update tutorials for robust

docs/tutorials/index.rst

@@ -36,3 +36,7 @@ Robust Optimization
 
     robust-optimization/index
 
+Artificial Intelligence
+-----------------------
+
+To come...

docs/tutorials/robust-optimization/index.rst

@@ -3,12 +3,26 @@
 Robust Optimization
 ===================
 
-.. warning::
+Robust optimization is a field of mathematical optimization that explicitly accounts for uncertainty in optimization problems.
+In many real-world applications, the input parameters—such as costs, demands, or resource availabilities—are not precisely known
+at the time decisions must be made. This uncertainty can arise from estimation errors, forecasting inaccuracies,
+or inherent variability in the system.
+Robust optimization provides a framework for making decisions that remain feasible and perform well across a range of
+possible realizations of the uncertain parameters.
 
-    This section is under construction.
+A key concept in robust optimization is the *uncertainty set*, which defines the range of possible values that uncertain
+parameters can take.
+Instead of assuming that uncertain parameters follow a known probability distribution (as, e.g., in stochastic optimization),
+robust optimization only requires that they belong to a predefined set. This set, typically denoted as :math:`U`, captures
+the worst-case deviations within a specified level of conservatism.
+By optimizing against the worst-case scenario within :math:`U`, robust optimization ensures that the solution remains
+feasible and performs satisfactorily under all realizations within the uncertainty set.
+
+There are mainly two types of problems that can be handled by idol: single-stage problems and two-stage problems.
+If you are new to robust optimization, we strongly advise you to start with the single-stage problems.
 
 .. toctree::
-    :maxdepth: 3
+    :maxdepth: 2
     :glob:
 
     single-stage/index

docs/tutorials/robust-optimization/single-stage/index.rst

@@ -3,9 +3,26 @@
 Single-stage Robust Optimization
 ================================
 
-.. warning::
+A classic robust optimization model can be formulated as follows:
+
+.. math::
+
+    \min_{x} \quad & c^\top x \\
+    \text{s.t.} \quad & \sum_{i=1}^j (\bar a_{ij} + \hat a_{ij}u_j)x_j \ge b_i \qquad \text{for all }u\in U_i, \qquad i=1,\dotsc,m,  \\
+     & x\in X.
+
+Here:
+
+- :math:`x` represents the decision variables.
+- :math:`c^\top x` is the objective function to be minimized.
+- The constraints involve uncertain coefficients :math:`a_{ij}`, which are modeled as :math:`\bar a_{ij} + \hat a_{ij} u_j`, where :math:`\bar a_{ij}` is the nominal value, and :math:`\hat a_{ij} u_j` represents the uncertainty.
+- :math:`U_i` is the uncertainty set, specifying the range of possible values for the uncertain parameters :math:`u_j`.
+- The goal is to find a solution :math:`x` that satisfies the constraints for all possible values of :math:`u` within :math:`U_i` for row :math:`i`.
+
+This formulation ensures that the solution is robust against the worst-case realizations of the uncertain parameters within the given uncertainty set.
+The choice of :math:`U` significantly impacts the conservatism of the solution: a larger uncertainty set leads to a more
+robust but potentially more conservative solution, while a smaller set provides less protection against extreme variations.
 
-    This section is under construction.
 
 .. toctree::
     :maxdepth: 3

docs/tutorials/robust-optimization/two-stage/ccg.rst

@@ -1,5 +1,5 @@
-Introduction to the Column-and-Constraint Generation
-====================================================
+The Column-and-Constