^m \bar x_{ij}^e \right) = 1 \quad j=1,...,n, \\ +& \sum_{e\in E} \lambda_e = 1, \\ +& \lambda_e \in \{ 0, 1 \} & \text{for all } e\in E.\end{split}\]
    +

    Though this model contains an exponential number of variables, it can be solved efficiently using +Column Generation and Branch-and-price. In such a case, the pricing problem is a Knapsack Problem.

    +

    In this tutorial, we focus on the continuous relaxation of (1).

    +
    +
    +
    +

    Automatic Reformulation

    +

    The simplest way to solve a problem using Column Generation and idol is through its automatic reformulation feature. +To use this, one simply needs to give the original space formulation of the problem +and to indicate which constraints should be moved to the pricing problem (here, the knapsack constraints).

    +

    We will start by modeling the problem in its natural form and then indicate which constraints should be moved to the pricing problem.

    +
    +

    The Natural Formulation

    +

    Before we start, we will use a GAP instance stored in a file. This file reads as follows.

    +
    3   8
+-27 -12 -12 -16 -24 -31 -41 -13
+-14  -5 -37  -9 -36 -25  -1 -35
+-34 -34 -20  -9 -19 -19  -3 -24
+21 13  9  5  7 15  5 24
+20  8 18 25  6  6  9  6
+16 16 18 24 11 11 16 18
+26 25 34
+
+http://www.or.deis.unibo.it/kp/Chapter7.pdf Example 7.3
+
    +
    +

    To read an instance of the GAP, we need to include the header file located in idol/mixed-integer/problems/generalized-assignment-problem/GAP_Instance.h.

    +

    Then, we can use the Problems::GAP::read_instance function to read the instance file.

    +
    const auto instance =
+        Problems::GAP::read_instance("assignment-bap.data.txt");
+
+const unsigned int n_agents = instance.n_agents();
+const unsigned int n_jobs = instance.n_jobs();
+
    +
    +

    We are now ready to model our problem (for more details, refer to this tutorial on modeling)

    +
    // Create optimization environment
+Env env;
+
+// Create model
+Model model(env);
+
+// Create assignment variables (x_ij binaries)
+auto x = model.add_vars(Dim<2>(n_agents, n_jobs), 0., 1., Binary, "x");
+
+// Create knapsack constraints (i.e., capacity constraints)
+for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+}
+
+// Create assignment constraints
+for (unsigned int j = 0 ; j < n_jobs ; ++j) {
+    model.add(idol_Sum(i, Range(n_agents), x[i][j]) == 1, "assignment_" + std::to_string(j));
+}
+
+// Set the objective function
+model.set_obj_expr(idol_Sum(i, Range(n_agents), idol_Sum(j, Range(n_jobs), instance.cost(i, j) * x[i][j])));
+
    +
    +
    +
    +

    Giving Decomposition Instructions

    +

    We are now at the crucial step of indicating which constraint should be moved to the pricing problem. In idol, this is done by using +annotations. Annotations are additional information associated to an optimization object (e.g., a constraint or a variable). +Note that annotations are global, i.e., they do not relate to a given optimization model.

    +

    Every annotation is formed with a template argument which is the value type of the annotation. Here, the Dantzig-Wolfe +decomposition expects an annotation with a value of type unsigned int and which corresponds +to the sub-problem index to which the constraint will be moved to.

    +

    We create the annotation as follows.

    +
    Annotation<unsigned int> decomposition(env, "decomposition", MasterId);
+
    +
    +

    Here, we pass three arguments to the constructor of Annotation<unsigned int>. First, we pass the optimization +environment which will store the annotation. Then, a name is given to the annotation: here, “decomposition”. +Finally, a default value is given and is set to MasterId. This will tell idol that constraints which have not been annotated +should remain in the master problem.

    +

    Now, observe how the annotation is applied to the capacity constraints.

    +
    for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    auto capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+    capacity.set(decomposition, i); // <== Annotating the capacity constraint
+}
+
    +
    +

    Here, the first capacity constraint is moved to the first pricing problem (id: 0), +the second constraint to the second pricing problem (id: 1), and so on.

    +

    Note that another decomposition would be materialized as follows.

    +
    for (unsigned int i = 0 ; i < n_agents ; ++i) {
+    Ctr capacity = model.add_ctr(idol_Sum(j, Range(n_jobs), instance.resource_consumption(i, j) * x[i][j]) <= instance.capacity(i), "capacity_" + std::to_string(i));
+    capacity.set(decomposition, 0); // <== Annotating the capacity constraint
+}
+
    +
    +

    Here, all the knapsack constraints would be moved to the same pricing problem (id: 0).

    +
    +
    +
    +

    Creating the Column Generation Algorithm

    +

    Now that the desired decomposition has been specified, we can set the desired optimizer to solve our model. +Here, we want to solve our the continuous relaxation of the Dantzig-Wolfe reformulation using column generation.

    +

    To begin with, we need to give some instructions about how each sub-problem will be solved. In other words, we need +to specify the optimizer(s) used for pricing during the column generation process. This is done by first creating a +DantzigWolfe::SubProblem object.

    +
    const auto sub_problem_specifications = DantzigWolfe::SubProblem()
+                                            .add_optimizer(Gurobi());
+
    +
    +

    Then, we can create the column generation algorithm (factory) in the following way.

    +
    const auto column_generation = DantzigWolfeDecomposition(decomposition)
+        .with_master_optimizer(Gurobi::ContinuousRelaxation())
+        .with_default_sub_problem_spec(sub_problem_specifications);
+
    +
    +

    We can now tell idol to use this algorithm for solving our model by using the Model::use method.

    +
    model.use(column_generation);
+
    +
    +
    +
    +

    Solving

    +

    As usual, one can simply call the Model::optimize method to solve the problem.

    +
    model.optimize();
+
    +
    +

    That’s it! The problem is being solved by column generation, and possibly branching on fractional variables.

    +

    The rest remains unchanged and one can retrieve the solution +through the usual methods such as Model::get_status and Model::get_var_primal.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.html b/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.html new file mode 100644 index 000000000..42cd86edb --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/in-out-stabilization.html @@ -0,0 +1,221 @@ + + + + + + + Using In-Out Stabilization [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using In-Out Stabilization [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/index.html b/tutorials/mixed-integer-programming/dantzig-wolfe/index.html new file mode 100644 index 000000000..abacbc331 --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/index.html @@ -0,0 +1,263 @@ + + + + + + + Column Generation and Branch-and-Price Algorithm + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Column Generation and Branch-and-Price Algorithm

    +

    Column generation is an algorithm used to solve large scale optimization problems which involve a large number of variables. +Instead of solving the problem in its entirety, column generation begins with a restricted version of the problem containing only a subset of variables. It then iteratively introduces new variables (or columns) that have the potential to improve the solution, based on the problem’s structure and constraints.

    +

    In practice, column generation is particularly effective for problems with block-angular structures, such as cutting stock, vehicle routing, and generalized assignment problems. The method splits the problem into a master problem, which handles the selection of variables, and a pricing problem, which identifies the most promising variables to add to the master problem. These subproblems are solved iteratively until no further improvements are possible.

    +
    +https://upload.wikimedia.org/wikipedia/commons/e/ec/DW_Block_Angular_Matrix.jpg + +
    +

    Block-angular matrix structure particularly suited for column generation.

    +
    +
    +

    The Branch-and-Price algorithm extends column generation to integer programming. While column generation operates on the linear relaxation of the problem, Branch-and-Price integrates it into a Branch-and-Bound framework to handle integer constraints. This combination allows efficient exploration of the solution space while exploiting the power of decomposition techniques. Each node of the Branch-and-Bound tree employs column generation to solve the relaxed problem, providing tight bounds for pruning and accelerating convergence.

    +

    In this series of tutorials, we will see how column generation and, more precisely, Dantzig-Wolfe decomposition can be implemented in idol.

    +
    +

    Hint

    +

    For more details on column generation, we refer to the book [13].

    +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.html b/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.html new file mode 100644 index 000000000..707a9eee6 --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/integer-master.html @@ -0,0 +1,221 @@ + + + + + + + The Integer Master Heuristic [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    The Integer Master Heuristic [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.html b/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.html new file mode 100644 index 000000000..df89257bc --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/strong-branching.html @@ -0,0 +1,417 @@ + + + + + + + Using Strong Branching + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using Strong Branching

    +

    Strong Branching is a technique that falls into the category of variable selection rules, a crucial aspect of +Branch-and-Bound algorithms.

    +

    More specifically, the task is to decide which variable to branch on at each node of the Branch-and-Bound tree, i.e, +among a set of branching candidates whose value must be integer, one must +decide which variable with fractional value in the current solution of the relaxation to choose for creating +child nodes.

    +

    The most common rule is the so-called Most-Infeasible rule, which selects a variable whose fractional +part is closest to 0.5. Unfortunately, this rule performs badly in practice. Most importantly, if solving a node is +computationally hard, it makes sense to spend some time in carefully choosing the variable to branch on. This is typically +the case when nodes are solved using Column Generation.

    +
    +

    Hint

    +

    Clearly, Strong Branching is not only used in the context of column generation. It is a general technique that can be +used in any context where solving a node is computationally expensive. Thus, this tutorial is not specific to the +context of column generation, though we will use it as an example.

    +
    +

    The idea of Strong Branching is to evaluate the effect of branching on a variable before branching actually happens.

    + +
    +

    Formal Definition

    +

    Let \(C\) be a set of indices for branching candidates at a given node, i.e., for each \(j\in C\), +\(x_j\) is an integer variable in the original problem but with \(x_j^*\notin\mathbb Z\) at the current node. +Strong Branching tries to evaluate the effect of applying branching constraints \(x_j \le \lfloor x_j^* \rfloor\) and +\(x_j \ge \lceil x_j^* \rceil\) to the current node. To do so, it solves, before branching happens, and for each \(j\in C\), +both the left and right child node. Let \(z_i^\le\) and \(z_i^\ge\) denote the (optimal) value of the +left and right nodes if branching is performed on \(x_j\). The “effect of branching on \(x_j\)” is then estimated by +computing a score, noted \(\text{Score}(j)\), based on \(z_j^\le\) and \(z_j^\ge\). Then Strong Branching +selects the variable with an index \(j^*\) such that (for minimization problems)

    +
    +\[j^* \in \text{argmax}\{ \text{Score}(j) : j\in C \}.\]
    +

    Empirically, Strong Branching is known to produce substantially smaller Branch-and-Bound trees compared to other +branching rules. Unfortunately, computing \(\text{Score}(j)\) typically requires a lot of time. To avoid this, +several techniques have been designed such as Restricted Strong Branching and Strong Branching with Phases (see below).

    +

    For more details, please refer to [1].

    +
    +

    Scoring Functions

    +

    Two common scoring functions \(\text{Score}(j)\) are found in the literature. The linear formula [9]

    +
    +\[\text{LinearScore}(j) := (1 - \mu) \min(\Delta_j^\le, \Delta_j^\ge) + \mu \max(\Delta_j^\le, \Delta_j^\ge),\]
    +

    and the product formula

    +
    +\[\text{ProductScore}(j) := \max(\Delta_j^\le, \varepsilon) \max(\Delta_j^\ge, \varepsilon),\]
    +

    in which \(\Delta_j^\le := z_j^\le - z^*\) and \(\Delta_j^\ge := z_j^\ge - z^*\) with \(z^*\) denoting the +(optimal) value of the current node. Parameters \(\mu\in[0,1]\) and \(\varepsilon > 0\) are given. +In idol, \(\mu = 1/6\) and \(\varepsilon = 10^{-6}\).

    +
    +
    +

    Variants

    +

    There are several variants of Strong Branching. The most common ones are:

    +
      +

    • Full Strong Branching denotes the standard Strong Branching rule which solves all \(2|C|\) nodes at each branching +decision. The drawback of this approach is that it may take a lot of time to solve all these sub-problems before branching +actually happens.

      • +

    • Restricted Strong Branching is an attempt to reduce the computational burden of Full Strong Branching. The idea is to +consider only a maximum of \(K\) branching candidates at each branching decision instead of the whole set \(C\). +Thus, \(C\) is replaced by a smaller set \(R\subseteq C\) such that \(|R| = K\) with \(K\) fixed. +The “restricted branching candidate set” \(R\) is created by taking the \(K\) first variables selected by, yet +another, branching rule, e.g., the most-infeasible rule.

      • +

    • Strong Branching with Look Ahead is similar to Restricted Strong Branching yet differs from it by not specifying a +fixed size for the “restricted branching candidate set” \(R\). Instead, it considers a look ahead parameter, noted +\(L\), and applies the Full Strong Branching rule. However, if the branching candidate does not change after \(L\) +iterations, the algorithm stops and the current branching candidate is returned.

      • +

    • Strong Branching with Phases is a combination of the above three approaches which applies different schemes depending +on the level of the current node in the Branch-and-Bound tree. Additionally, it allows to solve each node only approximately +by, e.g., imposing a maximum number of iterations for the underlying Column Generation algorithm.

      • +
    +
    +
    +
    +

    Implementation

    +

    This section explains how to use the Strong Branching rule in idol. +It is based on the Generalized Assignment Problem example from the Column Generation. +More specifically, we will assume that you have a variable +model of type Model which has a decomposable structure specified by the annotation (Annotation<unsigned int>) decomposition.

    +
    +

    Full Strong Branching

    +

    Recall that the Branch-and-Price algorithm is created by the following code.

    +
    const auto column_generation =
+    DantzigWolfeDecomposition(decomposition)
+        .with_master_optimizer(Gurobi::ContinuousRelaxation())
+        .with_default_sub_problem_spec(
+            DantzigWolfe::SubProblem()
+                .add_optimizer(Gurobi())
+        );
+
    +
    +

    Now, we will show how to use Strong Branching as a branching rule. This is done while creating our Branch-and-Bound algorithm. In +particular, we will use the StrongBranching class to define our branching rule. We can, for instance, simply +declare

    +
    const auto branching_rule =
+    StrongBranching();
+
    +
    +

    which will create a new Full Strong Branching rule. Just like any other branching rule, it can be used by calling the +BranchAndBound::with_branching_rule method.

    +
    const auto branch_and_bound =
+    BranchAndBound()
+        .with_branching_rule(branching_rule)
+        .with_node_selection_strategy(BestBound());
+
    +
    +

    Then, we can write a Branch-and-Price algorithm and solve our problem as follows.

    +
    const auto branch_and_price = branch_and_bound + column_generation;
+
+model.use(branch_and_price);
+
+model.optimize();
+
    +
    +

    Beware that here, we only implemented Full Strong Branching which, as we saw, is not computationally convenient… +Let’s see how to implemented Restricted Strong Branching.

    +
    +
    +

    Restricted Strong Branching

    +

    To implement Restricted Branching, one simply needs to call the StrongBranching::with_max_n_variables method. +This is done as follows.

    +
    const auto branching_rule =
+        StrongBranching()
+            .with_max_n_variables(50);
+
    +
    +

    Here, we set the maximum number of considered variables equal to \(K = 50\).

    +
    +
    +

    Phases

    +

    In this section, we will discuss how to implement phases with the strong branching rule. This is done by using the +StrongBranching::add_phase method. This method takes three arguments: a phase type, which is used to indicate +how each node should be solved, e.g., with some iteration limit, a maximum number of variables to consider, for restricted +strong branching, and a maximum depth, used to trigger the phase based on the level of the current node in the Branch-and-Bound +tree.

    +

    Here is an instance of strong branching with phases which, for nodes whose level is below or equal to 3, applies Full +Strong Branching, then switches to Restricted Strong Branching with \(K = 30\) and which solves nodes with an iteration +limit of 20.

    +
    const auto branching_rule =
+            StrongBranching()
+                .add_phase(StrongBranchingPhases::WithNodeOptimizer(), std::numeric_limits<unsigned int>::max(), 3)
+                .add_phase(StrongBranchingPhases::WithIterationLimit(20), 30, std::numeric_limits<unsigned int>::max());
+
    +
    +

    Observe how we used std::numeric_limits<unsigned int>::max() to remove restrictions on the number of +considered variables and on the maximum depth for the final phase. Note that, by default, if no phase is triggered for a +given depth, e.g., because it was not specified, Full Strong Branching is applied. Here, however, we make sure that the +second phase is always triggered.

    +
    +
    +
    +

    Changing the Scoring Function

    +

    The scoring function can be changed by calling the StrongBranching::with_scoring_function method. This method +takes a scoring function as an argument. The scoring function is a sub-class of NodeScoreFunction and can be +Linear or Product.

    +

    By default, idol uses the product scoring function. To change it to the linear scoring function, one can simply write

    +
    const auto branching_rule =
+    StrongBranching()
+        .with_scoring_function(NodeScoreFunctions::Linear());
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.html b/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.html new file mode 100644 index 000000000..dd575689b --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-cut-and-price.html @@ -0,0 +1,221 @@ + + + + + + + Writing A Branch-and-Cut-and-Price Algorithm [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Writing A Branch-and-Cut-and-Price Algorithm [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.html b/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.html new file mode 100644 index 000000000..2af79c32e --- /dev/null +++ b/tutorials/mixed-integer-programming/dantzig-wolfe/writing-branch-and-price.html @@ -0,0 +1,305 @@ + + + + + + + Writing A Branch-and-Price Algorithm + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Writing A Branch-and-Price Algorithm

    +

    This tutorial is a follow-up to the Dantzig-Wolfe decomposition tutorial. +In this tutorial, we will see how to implement a Branch-and-Price algorithm in idol to, not only solve +the continuous relaxation of the Generalized Assignment Problem (GAP), but also handle the integrality constraints.

    + +
    +

    Prerequisites

    +

    We will assume that you have already defined your model as well as the column generation optimizer factory. +If you haven’t done so, we recommend you to read the Dantzig-Wolfe decomposition tutorial.

    +

    Hence, you should already have something like this:

    +
    const auto sub_problem_specifications = DantzigWolfe::SubProblem()
+                                            .add_optimizer(Gurobi());
+
+const auto column_generation = DantzigWolfeDecomposition(decomposition)
+        .with_master_optimizer(Gurobi::ContinuousRelaxation())
+        .with_default_sub_problem_spec(sub_problem_specifications);
+
    +
    +

    Moreover, we will assume that your model is called model and that the decomposition annotation is called decomposition.

    +
    +
    +

    Creating the Branch-and-Price Algorithm

    +

    Our remaining task is to embed our column generation routine inside of a Branch-and-Bound algorithm.

    +

    Hence, we create a branch-and-bound algorithm as follows.

    +
    const auto branch_and_bound = BranchAndBound()
+
+    /* Variables are selected for branching using
+       the most-infeasible rule */
+    .with_branching_rule(MostInfeasible())
+
+    /* Nodes are selected using the best-bound rule */
+    .with_node_selection_rule(BestBound())
+
+    /* The algorithm will run with a time limit of 3600 */
+    .with_time_limit(3600)
+
+);
+
    +
    +

    Here, variables are selected for branching using the most-infeasible rule, and nodes are selected using the best-bound rule. +We also set a time limit of one hour.

    +

    The column generation algorithm can easily be combined with the branch-and-bound algorithm using the BranchAndBound::with_node_optimizer +method, or by simply adding the two algorithms together.

    +

    For instance, the following line creates a branch-and-price algorithm.

    +
    model.use(branch_and_bound + column_generation);
+
    +
    +
    +
    +

    Solving

    +

    As usual, one can simply call the Model::optimize method to solve the problem.

    +
    model.optimize();
+
    +
    +

    That’s it! The problem is being now solved by a branch-and-price and the integrality constraints are handled automatically!

    +

    The rest remains unchanged and one can retrieve the solution +through the usual methods such as Model::get_status and Model::get_var_primal.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/index.html b/tutorials/mixed-integer-programming/index.html new file mode 100644 index 000000000..abe561ac7 --- /dev/null +++ b/tutorials/mixed-integer-programming/index.html @@ -0,0 +1,290 @@ + + + + + + + Mixed-Integer Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Mixed-Integer Optimization

    +

    Mixed-integer optimization deals with problems of the following form:

    +
    +(1)\[\begin{split}\begin{align} + \min_{x} \quad & c^\top x + x^\top D x + c_0 \\ + \text{s.t.} \quad & a_{i\cdot}^\top x + x^\top Q^i x \le b_i, \quad i = 1, \ldots, m, \\ + & x_j \in \mathbb{Z}, \quad j \in I \subseteq \{ 1, \dotsc, n \}. +\end{align}\end{split}\]
    +

    Here, \(x\) are the decision variables, while \(c\), \(D\), \(c_0\), \(a_i\), \(Q^i\), and \(b_i\) are given data. +Some of the decision variables are required to be integer-valued and are indexed by \(I\).

    +

    We say that (1) is an integer problem if \(I = \{ 1, \dotsc, n \}\), i.e., if all variables are required to +be integer. It is said to be mixed-integer if \(I \neq \emptyset\). Otherwise, we say that (1) is a continuous problem.

    +

    An important class of problems is when \(D = 0\) and \(Q^i = 0\) for all \(i\), i.e., when the objective function and the constraints are linear. +In such a case, we say that (1) is a mixed-integer linear problem (MILP), or a linear problem (LP) if all variables are continuous.

    +
    +https://upload.wikimedia.org/wikipedia/commons/0/06/IP_polytope_with_LP_relaxation.svg + +
    +

    The feasible region of an integer problem and its linear relaxation.

    +
    +
    +

    Table of Contents

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/constraints.html b/tutorials/mixed-integer-programming/modeling/constraints.html new file mode 100644 index 000000000..71aa4ebab --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/constraints.html @@ -0,0 +1,370 @@ + + + + + + + Constraints + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Constraints

    +

    Constraints are mathematical expressions that must be satisfied by the decision variables of an optimization problem. +They are used to model relationships between variables, and to restrict the feasible region of the problem.

    +

    There are mainly two types of constraints:

    +
      +

    • Linear Constraints: constraints that are linear in the decision variables.

      • +

    • Quadratic Constraints: constraints that are non-linear in the decision variables.

      • +
    + +
    +

    Linear Constraints

    +
    +

    Creating Constraints

    +

    Similarly to variables, constraints are easily created and added to a given Model.

    +

    Constraints can be created by calling the constructor of the Ctr class and added to a model by means of +Model::add or by calling the Model::add_ctr method.

    +

    Using the Ctr class directly creates a variable that is not associated to any model. We will then need to add it +explicitly to a model. This is done by calling the Model::add method. See for instance the following code.

    +
    Env env;
+Model model(env);
+
+Var x_0(env, 0., Inf, Continuous, "x_0");
+Var x_1(env, 0., Inf, Continuous, "x_1");
+Ctr constraint(env, x_0 + x_1 >= 1);
+
+model.add(x_0);
+model.add(x_1);
+model.add(constraint);
+
    +
    +

    A more compact version of this code is obtained by making use of the Model::add_vars and Model::add_ctr methods.

    +
    Env env;
+Model model(env);
+
+const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, 0, "x");
+const auto constraint = model.add_ctr(x[0] + x[1] >= 1);
+
    +
    +
    +
    +

    Temporary Constraints

    +

    As you can see, a constraint is created using the pattern {expression} {sign} {expression} where

    +
      +

    • {sign} is one of <=, >= and ==;

      • +

    • {expression} is an expression, i.e., an instance of AffExpr.

      • +
    +

    Actually, the pattern {expression} {sign} {expression} only creates a “temporary” constraint, i.e., a constraint +which is not associated to any model. This is why we need to add it to a model by calling the Model::add_ctr method. +Temporary constraints are objects of the class TempCtr. An equivalent code would be.

    +
    Env env;
+Model model(env);
+
+const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x");
+const auto temporary_constraint = TempCtr(x[0] + x[1], GreaterOrEqual, 1);
+
+model.add_ctr(temporary_constraint);
+
    +
    +

    Here, the sign of the constraint is +specified by the second argument of the constructor of the TempCtr class, and can take values +LessOrEqual, GreaterOrEqual and EqualTo.

    +
    +
    +

    Accessing Constraints

    +

    Information about a given constraint in a model can be accessed by calling the corresponding methods of the model. +For instance, one can access the right-hand side of a constraint by calling the Model::get_ctr_rhs method. +Here is a list of the most common methods to access information about a constraint.

    +
      +

    • Model::get_ctr_rhs: get the right-hand side of a constraint,

      • +

    • Model::get_ctr_type: get the type of a constraint,

      • +

    • Model::get_ctr_row: get the row of a constraint,

      • +

    • Model::get_ctr_index: get the index of a constraint.

      • +
    +

    When available, the values associated to the constraint in a given solution can be accessed in a similar way. +Here is a list of the most common methods to access information about a constraint in a solution.

    +
      +

    • Model::get_ctr_dual: get the dual value of a constraint,

      • +

    • Model::get_ctr_farkas: get the Farkas certificate of a constraint (for infeasible systems).

      • +
    +

    The Model::has method can be used to check if a given constraint is in the model.

    +

    For more details, see the Model class.

    +
    +
    +

    Modifying Constraints

    +

    Similarly to accessing constraints, the attributes of a constraint can be modified by calling the corresponding methods of the model. +Here is a list of the most common methods to modify a constraint.

    +
      +

    • Model::set_ctr_rhs: set the right-hand side of a constraint,

      • +

    • Model::set_ctr_type: set the type of a constraint,

      • +

    • Model::set_ctr_row: set the row of a constraint.

      • +
    +

    The row of a constraint in the model can be modified by calling the Ctr::set_row method. +For instance.

    +
    LinExpr row;
+row.set(x, coefficient_for_x_in_constraint);
+row.set(y, coefficient_for_y_in_constraint);
+
+model.set_ctr_row(constraint, row);
+
    +
    +

    For more details, see the Model class.

    +
    +
    +

    Removing Constraints

    +

    A constraint can be removed from a model by calling the Model::remove method.

    +
    +
    +
    +

    Quadratic Constraints

    +

    Creating, accessing and modifying quadratic constraints is similar to linear constraints. The main difference is that +quadratic constraints are created using the QCtr class. Moreover, the corresponding methods in Model +use qctr instead of ctr. For instance, the following code accesses the type of a quadratic constraint.

    +
    model.get_qctr_type(quadratic_constraint);
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/environment.html b/tutorials/mixed-integer-programming/modeling/environment.html new file mode 100644 index 000000000..c5e400ca4 --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/environment.html @@ -0,0 +1,249 @@ + + + + + + + The Environment + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    The Environment

    +

    Every optimization object (such as variables and constraints) are managed by an “optimization environment”. +It is the environment that controls the death and life of such objects. It is also through the environment that idol +manages the different versions each optimization object may have during the execution of your program.

    +

    Typically, only one environment should be used by your code. Yet, it is not forbidden to have several environments at the same time (not advised).

    +

    Environments are objects of the Env class, and can be created as follows.

    +
    Env env; // Creates a new optimization environment.
+
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/expressions.html b/tutorials/mixed-integer-programming/modeling/expressions.html new file mode 100644 index 000000000..0b71b393f --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/expressions.html @@ -0,0 +1,309 @@ + + + + + + + Expressions + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Expressions

    +

    An expression generically refers to any mathematical expression involving variables or constraints. In idol, expressions +are represented by the QuadExpr, AffExpr and LinExpr classes. These classes are used to represent +quadratic, affine and linear expressions, respectively.

    +

    An expression can be created by adding, subtracting or multiplying variables together. For instance, +the following code creates the mathematical expression \(1 + 3 x_0 + x_1 + x_0 + 2 x_0 x_1\).

    +
    const AffExpr expr = 1 + 3 * x[0] + x[1] + x[0] + 2 * x[0] * x[1];
+
+std::cout << expr << std::endl;
+
    +
    + +
    +

    LinExpr: Linear Expressions

    +

    The LinExpr class is used to represent linear expressions. A linear expression is a mathematical expression +that is linear in the variables. For instance, the following code creates the mathematical expression \(1 + 3 x_0 + x_1\).

    +
    const LinExpr expr = 1 + 3 * x[0] + x[1];
+
+std::cout << expr << std::endl; // "1 + 3 * x[0] + 1 * x[1]"
+
    +
    +
    +

    Linear in What?

    +

    Actually, LinExpr is a template class with one parameter, which is the type of the “variables” in the linear expression. +For instance, it is possible de create a linear expression of Ctr objects, which are constraints. The following code +creates the mathematical expression \(1 + 3 c_0 + c_1\).

    +
    const LinExpr<Ctr> expr = 1 + 3 * c[0] + c[1];
+
+std::cout << expr << std::endl; // "1 + 3 * c[0] + 1 * c[1]"
+
    +
    +
    +

    It is possible to iterate over the terms in the expression as follows.

    +
    for (const auto& [var, constant] : expr) {
+    std::cout << constant << " multiplied by " << var << std::endl;
+}
+
    +
    +
    +
    +

    AffExpr: Affine Expressions

    +

    The AffExpr class is used to represent affine expressions. An affine expression is a mathematical expression +that is linear in the variables and has a constant term.

    +

    The linear part of the expression is accessed by the AffExpr::linear() method, and the constant term is accessed +by the AffExpr::constant() method.

    +
    +
    +

    QuadExpr: Quadratic Expressions

    +

    The QuadExpr class is used to represent quadratic expressions. A quadratic expression is a mathematical expression +which contains an affine part and a quadratic part. The affine part can be accessed by the QuadExpr::affine() method.

    +

    It is possible to iterate over the terms in the quadratic part of the expression as follows.

    +
    for (const auto& [pair, constant] : expr) {
+    std::cout << constant << " multiplied by " << pair.first << " and " << pair.second << std::endl;
+}
+
+for (const auto& [var, constant] : expr.affine().linear()) {
+    std::cout << constant << " multiplied by " << var << std::endl;
+}
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/index.html b/tutorials/mixed-integer-programming/modeling/index.html new file mode 100644 index 000000000..cd392ca76 --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/index.html @@ -0,0 +1,257 @@ + + + + + + + Modeling a MIP with idol + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Modeling a MIP with idol

    +

    This page introduces the basic concepts of modeling optimization problems in idol. +We will discuss how to create optimization models and add variables, constraints and objective functions to that model. +We will also see how to access the different components of an existing model.

    +

    All classes which are used for modeling (standard) optimization problems can be accessed by including #include <idol/modeling.h>.

    +

    To simplify things, we will use the namespace idol in the following examples. This dispenses us from prefixing +every class with idol::. For instance, we will use Model instead of idol::Model.

    +

    Let’s get started.

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/models.html b/tutorials/mixed-integer-programming/modeling/models.html new file mode 100644 index 000000000..2507f2d7a --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/models.html @@ -0,0 +1,317 @@ + + + + + + + Models + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Models

    +

    The Model class is used to represent a (standard) optimization model of the form

    +
    +\[\begin{split}\begin{align} + \min_{x} \quad & c^\top x + x^\top D x + c_0 \\ + \text{s.t.} \quad & a_{i\cdot}^\top x + x^\top Q^i x \le b_i, \quad i = 1, \ldots, m, \\ + & x_j \in \mathbb{Z}, \quad j \in I \subseteq \{ 1, \dotsc, n \}. +\end{align}\end{split}\]
    +

    Here, \(x\) are the decision variables, while \(c\), \(D\), \(c_0\), \(a_i\), \(Q^i\), and \(b_i\) are given data. +Some of the decision variables are required to be integer-valued and are indexed by \(I\).

    +

    In what follows, we will dive into the Model class and see how to create, read, and write models to files.

    + +
    +

    Creating a Model

    +

    A Model is created by calling the constructor of the Model class. Note that it is necessary to pass an environment +to the constructor.

    +

    The following code creates a new optimization model.

    +
    Env env;
+Model model(env);
+
    +
    +

    We can now define our decision variables and constraints, and add an objective function to our model. +This is detailed in the Variables, Constraints and Objective sections, respectively.

    +
    +
    +

    Reading a Model from a File

    +

    A Model can also be created by reading a model from a file (typically, a .mps or an .lp file). +To do this, idol relies on an external solver. The following code reads a model from a file using Gurobi.

    +
    Env env;
+auto model = Gurobi::read_from_file(env, "/path/to/model.mps");
+// auto model = GLPK::read_from_file(env, "/path/to/model.mps");
+
    +
    +
    +
    +

    Writing a Model to a File

    +

    To write an optimization model to a file, the easiest way is again to rely on an external solver. +This is done by attaching a solver to a model, then by calling the Model::write method.

    +
    Env env;
+Model model(env);
+
+// Add variables and constraints HERE...
+
+model.use(Gurobi()); // Set the optimizer as Gurobi
+
+model.write("instance.lp"); // Creates a new file "instance.lp" storing the model
+
    +
    +
    +
    +

    Iterating over the Variables and Constraints

    +

    The Model class provides methods to iterate over the variables and constraints of the model. +See for instance, the following example.

    +
    for (const auto& var : model.vars()) {
+    std::cout << "Variable " << var.name() << " belongs to the model." << std::endl;
+}
+
+for (const auto& ctr : model.ctrs()) {
+    std::cout << "Constraint " << ctr.name() << " belongs to the model." << std::endl;
+}
+
    +
    +

    The number of variables and constraints can be obtained by doing the following.

    +
    std::cout << "Nb. of variables: " << model.vars().size() << std::endl;
+std::cout << "Nb. of constraints: " << model.ctrs().size() << std::endl;
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/objective-function.html b/tutorials/mixed-integer-programming/modeling/objective-function.html new file mode 100644 index 000000000..f23b03025 --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/objective-function.html @@ -0,0 +1,291 @@ + + + + + + + Objective Functions + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Objective Functions

    +

    The objective function of an optimization model is a quadratic expression of the decision variables. +It is used to guide the optimization process by defining the quantity to be minimized or maximized.

    + +
    +

    Adding an Objective Function

    +

    The objective function of an optimization model can specified by the Model::set_obj_expr method. The objective function is a linear expression of the decision variables.

    +

    Here is an example which sets the objective function to \(-x_0 + 2 x_1\);

    +
    model.set_obj_expr(-x_0 + 2 * x_1);
+
    +
    +
    +
    +

    Accessing the Objective Function

    +

    Here is a list of methods to access the objective function of a given model:

    +
      +

    • Model::get_obj_expr: Returns the objective function of the model.

      • +

    • Model::get_obj_sense: Returns the optimization sense of the model.

      • +
    +

    If a given model has been solved, one can also query the best objective function value and the best bound.

    +
      +

    • Model::get_best_obj: Returns the best objective function value.

      • +

    • Model::get_best_bound: Returns the best bound.

      • +
    +
    +
    +

    Changing the Optimization Sense

    +

    To change the optimization sense, use the Model::set_obj_sense method. +The optimization sense can be either Minimize or Maximize. For instance,

    +
    model.set_obj_sense(Maximize);
+
    +
    +

    Alternatively, one can use the constructor of the Model class to set the optimization sense.

    +
    Env env;
+Model model(env, Maximize); // Creates a model for maximization
+
    +
    +
    +

    Warning

    +

    idol offers minimal support for maximization problems. +We recommend to use minimization problems whenever possible.

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/modeling/variables.html b/tutorials/mixed-integer-programming/modeling/variables.html new file mode 100644 index 000000000..4ea3eeca6 --- /dev/null +++ b/tutorials/mixed-integer-programming/modeling/variables.html @@ -0,0 +1,424 @@ + + + + + + + Variables + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Variables

    +

    Variables are the decision variables of an optimization problem. They are the objects that we want to find the best +values for, with respect to some objective function given the specified constraints.

    + +
    +

    Creating Variables

    +

    There are mainly two ways to create variables in idol. The first one is to use the Var class directly, and the +second one is to use the Model::add_var method.

    +
    +

    Using the Var class and Model::add

    +

    Using the Var class directly creates a variable that is not associated to any model. We will then need to add it +explicitly to a model. This is done by calling the Model::add method. See for instance the following code which +creates a continuous variable \(x\), with bounds \([0,\infty)\), and adds it to the model.

    +
    Var x(env, 0., Inf, Continuous, 0, "x");
+
+model.add(x); // Variable x is added to the model
+
    +
    +

    Note that a variable may belong to several models at the same time. Each version of the variable in each model is then independent. +For instance, one could do the following.

    +
    Var x(env, 0., Inf, Continuous, "x");
+
+model.add(x);
+
+Model model2(env);
+model2.add(x);
+model2.set_var_ub(x, 10.);
+
    +
    +

    In this example, the variable \(x\) is added to two different models. The upper bound of \(x\) in the second model +is then set to 10. The upper bound of \(x\) in the first model is not affected by this change.

    +

    Also, it is possible to add a variable to a model and set its attributes (bounds and type) at the same time. For instance, +the following code is equivalent to the previous one.

    +
    Var x(env, 0., Inf, Continuous, "x");
+
+model.add(x);
+
+Model model2(env);
+model2.add(x, TempVar(0, 10, Continuous, 0));
+
    +
    +

    Here, we used the class TempVar to create a temporary variable. A temporary variable is a variable +which has not been instantiate yet. It is only a “template” of a variable specifying its bounds, type an objective coefficient. Here, we therefore +add the variable \(x\) to the second model and directly set its attributes (bounds and type) accordingly.

    +
    +
    +

    Using Model::add_var

    +

    A more straightforward way to create variables is to call the add_var method of the Model class. +For instance, one can do:

    +
    const auto x = model.add_var(0, Inf, Continuous, 0, "x");
+
    +
    +

    Here, we do not need to repeat the environment since the model’s environment is automatically used. Moreover, we do not need to +explicitly add the variable to the model since it is done by the add_var method.

    +

    Again, a variable may belong to several models at the same time. And we can do as follows.

    +
    const auto x = model.add_var(0, Inf, Continuous, "x");
+
+Model model2(env);
+model2.add(x);
+model2.set_var_ub(x, 10.);
+
    +
    +

    Note that an even more compact version of the previous code is obtained by using the Model::add method with additional +parameters. For instance, the following code is equivalent to the previous one.

    +
    const auto x = model.add(0, Inf, Continuous, "x");
+
+Model model2(env);
+model2.add(x, TempVar(0, 10, Continuous, 0));
+
    +
    +
    +
    +
    +

    Creating Several Variables at Once

    +

    Sometimes, you will find it convenient to create several variables at once. This can be done by calling the Var::make_vector +function, or the Model::add_vars method. These functions require +an extra parameter specifying the dimension of the new variable.

    +
    +

    Using Var::make_vector and Model::add_vector

    +

    The following code creates variables \(y_{ij}\) with \(i=1,...,K\) and \(j=1,...,T\).

    +
    const auto y = Var::make_vector(env, Dim<2>(K, T), 0., Inf, Continuous, "y");
+
+model.add_vector<Var, 2>(y);
+
+std::cout << y[0][0] << std::endl; // "y_0_0"
+
    +
    +

    Here, we use the Dim class to specify the dimension of the new variable. The Dim class is a template class +that takes an integer as a template parameter. The integer specifies the dimension of the new variable. In this case, we use +2 to specify that we want to create a two-dimensional variable. Then, we specify the size of each dimension by passing the +appropriate arguments to the constructor of the Dim class. Here, we specify that the first dimension has size \(K\) and the +second dimension has size \(T\).

    +

    Once the variables are created, we add them to the model by calling the Model::add_vector method.

    +
    +
    +

    Using Model::add_vars

    +

    One alternative is to use the more direct Model::add_vars method.

    +
    const auto y = model.add_vars(Dim<2>(K, T), 0., Inf, Continuous, "y");
+
+std::cout << y[0][0] << std::endl; // "y_0_0"
+
    +
    +

    Note that the Dim class is used in the same way as in the previous example.

    +
    +
    +
    +

    Variables Types

    +

    Variables can be of different types. In idol, three types of variables are available:

    +
      +

    • Continuous: continuous variables,

      • +

    • Binary binary variables,

      • +

    • Integer: integer variables.

      • +
    +
    +
    +

    Accessing Variables

    +

    Information about a given variable in a model can be accessed by calling the corresponding methods of the model. For instance, +one can access the lower bound of a variable by calling the Model::get_var_lb method. Here is a list of the most common +methods to access information about a variable.

    +
      +

    • Model::get_var_lb: returns the lower bound of a variable,

      • +

    • Model::get_var_ub: returns the upper bound of a variable,

      • +

    • Model::get_var_type: returns the type of a variable,

      • +

    • Model::get_var_column: returns the column of a variable,

      • +

    • Model::get_var_obj: returns the objective coefficient of a variable,

      • +

    • Model::get_var_index: returns the index of a variable.

      • +
    +

    When available, the value of the variable in a given solution can be accessed in a similar way. +Here is a list of the most common methods to access information about a variable in a solution.

    +
      +

    • Model::get_var_primal: returns the value of a variable in a solution,

      • +

    • Model::get_var_reduced_cost: returns the reduced cost of a variable in a solution,

      • +

    • Model::get_var_ray: returns the primal ray of a variable in a solution.

      • +
    +

    The Model::has method can be used to check if a given variable is in the model.

    +

    For more details, see the Model class.

    +
    +
    +

    Modifying Variables

    +

    Similarly to accessing variables, the attributes of a variable can be modified by calling the corresponding methods of the model. +Here is a list of the most common methods to modify a variable.

    +
      +

    • Model::set_var_lb: sets the lower bound of a variable,

      • +

    • Model::set_var_ub: sets the upper bound of a variable,

      • +

    • Model::set_var_type: sets the type of a variable,

      • +

    • Model::set_var_obj: sets the objective coefficient of a variable,

      • +

    • Model::set_var_column: sets the column of a variable.

      • +
    +

    For instance, the following code updates the column of a given variable.

    +
    LinExpr<Ctr> column(objective_coefficient_for_x);
+column.set(constraint1, constraint1_coefficient_for_x);
+column.set(constraint2, constraint2_coefficient_for_x);
+
+model.set_var_column(x, column);
+
    +
    +

    Here, we use the LinExpr<Ctr> class to represent the column of the variable \(x\).

    +

    For more details, see the Model class.

    +
    +
    +

    Removing Variables

    +

    A variable can be removed from a model by calling the Model::remove method.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/access-optimizer.html b/tutorials/mixed-integer-programming/optimizers/access-optimizer.html new file mode 100644 index 000000000..67de44039 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/access-optimizer.html @@ -0,0 +1,271 @@ + + + + + + + Getting Access to The Underlying Optimizer + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Getting Access to The Underlying Optimizer

    +

    In some advanced situations, you may want to access the underlying optimizer of an optimization model. +For instance, this could be the case if you want to get optimizer-specific information which are not exposed by the Model interface.

    +

    In this case, you can use the Model::optimizer method. Note that this method +will return a reference of type Optimizer&.

    +

    To access optimizer-specific routines, you will need to cast the reference to the appropriate optimizer type. +This is made easier by the Optimizer::as and Optimizer::is methods, which allow you to cast the optimizer to a specific type or check if it is of a specific type.

    +

    For instance, the following code shows how to access the underlying Gurobi optimizer of model.

    +
    Env env;
+Model model(env);
+auto x = model.add_var(0.0, 1.0, Continuous, -1, "x");
+
+model.use(Gurobi());
+model.optimize();
+
+if (!model.optimizer().is<Optimizers::Gurobi>()) {
+    throw Exception("The optimizer is not Gurobi");
+}
+
+auto& gurobi_optimizer = model.optimizer().as<Optimizers::Gurobi>();
+
+// Access the optimizer-specific routines
+GRBVar& var = gurobi_optimizer[x];
+
    +
    +
    +

    Warning

    +

    A common mistake is to try to cast the optimizer to the wrong type. In particular, to cast optimizer to its +optimizer factory type (e.g., Gurobi instead of Optimizers::Gurobi). +If so, this will result in a runtime error.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/create-optimizer.html b/tutorials/mixed-integer-programming/optimizers/create-optimizer.html new file mode 100644 index 000000000..890f81b89 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/create-optimizer.html @@ -0,0 +1,221 @@ + + + + + + + Creating Your Own Optimizer (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Creating Your Own Optimizer (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/create-universal-callback.html b/tutorials/mixed-integer-programming/optimizers/create-universal-callback.html new file mode 100644 index 000000000..dbedc4403 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/create-universal-callback.html @@ -0,0 +1,449 @@ + + + + + + + Creating Your Own Callback + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Creating Your Own Callback

    +

    In this page, we see how to create your own universal callback. +Universal callbacks are callbacks which are not specific to a particular optimizer. +In that sense, they are generic and can be used with different optimizers without any modification.

    +

    Creating your own callback can useful if you want to create a callback that is not included in the +default set of callbacks implemented in idol. +If you are looking for quick and easy-to-use callbacks for separating user cuts or lazy constraints, +you can refer to this page.

    +
    +

    Hint

    +

    Note that there are also callbacks specific to the BranchAndBound optimizer. +If you are looking for this, you can refer to this page.

    +
    + +
    +

    The Basics

    +

    Creating your callback is done by creating a sub-class of the Callback class and overriding the +Callack::operator() method. It is this method that will be called by the solver whenever an incumbent is found.

    +

    Note, however, that callbacks cannot be given “as-is” to an optimizer but must be passed through a CallbackFactory. A callback +factory is a class whose role is to create a new callback object whenever it is needed. Every callback factories must be +a child (or little child) of the CallbackFactory class.

    +

    The following code shows how to create a callback factory and a callback that prints the value of the primal solution at each +iteration.

    +
    /* Callback factory implementation */
+class MyCallback : public CallbackFactory {
+public:
+
+    /* Actual callback implementation */
+    class Strategy {
+    protected:
+
+        /* This method is called whenever an event occurs
+           during the solution process */
+        void operator()(CallbackEvent t_event) {
+
+               if (t_event != IncumbentSolution) {
+                    return;
+               }
+
+               std::cout << primal_solution() << std::endl;
+        }
+
+    }
+
+    /* This method creates a new callback object */
+    Callback* operator()() {
+        return new Strategy();
+    }
+
+    /* This method creates a copy of the callback factory */
+    CallbackFactory* clone() const {
+        return new MyCallback(*this);
+    }
+
+}
+
    +
    +

    As you can see, the callback factory has two important methods: operator() and clone(). The operator() +method is used to create a new callback object, while the clone() method is used to create a copy of the callback factory.

    +

    The nested class Strategy is the actual callback implementation. It is a sub-class of the Callback class and +overrides the operator() method. In this example, the callback prints the value of the primal solution whenever the event +triggering the callback is IncumbentSolution. In other words, this callback will print out all incumbent solutions found by the solver.

    +

    As for the UserCutCallback and LazyConstraintCallback classes, +our new callback can be added to an optimizer as follows.

    +
    model.use(
+    Gurobi().add_callback(MyCallback())
+);
+
+model.optimize();
+
    +
    +
    +
    +

    List of Optimizers Supporting Universal Callbacks

    +

    The following solvers support universal callbacks:

    +
      +

    • Gurobi

      • +

    • BranchAndBound

      • +

    • Mosek

      • +
    +

    Hence, for these solvers, you can create your own callback and add it to the optimizer without having to +worry about the underlying solver.

    +
    +
    +

    An Example: Knapsack Cover Cuts

    +
    +

    Hint

    +

    This section is dedicated to the “advanced topic” of knapsack cover inequalities. +Rudimentary notions on Knapsack problems and +Cover inequalities are recommended.

    +
    +

    In this example, we will show how to create a callback that separates knapsack cover cuts. A knapsack cover cut is a valid inequality +for the knapsack problem. It is defined as follows:

    +
    +\[\sum_{i \in C} x_i \leq |C| - 1\]
    +

    where \(C\) defines a cover of the knapsack, i.e., a set of items such that the sum of their weights is greater than the capacity of the knapsack.

    +

    Given a solution \(\hat x\) to the continuous relaxation of the knapsack problem, we can check whether it violates a cover inequality. +This is done by solving the following separation problem.

    +
    +\[\begin{split}\begin{align} + \max_{z} \quad & (1 - \hat x)^\top z \qquad \ge 1 \\ + \text{s.t.} \quad & w^\top z \ge W + 1, \\ + & z\in\{0,1\}^n. +\end{align}\end{split}\]
    +

    A cover inequality is violated if and only if the optimal objective value of this problem is strictly less than 1. +In such a case, a new cut should be added.

    +

    We will write a callback that separates knapsack cover cuts.

    +

    To this end, we first create our knapsack problem model. This is done as follows.

    +
    Env env;
+Model knapsack(env, Maximize);
+
+const auto x = knapsack.add_vars(Dim<1>(n), 0, 1, Binary, 0, "x");
+
+knapsack.add_ctr(idol_Sum(i, Range(n_items), w[i] * x[i]) <= W);
+knapsack.set_obj_expr(idol_Sum(i, Range(n_items), p[i] * x[i]));
+
    +
    +

    Then, we create our callback factory. It is this factory that will be used to create a new callback object when needed. +Since we need to pass some parameters to the callback, we will use the constructor of the callback factory to pass these parameters. +This is done as follows.

    +
    class KnapsackCover : public CallbackFactory {
+    const std::vector<Var> m_x;
+    const std::vector<double> m_weights;
+    const std::vector<double> m_profits;
+    const double m_capacity;
+public:
+    KnapsackCover(const std::vector<Var>& t_x,
+                  const std::vector<double>& t_weights,
+                  const std::vector<double>& t_profits,
+                  double t_capacity)
+                    : m_x(t_x), m_weights(t_weights),
+                      m_profits(t_profits), m_capacity(t_capacity) {}
+
+    class Strategy;
+
+    Callback* operator()() {
+        return new Strategy(m_x, m_weights, m_profits, m_capacity);
+    }
+
+    CallbackFactory* clone() const {
+        return new MyCallback(*this);
+    }
+
+}
+
    +
    +

    The actual implementation of the callback is done in the nested class Strategy. +This class is a sub-class of the Callback class and is defined as follows.

    +
    class KnapsackCover::Strategy {
+    const std::vector<Var> m_x;
+    const std::vector<double> m_weights;
+    const std::vector<double> m_profits;
+    const double m_capacity;
+protected:
+    Strategy(const std::vector<Var>& t_x,
+             const std::vector<double>& t_weights,
+             const std::vector<double>& t_profits,
+             double t_capacity)
+                : m_x(t_x), m_weights(t_weights),
+                  m_profits(t_profits), m_capacity(t_capacity) {}
+
+    void operator()(CallbackEvent t_event) {
+
+           if (t_event != InvalidSolution) {
+                return;
+           }
+
+           auto& env = parent().env();
+           const auto fractional_point = primal_solution();
+
+            Model separation(env, Maximize);
+
+            const auto z = separation.add_vars(Dim<1>(m_x.size()), 0, 1, Binary, "z");
+            separation.add_ctr(idol_Sum(i, Range(m_x.size()), m_weights[i] * z[i]) >= m_capacity + 1);
+            separation.set_obj_expr(idol_Sum(i, Range(m_x.size()), (1 - fractional_point[i]) * z[i]));
+
+            separation.use(Gurobi());
+
+            separation.optimize();
+
+            if (separation.get_best_obj() < 1) {
+                return;
+            }
+
+            const auto cut = idol_Sum(i, Range(m_x.size()), separation.get_var_primal(z[i]) * (1 - x[i])) >= 1;
+
+            add_user_cut(cut);
+
+    }
+}
+
    +
    +

    Finally, we can add our callback to the optimizer as follows.

    +
    knapsack.use(
+    Gurobi::Continuous().add_callback(KnapsackCover(x, w, p, W))
+);
+
+knapsack.optimize();
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/index.html b/tutorials/mixed-integer-programming/optimizers/index.html new file mode 100644 index 000000000..b3783f588 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/index.html @@ -0,0 +1,252 @@ + + + + + + + Solving a MIPs + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Solving a MIPs

    +

    This series of tutorials covers the basics of solving mixed-integer problems (MIPs) in idol. +We assume that you already know how to create a model and add variables, constraints, and objectives to it.

    +

    Let’s get started!

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/optimizers.html b/tutorials/mixed-integer-programming/optimizers/optimizers.html new file mode 100644 index 000000000..32755f4be --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/optimizers.html @@ -0,0 +1,340 @@ + + + + + + + The Concept of Optimizer and OptimizerFactory + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    The Concept of Optimizer and OptimizerFactory

    +

    This page discusses the concept of optimizers and optimizer factories in idol. +We will discuss how to set up an optimizer for solving a model and how to access the solution of the model.

    +

    In idol, an optimizer is a class that is responsible for solving a given optimization problem. +It is created by an optimizer factory, which is a class that is responsible for assembling and creating optimizers.

    + +
    +

    A First Example

    +

    We start with an example. Consider the following code, which models a simple knapsack problem:

    +
    Env env;
+Model model(env, Maximize);
+const auto x = model.add_vars(Dim<1>(3), 0, 1, Binary, 0, "x");
+model.add_ctr(x[0] + 2 * x[1] + 3 * x[2] <= 5);
+model.set_obj_expr(x[0] + x[1] + x[2]);
+
    +
    +

    The code creates a model with three binary variables, and adds a constraint and an objective function to it. +Currently, the model does not have an optimizer, so it cannot be solved. +Calling model.optimize() will result in an exception being thrown.

    +

    To set up an optimizer, we need to call the Model::use method, which takes an optimizer factory as an argument. +For this example, let us use the GLPK optimizer factory, which creates an optimizer using GLPK to solve our model; see GLPK.

    +
    model.use(GLPK());
+
    +
    +

    Here, we assume that idol was linked with the GLPK library during installation. If this is not the case, please, refer to +the installation guidelines.

    +

    Now, calling model.optimize() will cause the optimizer factory to create an optimizer, which will solve the model. +Since we are using the GLPK optimizer factory, an instance of Optimizers::GLPJ +will be created and used to solve the model; see Optimizers::GLPK.

    +

    Note that we can modify the model after setting up the optimizer. The optimizer will be updated accordingly. For instance.

    +
    model.add_ctr(x[0] + x[1] <= 1); // Add a new constraint
+model.optimize(); // Re-optimize
+
    +
    +

    idol provides several optimizer factories, each of which creating an optimizer using different solvers or implementing different algorithms. +For instance, the Gurobi optimizer factory creates an optimizer using the Gurobi solver, +while the BranchAndBound optimizer factory creates an optimizer implementing a branch-and-bound algorithm.

    +

    Typically, users only work with optimizer factories, and do not need to create optimizers directly. +Passing arguments to an optimizer is always possible at creation time through the optimizer factory. +For instance, here is a small example showing how to pass a time limit to the GLPK optimizer:

    +
    model.use(GLPK().with_time_limit(10)); // add time limit of 10 seconds
+
    +
    +

    As it can be seen, arguments are given by calling the with_* methods of the optimizer factory, followed by the name of the argument.

    +
    +
    +

    Combining Optimizers

    +

    In some cases, it can useful to combine optimizers together. For instance, this is useful if one wants to use an optimizer +to solve a sub-problem arising in another optimizer. +The process of combining optimizers is straightforward and follows the same pattern as what we have seen so far.

    +

    For instance, consider the following code, which implements a simple branch-and-bound algorithm to solve our knapsack problem.

    +
    model.use(
+    /* The overall algorithm is a branch-and-bound */
+    BranchAndBound()
+
+        /* Each node is solved by the continuous relaxation
+           of the problem, with GLPK */
+        .with_node_optimizer(GLPK::ContinuousRelaxation())
+
+        /* Variables are selected for branching using the
+           most-infeasible rule */
+        .with_branching_rule(MostInfeasible())
+
+        /* Nodes are selected using the best-bound rule */
+        .with_node_selection_rule(BestBound())
+
+        /* Turn on logs */
+        .with_logs(true)
+
+        /* The algorithm will run with a time limit of 3600 */
+        .with_time_limit(3600)
+    )
+);
+
    +
    +

    In this example, we create a branch-and-bound algorithm to solve the model, and we use GLPK to solve the continuous relaxation of the problem at each node. +Also note that we can nest optimizers as many times as we want with no restrictions.

    +

    To simplify the writing of complex optimizer factories, it may be useful to use temporary variables to store intermediate results. +For instance.

    +
    const auto continuous_relaxation = GLPK::ContinuousRelaxation();
+const auto branching_rule = MostInfeasible();
+const auto node_selection_rule = BestBound();
+
+const auto branch_and_bound = BranchAndBound()
+    .with_node_solver(continuous_relaxation)
+    .with_branching_rule(branching_rule)
+    .with_node_selection_rule(node_selection_rule)
+    .with_logs(true)
+    .with_time_limit(3600);
+
+model.use(branch_and_bound);
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/solving.html b/tutorials/mixed-integer-programming/optimizers/solving.html new file mode 100644 index 000000000..7654c7049 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/solving.html @@ -0,0 +1,443 @@ + + + + + + + Using an External Solver and Accessing the Solution + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using an External Solver and Accessing the Solution

    +

    This page shows how to solve a model and access the solution. +The reader should be familiar with the concept of optimizer and optimizer factories. If this is not the case, +please refer to the page on Optimizers.

    + +
    +

    Modeling and Solving with an External Solver (e.g., GLPK)

    +

    Let us consider the following code.

    +
    using namespace idol;
+
+const unsigned int n_items = 5;
+const double[] profit = { 40., 50., 100., 95., 30., };
+const double[] weight = { 2., 3.14, 1.98, 5., 3., };
+const double capacity = 10.;
+
+Env env;
+Model model(env, Maximize);
+
+auto x = model.add_vars(Dim<1>(n_items), 0., 1., Binary, 0, "x");
+model.add(idol_Sum(j, Range(n_items), weight[j] * x[j] ) <= capacity);
+model.set_obj_expr(idol_Sum(j, Range(n_items), profit[i] * x[i]);
+
    +
    +

    This code creates a model for the knapsack problem.

    +

    As described in the page on this page, +we will now set up an optimizer and solve the model. For this example, we use GLPK.

    +
    model.use(GLPK());
+
    +
    +

    Solving the model is then done by calling the optimize method.

    +
    model.optimize();
+
    +
    +
    +
    +

    Accessing the Solution

    +

    idol provides several methods to access the solution.

    +

    First, the status of the solution can be accessed using the get_status method. +Here is a detailed list of possible statuses and reasons:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Status

    Description

    Loaded

    The model has been loaded but not solved.

    Optimal

    An optimal solution has been found.

    Feasible

    A feasible solution has been found.

    Infeasible

    No feasible solution could be found.

    InfOrUnbnd

    The model is infeasible or unbounded.

    Unbounded

    The model is unbounded.

    Fail

    The solver failed to solve the model.

    SubOptimal

    A suboptimal solution has been found.

    +

    Related to a status, the reason for the status can be accessed using the get_reason method.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Reason

    Description

    NotSpecified

    No specific reason is available.

    Proved

    The solver proved optimality.

    TimeLimit

    The solver reached the time limit.

    IterLimit

    The solver reached the iteration limit.

    ObjLimit

    The solver reached the objective limit.

    Numerical

    A numerical issue occurred during the solution process.

    MemoryLimit

    The solver ran out of memory.

    Cycling

    The solver encountered cycling (e.g., in simplex method).

    SolutionLimit

    The solver reached the solution limit (e.g., number of solutions).

    +

    Then, the following methods can be used to access the solution:

    +
      +

    • get_best_obj returns the best known objective value (this always refers to feasible solutions),

      • +

    • get_best_bound returns the best known objective value bound,

      • +

    • get_relative_gap returns the relative optimality gap,

      • +

    • get_absolute_gap returns the absolute optimality gap; see this page for more details about gaps and tolerances.

      • +
    +

    Accessing the primal and dual values can be done with the following methods:

    +
      +

    • get_var_primal returns the primal value of a given variable (Feasible and Optimal status only),

      • +

    • get_var_ray returns the primal ray value of a given variable (Unbounded status only),

      • +

    • get_ctr_dual returns the dual value of a given constraint (Continuous models only),

      • +

    • get_ctr_farkas returns the Farkas certificate value of a given constraint (Continuous models and Infeasible status only).

      • +
    +
    +
    +

    Saving a Solution

    +

    Sometimes, you will find it useful to save a solution to access it later.

    +

    idol provides the following functions to do so: +save_primal, save_ray, save_dual and save_farkas. +Each of these functions takes a model as argument and returns an object of the class Point with template parameter Var or Ctr depending on the function. +The returned object stores the results of corresponding calls to get_var_primal, get_var_ray, get_ctr_dual or get_ctr_farkas methods.

    +
    +

    Example

    +

    This example shows how to solve a model using HiGHS and retrieves some piece of information about its solution.

    +
    model.use(HiGHS());
+
+model.optimize();
+
+const auto status = model.get_status();
+
+if (status == Optimal) {
+
+    std::cout << "Optimal solution found!" << std::endl;
+
+    const auto primal_values = save_primal(model);
+
+    std::cout << primal_values << std::endl;
+
+} else {
+
+    std::cout << "An optimal solution could not be found." << std::endl;
+
+    std::cout << "HiGHS returned status " << status << std::endl;
+
+    std::cout << "The reason for this status is " << model.get_reason() << std::endl;
+
+    if (status == Feasible) {
+
+        std::cout << "The optimality gap is " << model.get_relative_gap() * 100 << " %" << std::endl;
+
+    } else if (status == Unbounded) {
+
+        std::cout << "An unbounded ray is" << std::endl;
+
+        const auto primal_ray = save_ray(model);
+
+        std::cout << primal_ray << std::endl;
+
+    } else if (status == Infeasible) {
+
+        std::cout << "A Farkas certificate is" << std::endl;
+
+        const auto farkas = save_farkas(model);
+
+        std::cout << farkas << std::endl;
+
+    }
+
+}
+
    +
    +
    +
    +
    +

    Saving a Projected Solution

    +

    In a more advanced solution scheme, you may deal with extended formulations of an original model, and may want to save +the projected solution on the original problem space. +In such a case, you can use the functions save_* with an additional argument to specify the original model. +For instance.

    +
    const auto primal_values = save_primal(original_model, higher_dimensional_model);
+
    +
    +

    This code will return an object of the class Point storing the results of corresponding calls to get_var_primal methods on the higher dimensional model +for the original model variables.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/mixed-integer-programming/optimizers/universal-callbacks.html b/tutorials/mixed-integer-programming/optimizers/universal-callbacks.html new file mode 100644 index 000000000..ceea163f8 --- /dev/null +++ b/tutorials/mixed-integer-programming/optimizers/universal-callbacks.html @@ -0,0 +1,446 @@ + + + + + + + Adding User Cuts and Lazy Constraints + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Adding User Cuts and Lazy Constraints

    +

    When solving a mixed-integer program (MIP), the underlying optimizers typically make use of a branch-and-cut algorithm. +This algorithm iteratively solves a(n LP) relaxation of the problem, and then adds cuts to the problem to strengthen the relaxation. +Typically, these cuts are generated by the solver itself. However, the user can also add his or her own cuts to the problem. +This is useful when the user has domain-specific knowledge that can be used to strengthen the relaxation.

    +

    Classically, there are two types of cuts that can be added to a MIP: user cuts and lazy constraints.

    +
      +

    • User cuts are cuts which are not necessary to define the feasible region of the problem, but which can be used to strengthen the relaxation. As a matter of fact, User cuts never cut off feasible solutions to the original problem.

      • +

    • Lazy constraints are constraints which are necessary to define the feasible region of the problem but are either unlikely to be violated or impractical to generate in advance. Lazy constraints are only added to the problem if they are violated by a current solution.

      • +
    +

    In both cases, user cuts and lazy constraints are added to the problem within a callback function, given to the optimizer. +Then, the optimizer will call this callback function at each node of the branch-and-cut tree, allowing to look for violated cuts and constraints that can be added to the problem.

    +
    +

    Hint

    +

    Though it is possible for the user to create his or her own callback functions, +the idol library provides a simple way to add user cuts and lazy constraints to a MIP, using the UserCutCallback and LazyCutCallback classes. +In case you are interested in creating your own callback functions, you can refer to this page.

    +
    +

    In the next section, we will show how to implement

    +
      +

    • a simple separation procedure for knapsack cover inequalities using the UserCutCallback, and

      • +

    • a straightforward Bender’s decomposition algorithm using the LazyCutCallback class.

      • +
    + +
    +

    Introduction

    +

    Now, both classes are derived from the CallbackFactory class, and are used to create callback objects that can be passed to the optimizer. +They both have a similar interface: First, the user defines a model for the separation problem (i.e., the problem that will be solved to generate the cuts or constraints), +and the corresponding cut to be added to the original problem. +Then, the user creates a callback factory object, and passes the model and the cut to the factory. +The user also specifies which optimizer should be used to solve the separation problem. +Finally, the user passes the callback factory to the optimizer, which will manage the execution of the callback.

    +

    The main difference between the two classes is that the UserCutCallback class is called +whenever an invalid solution is found, e.g., a point which violates integer requirements, while the LazyCutCallback class is called +whenever a new valid solution is found to check that it satisfies all the lazy constraints.

    +
    +
    +

    An Example of User Cuts: Knapsack Cover Inequalities

    +
    +

    Hint

    +

    This section is dedicated to the “advanced topic” of knapsack cover inequalities. +Rudimentary notions on Knapsack problems and +Cover inequalities are recommended.

    +
    +

    Consider the knapsack problem:

    +
    +\[\begin{align} + \max_{x} \quad p^\top x \quad + \text{s.t.} \quad w^\top x \le W, \; x\in\{0,1\}^n. +\end{align}\]
    +

    Here, \(x\) is a binary vector, \(p\) is a vector of profits, \(w\) is a vector of weights, and \(W\) is the capacity of the knapsack.

    +

    It is well-known that the knapsack problem can be strengthened by adding cover inequalities. A cover inequality is a constraint of the form

    +
    +\[\sum_{i\in C} x_i \le |C| - 1,\]
    +

    where \(C\) defines a cover of the knapsack, i.e., a set of items such that the sum of their weights is greater than the capacity of the knapsack.

    +

    Given a solution \(\hat x\) to the continuous relaxation of the knapsack problem, we can check whether it violates a cover inequality +by solving the following separation problem.

    +
    +\[\begin{split}\begin{align} + \max_{z} \quad & (1 - \hat x)^\top z \qquad \ge 1 \\ + \text{s.t.} \quad & w^\top z \ge W + 1, \\ + & z\in\{0,1\}^n. +\end{align}\end{split}\]
    +

    A cover inequality is violated if and only if the optimal objective value of this problem is strictly less than 1. +In such a case, a new cut should be added.

    +

    As anticipated, we need to define three different things:

    +
      +

    • the original problem, i.e., the problem to be solved by the branch-and-cut algorithm;

      • +

    • the feasible region of the separation problem, i.e., the set of all cover inequalities;

      • +

    • the shape of the cuts to be added.

      • +
    +

    Defining the original problem is straightforward and can be done as follows.

    +
    Env env;
+Model knapsack(env, Maximize);
+
+auto x = knapsack.add_vars(Dim<1>(n), 0, 1, Binary, 0, "x");
+
+knapsack.add_ctr(idol_Sum(i, Range(n_items), w[i] * x[i]) <= W);
+knapsack.set_obj_expr(idol_Sum(i, Range(n_items), p[i] * x[i]));
+
    +
    +

    Similarly, the feasible region of the separation problem can be defined as follows.

    +
    Model cover(env);
+
+const auto z = cover.add_vars(Dim<1>(n), 0, 1, Binary, "z");
+
+cover.add_ctr(idol_Sum(i, Range(n_items), w[i] * z[i]) >= W + 1);
+
    +
    +

    Finally, we need to define the cuts to be added to the original problem for a given cover inequality \(C\). +Cuts are always expressed as if they were part of the original problem. What we mean by this is that, here, \(x\) +should be seen as a variable while \(z\) should be seen as a constant.

    +

    We therefore have, for a given \(z\),

    +
    const auto cover_cut = idol_Sum(i, Range(n_items), !z[i] * x[i]) <= idol_Sum(i, Range(n_items), 1 - !z[i]);
+
    +
    +

    See how the z variables are “turned into” constants by prepending them with an “!” symbol.

    +

    We are now ready to create the callback factory and pass it to the optimizer. This is done as follows.

    +
    knapsack.use(
+    Gurobi::Continuous()
+        .add_callback(
+            UserCutCallback(cover, cover_cut)
+                .with_separation_optimizer(Gurobi())
+        )
+);
+
+knapsack.optimize();
+
    +
    +

    Here, we solve the continuous relaxation of the knapsack problem using the Gurobi optimizer, and add the cover inequalities using the UserCutCallback.

    +
    +
    +

    An Example of Lazy Cut Constraints: Benders Optimality Cuts

    +
    +

    Hint

    +

    This section is dedicated to the “advanced topic” of Benders Decomposition. +Rudimentary notions on Linear Programming duality and +Benders Decomposition the following subjects are recommended.

    +
    +

    We will base our example on the following model taken from Blanco, V., (2016), Benders Decomposition, MINLP School: Theory +and Applications.

    +
    +\[\begin{split}\begin{align} + \min_{x,y} \quad & 2 x_0 + 3x_1 + 2y \\ + \text{s.t.} \quad & x_0 + 2x_1 + y \ge 3, \\ + & 2x_0 - x_1 + 3y \ge 4, \\ + & x\ge 0, \ y\in \mathbb N. +\end{align}\end{split}\]
    +

    The Benders reformulation of this problem, by considering \(y\) as the complicating variable, leads to

    +
    +\[\begin{split}\begin{align} + \min_{y,z} \quad & 2y + z \\ + \text{s.t.} \quad & z \ge \lambda_1 ( 3 - y ) + \lambda_2(4 - 3y) \qquad \text{for all } \lambda \in \Lambda, \\ + & z \ge 0, \ y\in\mathbb N, +\end{align}\end{split}\]
    +

    with \(\Lambda\) defined as the set of all dual feasible m_n_points_bound, i.e., those \(\lambda\in\mathbb R^2_+\) such that

    +
    +\[\begin{split}\begin{align} + & \lambda_0 + 2 \lambda_1 \le 2, \\ + & 2\lambda_0 - \lambda_1 \le 3. +\end{align}\end{split}\]
    +

    Now, we will show how to implement the Benders decomposition algorithm using the LazyCutCallback class. +This will be done so that constraints \(z \ge \hat \lambda_1 ( 3 - y ) + \hat \lambda_2(4 - 3y)\) are added to the master problem +whenever a violated Benders cut is found.

    +

    As anticipated, we need to define three different things:

    +
      +

    • the master problem, i.e., the problem to be solved at each node of the branch-and-cut tree;

      • +

    • the dual space \(\Lambda\), i.e., the feasible region of the separation problem;

      • +

    • the shape of the cuts to be added.

      • +
    +

    Defining the master problem is straightforward and can be done as follows.

    +
    Env env;
+
+Model master(env);
+
+const auto y = master.add_var(0, Inf, Integer, 0, "y");
+const auto z = master.add_var(0, Inf, Continuous, 0, "z");
+
+master.set_obj_expr(2 * y + z);
+
    +
    +

    Similarly, the dual space \(\Lambda\) can be defined as follows.

    +
    Model dual_space(env);
+
+const auto lambda = dual_space.add_vars(Dim<1>(2), 0, Inf, Continuous, "lambda");
+
+dual_space.add_ctr(lambda[0] + 2 + lambda[1] <= 2);
+dual_space.add_ctr(2 * lambda[0] - lambda[1] <= 3);
+
    +
    +

    Finally, we need to define the cuts to be added to the master problem for a given dual variable \(\lambda\). +Cuts are always expressed as if they were part of the master problem. What we mean by this is that, here, \(y\) +should be seen as a variable while \(\lambda\) should be seen as a constant.

    +

    We therefore have, for a given \(\lambda\),

    +
    const auto benders_cut = z >= !lambda[0] * (3 - y) + !lambda[1] * (4 - 3 * y);
+
    +
    +

    See how the lambda variables are “turned into” constants by prepending them with an “!” symbol.

    +

    We are now ready to create the callback factory and pass it to the optimizer. This is done as follows.

    +
    master.use(
+    Gurobi()
+        .add_callback(
+            LazyCutCallback(dual_space, benders_cut)
+                .with_separation_optimizer(Gurobi())
+        )
+        .with_lazy_cut(true)
+);
+
+master.optimize();
+
    +
    +

    That’s it! The optimizer will now call the callback function at each node of the branch-and-cut tree, and add the cuts to the master problem whenever a violated constraint is found.

    +
    +

    Hint

    +

    Here, we added a call to Gurobi::with_lazy_cut. This is because the Gurobi optimizer does not support lazy cuts by default +and one needs to explicitly enable them.

    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/index.html b/tutorials/robust-optimization/index.html new file mode 100644 index 000000000..a9de3298b --- /dev/null +++ b/tutorials/robust-optimization/index.html @@ -0,0 +1,264 @@ + + + + + + + Robust Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Robust Optimization

    +
    +

    Warning

    +

    This section is under construction.

    +
    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/single-stage/index.html b/tutorials/robust-optimization/single-stage/index.html new file mode 100644 index 000000000..438d65691 --- /dev/null +++ b/tutorials/robust-optimization/single-stage/index.html @@ -0,0 +1,245 @@ + + + + + + + Single-stage Robust Optimization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Single-stage Robust Optimization

    +
    +

    Warning

    +

    This section is under construction.

    +
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.html b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.html new file mode 100644 index 000000000..82cd332ac --- /dev/null +++ b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/index.html @@ -0,0 +1,249 @@ + + + + + + + Using Column-and-Constraint-Generation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using Column-and-Constraint-Generation

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.html b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.html new file mode 100644 index 000000000..0705ed7db --- /dev/null +++ b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/introduction.html @@ -0,0 +1,367 @@ + + + + + + + Introduction + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Introduction

    +

    The Column-and-Constraint Generation (CCG) algorithm is a classical method for solving two-stage robust optimization problems. +It was originally introduced by [17].

    +

    In idol, the implementation of CCG alows to solve a class of problems which is slightly more general than classical +two-stage robust optimization problems. This class of problems is defined in the following section.

    + +
    +

    Problem Definition and Notation

    +

    The CCG algorithm can solve optimization problems of the form

    +
    +(1)\[\begin{split}\begin{align} + \min_x \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & \forall \xi\in\Xi, \ \exists y\in Y(x,\xi), \ G(x,y,\xi) \le 0. +\end{align}\end{split}\]
    +

    in which \(f:\mathbb R^{n_x}\rightarrow\mathbb R\) is a given function, +\(X\subseteq\mathbb R^{n_x}\) is a given set, called the first-stage feasible set, +\(\Xi\subseteq\mathbb R^{n_\xi}\) is a given set, called the uncertainty set, typically compact, +\(Y(x,\xi) \subseteq \mathbb R^{n_y}\) is a set, defined for all \(x\in X\) and \(\xi\in\Xi\), called the second-stage feasible set, and +\(G:\mathbb R^{n_x+n_y+n_\xi}\rightarrow\mathbb R^\ell\) is a given vector of functions, defining the so-called coupling constraints between the uncertainty, the first- and the second-stage decisions.

    +
    +

    Regarding Coupling Constraints

    +

    It is clear that coupling constraints are redundant since they can be incorporated into the definition of the second-stage feasible set. +However, we will see that explicitly defining coupling constraints may lead to different implementations of the CCG algorithm. +We will dive into this aspect after introducing the concept of separators.

    +
    +
    +

    Hint

    +

    Consider the Min-Max-Min problem

    +
    +\[\min_{x\in X} \ \max_{\xi\in\Xi} \ \min_{y\in Y(x,\xi)} \ \psi(x,y,\xi).\]
    +

    Clearly, this is a special case of (1) since it can be written as

    +
    +\[\begin{split}\begin{align} + \min_{x_0,x} \quad & x_0 \\ + \text{s.t.} \quad & (x_0,x) \in\mathbb R\times X, \\ + & \forall \xi\in\Xi, \ \exists y\in Y(x,\xi), \ \psi(x,y,\xi) \le x_0. +\end{align}\end{split}\]
    +

    Here, there is only one coupling constraint, which is \(\psi(x,y,\xi) \le x_0\).

    +
    +
    +
    +

    The Algorithm

    +
    +

    Basic Idea

    +

    The idea of the CCG algorithm is to consider a finite subset of m_n_points_bound in \(\Xi\), say \(\{ \xi^1, \dotsc, \xi^k \}\), +and to solve the following problem instead of (1):

    +
    +(2)\[\begin{split}\begin{align} + \min_{x_0,x,y^1,\dotsc,y^K} \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & G(x,y^t,\xi^t) \le 0 \qquad k=1,\dotsc,K, \\ + & y^t\in Y(x,\xi^t) \qquad k=1,\dotsc,K. +\end{align}\end{split}\]
    +

    Here, a new variable \(y^t\) has been introduced for each \(t=1,...,k\), enforcing that, indeed, +there exists \(y^t\in Y(x,\xi^t)\) such that \(G(x,y^t,\xi^t) \le 0\).

    +

    Note that Problem (2) is a relaxation of Problem (1) since +any feasible point of (1) is also feasible for (2) (for some \(y^1,\dotsc,y^K\)).

    +

    Now, given a solution \(\hat x\in X\) to the relaxed problem (2), +one needs to check whether \(\hat x\) is feasible for Problem (1). +Thus, one seeks a scenario \(\xi^*\in\Xi\) such that, either \(Y(\hat x, \xi^*)\) is empty, or \(G(\hat x,y,\xi^*) > 0\) for all \(y\in Y(\hat x, \xi^*)\). +If no such scenario exists, then \(\hat x\) is feasible for (1). Otherwise, the new scenario \(\xi^*\) is added to the set of considered scenarios and the process is repeated.

    +

    Identifying a missing scenario is called separation, and can be done by solving the following problem:

    +
    +(3)\[ \max_{\xi\in \Xi} \ \max_{\ell=1,...,L} \left\{ \ \min_{ y\in Y(\hat x,\xi) } \ G_\ell(\hat x,y,\xi) \right\}.\]
    +

    If the optimal value of the separation problem is non-positive, then \(\hat x\) is feasible for (1). +Otherwise, the solution to the separation problem gives a new scenario \(\xi^*\) to be added to the set of scenarios.

    +

    Note that we use the convention \(\max \emptyset = -\infty\) and \(\min \emptyset = +\infty\).

    +
    +
    +

    Separators

    +

    Clearly, the separation problem (3) can be solved in many different ways. In idol, +it is therefore possible to give a user-defined functor, called a separator, which solves the separation problem. +Note that the most common ways to solve the separation problem are already implemented in idol. +Yet, if you wish to implement your own separator, you should refer to this tutorial.

    +

    Shortly put, the separator solves problems of the form

    +
    +(4)\[ \max_{\xi\in \Xi} \ \min_{ y\in Y(\hat x,\xi) } \ G_\ell(\hat x,y,\xi),\]
    +

    for a given \(G_\ell\) (\(\ell\in\{1,...,L\}\)).

    +

    Note that it is ensured that the separator always solves a problem which is feasible. +Indeed, in case Problem (3) +is not known to satisfy the complete recourse assumption (i.e., it is not known whether \(\forall x\in X, \forall\xi\in\Xi, \exists y\in Y(x,\xi)\) holds), +the CCG algorithm will first solve a feasibility version of the separation problem to check whether +\(\hat x\) is such that for all \(\xi\in\Xi\) there exists \(y\in Y(\hat x,\xi)\). +Fortunately, it is also possible to specify that the complete recourse assumption holds, in which case the feasibility version of the separation problem is not solved.

    +

    Let \(\xi^{\ell}\) denote the solution to the separation problem (4) for a given \(\ell\in\{1,...,L\}\). +Then, a scenario \(\xi^{\ell^*}\) is added to Problem (2) if and only if

    +
    +\[\ell^* \in \underset{\ell=1,...,L}{\text{argmax}} \ \min_{ y\in Y(\hat x,\xi^\ell) } \ G_\ell(\hat x,y,\xi^\ell) > \varepsilon_\text{feas}.\]
    +

    See the dedicated page for more details.

    +
    +
    +
    +

    On the Impact of Coupling Constraints

    +

    We now discuss the impact of the definition of the coupling constraints \(G\) on the implementation of the CCG algorithm. +Clearly, one obtains an equivalent problem to (1) by defining the second-stage feasible set as

    +
    +\[\tilde Y(x,\xi) = \{ y\in Y(x,\xi) \ | \ G(x,y,\xi) \le 0 \},\]
    +

    and by considering the problem

    +
    +\[\begin{split}\begin{align} + \min_x \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & \forall \xi\in\Xi, \ \exists y\in \tilde Y(\hat x,\xi). +\end{align}\end{split}\]
    +

    In this case, the separation problem becomes

    +
    +\[\max_{\xi\in\Xi} \ \min_{ y\in \tilde Y(\hat x,\xi) } \ 0,\]
    +

    which is a feasibility problem.

    +

    Though the two approaches are equivalent, in the sense that they will both lead to a solution to (1), +they may lead to different computational performances. An interested reader may refer to, e.g., [2] for more details.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.html b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.html new file mode 100644 index 000000000..ba2a77502 --- /dev/null +++ b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/trust-region-stabilization.html @@ -0,0 +1,351 @@ + + + + + + + Using Trust Region Stabilization + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Using Trust Region Stabilization

    +

    This tutorial describes how to use the trust region stabilization in the CCG algorithm. +This stabilization technique is inspired by the work of [3] on Benders decomposition.

    +
    +

    Assumption

    +

    This feature is only applicable if the first-stage decisions are binary, i.e., \(X \subseteq \{0,1\}^{n_x}\).

    +
    + +
    +

    Introduction

    +

    In this section, we discuss stabilization of the CCG algorithm if the first-stage decisions are binary, i.e., \(X \subseteq \{0,1\}^{n_x}\).

    +

    Let \(\bar x\) be a given stability center, i.e., a point that is thought to be a “good” solution to the problem. +The following constraint is called a local branching constraint:

    +
    +\[\Delta(x,\bar x) := \sum_{i:\bar x_i = 1} (1 - x_i) + \sum_{i:\bar x_i = 0} x_i \le \rho,\]
    +

    with \(\rho\) a given radius. Additionally, we call reversed local branching constraint the following constraint:

    +
    +\[\Delta(x,\bar x) \ge \rho + 1.\]
    +

    At each iteration, the stabilized CCG algorithm solves the following problem instead of (2):

    +
    +\[\begin{split}\begin{align} + \min_{x_0,x} \quad & f(x) \\ + \text{s.t.} \quad & x\in X, \\ + & G(x,y^t,\xi^t) \le 0 \quad t=1,\dotsc,k, \\ + & y^t\in Y(x,\xi^t) \quad t=1,\dotsc,k, \\ + & \Delta(x,\bar x) \le \rho, \\ + & \Delta(x,\bar x') \ge \rho' + 1 \quad \forall (\bar x', \rho') \in R, +\end{align}\end{split}\]
    +

    for some set \(R\subseteq X\times\mathbb N\) of reversed local branching constraints.

    +

    The complete stabilized CCG algorithm is described with the following pseudocode.

    +
    +    \begin{algorithm}
+    \caption{Stabilized CCG Algorithm}
+    \begin{algorithmic}
+    \REQUIRE An initial radius \( \rho\in\{ 1,\dotsc, n_x \} \) and an initial point \( \bar x\in X \).
+    \STATE Initialize \( k \gets 0 \), \( UB \gets +\infty \), \( LB \gets -\infty \), \( R \gets \emptyset \)
+    \STATE Solve the restricted master problem (RMP)
+    \IF{the RMP is infeasible}
+        \IF{ \( \rho \ge n_x \) }
+            \STATE STOP, \( UB \) is the optimal value.
+        \ENDIF
+        \STATE Add a reversed local branching constraint, \( R \gets R \cup (\bar x, \rho) \)
+        \STATE Increase \( \rho \)
+    \ELSE
+        \STATE Let \( x^k \) be the solution of the RMP and \( v^k \) be its value
+        \STATE Solve the separation problem, let \( \xi^k \) be the solution and \( s^k \) be its value
+        \IF{ \( s^k \le \varepsilon_\text{feas} \) }
+            \STATE \( UB \gets \min\{ UB, v^k \} \)
+            \STATE Solve the RMP without the stabilization constraints, let $\underline v^k$ be its value, set \( LB \gets \underline v^k \)
+            \IF{ \( UB - LB \le \varepsilon \) }
+                \STATE STOP, \( UB \) is the optimal value.
+            \ENDIF
+            \STATE Add a reversed local branching constraint, \( R \gets R \cup (x^k, \rho) \)
+            \STATE Update the stability center \( \bar x \gets x^k \)
+            \STATE Optionally, reset \( \rho \gets 1 \)
+        \ENDIF
+        \STATE \( k \gets k + 1 \)
+        \STATE Go back to step 2
+    \ENDIF
+    \end{algorithmic}
+    \end{algorithm}
+
    +

    Note that if \(\rho \ge n_x\), the stabilized CCG is exactly the CCG algorithm.

    +
    +
    +

    Implementation in idol

    +

    Activating the trust region stabilization in idol is done through the method with_stabilization of the idol::Robust::ColumnAndConstraintGeneration class. +An object of the class Robust::CCGStabilizers::TrustRegion must be passed as an argument to the method.

    +

    The following code shows how to use the trust region stabilization in idol.

    +
    model.use(
+        Robust::ColumnAndConstraintGeneration(stages, uncertainty_set)
+                .with_master_optimizer(Gurobi())
+                .with_separator(Robust::CCGSeparators::Bilevel())
+                .with_stabilization(Robust::CCGStabilizers::TrustRegion())
+                .with_logs(true)
+);
+
+model.optimize();
+
    +
    +

    Note that the radius \(\rho\) is set to

    +
    +\[\rho \gets \lceil \mu_i n_x \rceil\]
    +

    where \(\mu_i\) is a parameter controlling the size of the trust region and \(n_x\) is the number of (binary) first-stage variables. By default, \(\mu_i\) takes value in +:\(\lbrace .01, .02, .5 \rbrace\). +You can set the values of \(\mu_i\) by calling the method with_trust_factors of the class Robust::CCGStabilizers::TrustRegion. +For instance, the following code sets the trust factors to \(\lbrace .02, .5 \rbrace\).

    +
    model.use(
+        Robust::ColumnAndConstraintGeneration(stages, uncertainty_set)
+                .with_master_optimizer(Gurobi())
+                .with_separator(Robust::CCGSeparators::Bilevel())
+                .with_stabilization(
+                    Robust::CCGStabilizers::TrustRegion()
+                        .with_trust_factors({.02, .5})
+                )
+                .with_logs(true)
+);
+
    +
    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.html b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.html new file mode 100644 index 000000000..052750bc1 --- /dev/null +++ b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/write-ccg.html @@ -0,0 +1,279 @@ + + + + + + + Writing a Column-and-Constraint-Generation Algorithm + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Writing a Column-and-Constraint-Generation Algorithm

    +

    In this tutorial, we will see how to write a column-and-constraint-generation to solve a two-stage robust problem.

    +

    To this end, we will assume that you have your two-stage robust problem modeled already in idol. In particular, +we consider that you have

    +
      +

    1. (idol::Model) model which is the deterministic model of the problem in which the uncertain data are seen as parameters.

      2. +

    2. (idol::Model) uncertainty_set which is the uncertainty set of the robust problem.

      3. +

    3. (idol::Robust::StageDescription) stages which stores the assignments of variables and constraints to each stage.

      4. +
    +

    If you do not know what these are, please refer to the tutorial on how to model a two-stage robust problem.

    +

    Then, you can solve this two-stage robust problem using a column-and-constraint-generation algorithm as follows:

    +
     model.use(
+        Robust::ColumnAndConstraintGeneration(stages, uncertainty_set)
+                .with_master_optimizer(Gurobi())
+                .with_separator(Robust::CCGSeparators::Bilevel())
+                .with_logs(true)
+);
+
+model.optimize();
+
+std::cout << save_primal(model) << std::endl;
+
    +
    +

    Notice that the optimizer is attached to the deterministic model and that both the uncertainty set and the stages are passed as arguments. +An optimizer to solve the master problem is necessary and will be called when needed. Here, we use the Gurobi optimizer.

    +

    Most importantly, it is also necessary to specify a separator. The separator is a sub-routine of the CCG algorithm +which solves the separation problem, i.e., it finds the worst-case scenario for a given solution to the master problem. +In this example, we use the Bilevel separator which calls the MibS bilevel optimization solver at each iteration.

    +

    Finally, the method optimize is called to solve the problem and the solution is printed.

    +
    +

    Hint

    +

    Here, we have assumed that the problem does not satisfy the complete recourse assumption, i.e., it is not known if +\(\forall x\in X, \forall\xi\in\Xi, \exists y\in Y(x,\xi)\). If, to the contrary, this assumption holds, +it can be communicated to the solver by calling the method with_complete_recourse(true). By doing this, +the CCG algorithms will not solve the feasibility separation problem which is most likely to result in a faster convergence.

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.html b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.html new file mode 100644 index 000000000..c400af909 --- /dev/null +++ b/tutorials/robust-optimization/two-stage/column-and-constraint-generation/writing-separator.html @@ -0,0 +1,221 @@ + + + + + + + Writing Your Own Separator (Advanced) [TODO] + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Writing Your Own Separator (Advanced) [TODO]

    +
    +

    Warning

    +

    This is a work in progress. Thank you for your understanding.

    +
    +
    + + +
    +
    +
      +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/index.html b/tutorials/robust-optimization/two-stage/index.html new file mode 100644 index 000000000..5ef002535 --- /dev/null +++ b/tutorials/robust-optimization/two-stage/index.html @@ -0,0 +1,270 @@ + + + + + + + Adjustable Robust Optimization (Two-stage) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Adjustable Robust Optimization (Two-stage)

    +
    + +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file diff --git a/tutorials/robust-optimization/two-stage/modeling.html b/tutorials/robust-optimization/two-stage/modeling.html new file mode 100644 index 000000000..809861843 --- /dev/null +++ b/tutorials/robust-optimization/two-stage/modeling.html @@ -0,0 +1,424 @@ + + + + + + + Modeling Adjustable Robust Problems + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + idol + + + +
    + + + + + +
    + + Github + +
    + + +     +
    +     + + +
    +
    + + + + + + + + +
    + + Github + +
    + + + +     +     + + + +
    +
    + +
    +

    Modeling Adjustable Robust Problems

    +

    In this tutorial, we will see how to model a two-stage robust problem in idol.

    +

    To follow this tutorial, you should be familiar with two-stage robust optimization and modeling optimization problems in idol. +If this is not the case, we recommend you to read the tutorial on MIP modeling.

    + +
    +

    A Two-Stage Robust Facility Location Problem

    +

    We consider a two-stage robust facility location problem (FLP) where demands are uncertain.

    +

    Given a set of potential facility locations \(V_1\) and a set of customers \(V_2\), the goal is to select a subset of facility locations +to activate in order to serve all customers’ demand, while minimizing the total cost. +This version introduces uncertainty in the customers’ demands.

    +

    Note that there is also an example for the deterministic version of the FLP using Column Generation.

    +

    Each facility \(i\in V_1\) has an opening cost \(f_i\) and a maximum capacity \(q_i\). +Each customer \(j\in V_2\) has a demand \(d_j\). +The unitary cost for serving customer \(j\in V_2\) from facility \(i\in V_1\) is \(t_{ij}\). +The uncertainty in customer demands is controlled by a parameter \(\Gamma\).

    +

    In this robust variant, we consider that the demands are uncertain and can be expressed as \(d_j(\xi) = d_j(1 + p\xi_j)\) +with \(p\) being the maximum increase in demand and \(\xi\) being an unknown vector taken in the uncertainty set

    +
    +\[\Xi := \left\{ \xi\in[ 0, 1 ]^{|V_2|} : \sum_{j\in V_2} \xi_j \le \Gamma \right\}.\]
    +

    We model the two-stage robust FLP as

    +
    +\[\min_{x\in \{0,1\}^{|V_1|}} \ \left\{ \sum_{i\in V_1} f_i x_i + \max_{\xi\in \Xi} \ \min_{y\in Y(x,\xi)} \ \sum_{i\in V_1} \sum_{j\in V_2} t_{ij} y_{ij} \right\}\]
    +

    where \(Y(x,\xi)\) is the set of feasible solutions for the second stage problem, given the first stage solution \(x\) and the realization \(\xi\) of the uncertain demand vector. +It is defined as the set of vectors \(y\in \mathbb{R}^{|V_1|\times|V_2|}\) that satisfy the following constraints

    +
    +\[\begin{split}\begin{align*} + & \sum_{i\in V_1} y_{ij} = d_j(\xi) && j\in V_2, \\ + & \sum_{j\in V_2} y_{ij} \le q_i x_i && i\in V_1, \\ + & y_{ij} \ge 0 && i\in V_1, j\in V_2. +\end{align*}\end{split}\]
    +

    In what follows, we will assume that we have a variable instance of type idol::Problems::FLP::Instance +that contains the data of the problem. Most typically, you will want to read the instance from a file. This is done as follows.

    +
    // Read instance
+const auto instance = Problems::FLP::read_instance_1991_Cornuejols_eal("robust_ccg.data.txt");
+
    +
    +

    Additionally, we define an optimization environment env and some parameters.

    +
    Env env;
+
+const double Gamma = 3;
+const double percentage_increase = .2;
+
    +
    +
    +
    +

    Modeling Steps

    +

    To model a two-stage robust problem, one needs to perform the following steps:

    +
      +

    1. Define an uncertainty set \(\Xi\).

      2. +

    2. Define the deterministic model in which \(\xi\) is a parameter.

      3. +

    3. Assign a stage to each variable and constraint.

      4. +
    +

    Let’s see how these steps are done in idol.

    +
    +

    Defining the Uncertainty Set

    +

    Modeling the uncertainty set \(\Xi\) is done in the same way as modeling any classical optimization problem. +For instance, one can do as follows.

    +
    const unsigned int n_customers = instance.n_customers();
+
+Model uncertainty_set(env);
+
+auto xi = uncertainty_set.add_vars(Dim<1>(n_customers), 0., 1, Binary, "xi");
+uncertainty_set.add_ctr(idol_Sum(j, Range(n_customers), xi[j]) <= Gamma);
+
    +
    +

    Note that defining an objective function is not necessary since the uncertainty set is not optimized over. +If an objective function is defined, it will be ignored by the optimizer.

    +
    +
    +

    Defining the Deterministic Model

    +

    The deterministic model underlying the two-stage robust FLP is the same as the classical FLP, except that the demand is seen as a parameter.

    +

    Recall that a variable, e.g., xi[0], can be turned into a parameter by prepending it with !.

    +

    Hence, +we can define the deterministic model as follows.

    +
    const unsigned int n_facilities = instance.n_facilities();
+
+Model model(env);
+
+const auto x = model.add_vars(Dim<1>(n_facilities), 0., 1., Binary, "x");
+const auto y = model.add_vars(Dim<2>(n_facilities, n_customers), 0., Inf, Continuous, "y");
+
+// Capacity constraints
+for (unsigned int i = 0 ; i < n_facilities ; ++i) {
+    model.add_ctr(idol_Sum(j, Range(n_customers), y[i][j]) <= instance.capacity(i) * x[i]);
+}
+
+// Demand satisfaction constraints
+for (unsigned int j = 0 ; j < n_customers ; ++j) {
+    // IMPORTANT: here we use the parameter "!xi[j]" instead of the variable "xi[j]"
+    model.add_ctr(idol_Sum(i, Range(n_facilities), y[i][j]) == instance.demand(j) * (1 + percentage_increase * !xi[j]));
+}
+
+// Objective function
+model.seobj_expr(idol_Sum(i, Range(n_facilities),
+                            instance.fixed_cost(i) * x[i]
+                            + idol_Sum(j, Range(n_customers),
+                                       instance.per_unit_transportation_cost(i, j) * y[i][j]
+                            )
+                   )
+);
+
    +
    +
    +
    +

    Assigning Stages

    +

    The last step is to assign a stage to each variable and constraint. Here, variables \(x\) are first-stage variables +and variables \(y\) are second-stage variables, i.e., they depend on the realization of the uncertain demand. +Similarly, all constraints are second-stage constraints since they are part of the second-stage feasible region.

    +

    Assigning stages is done by creating a new object of type idol::Robust::StageDescription. +Under the hood, this object does nothing more but defining new annotations for variables and constraints storing +the assigned stage of each variable and constraint. It is created as follows.

    +
    Robust::StageDescription stages(env);
+
    +
    +

    By default, all variables and constraints are assigned to the first stage. +To assign a variable or constraint to the second stage, one can use the method set_stage of the object stages. +For instance, one can do as follows.

    +
    for (const auto& var : model.vars()) {
+    if (var.name().front() != 'x') {
+        stages.set_stage(var, 2);
+    }
+}
+
    +
    +

    Similarly, since all constraints are second-stage constraints, one can do as follows.

    +
    for (const auto& ctr : model.ctrs()) {
+    stages.set_stage(ctr, 2);
+}
+
    +
    +
    +

    About stage annotations

    +

    Note that it is also possible to define your own annotations to assign variables and constraints to stages. +This is a rather advanced feature and it is your responsability to ensure that the annotations are consistent with the model.

    +

    The annotations are based on the following conventions: all first-stage variables and constraints have the annotation evaluating to MasterId. +All second-stage variables and constraints have the annotation evaluating to 0.

    +

    For instance, the following code is equivalent to the previous one.

    +
    Annotation<Var, unsigned int> stage_vars(model, "stage_vars", MasterId); // By default, all variables are first-stage variables
+Annotation<Ctr, unsigned int> stage_ctrs(model, "stage_ctrs", MasterId); // By default, all constraints are first-stage constraints
+
+for (const auto& var : model.vars()) {
+    if (var.name().front() != 'x') {
+        var.set(stage_vars, 0); // Assign variable to the second stage
+    }
+}
+
+for (const auto& ctr : model.ctrs()) {
+    ctr.set(stage_ctrs, 0); // Assign constraint to the second stage
+}
+
+idol::Robust::StageDescription stages(stage_vars, stage_ctrs);
+
    +
    +

    By doing so, a call to stages.stage(var) will return “1” for all first-stage variables and “2” for all second-stage variables. +The underlying annotation can be obtained using

    +
    Annotation<Var, unsigned int> stage_vars = stages.stage_vars()
+
    +
    +

    Finally, also note the method stages.stage_index(var) that will return “0” for all first-stage variables and “1” for all second-stage variables.

    +
    +

    That’s it! We have now modeled a two-stage robust FLP in idol. Note that you will now need +to attach an optimizer to the model to solve it. +To this end, be sure to check the tutorials on optimizers for two-stage robust problems, e.g., the column-and-constraint generation tutorial.

    +
    +
    +
    +

    Complete Example

    +

    A complete example is given here

    +
    +
    + + +
    +
    +
    +
    +
    +     +
    + + + + \ No newline at end of file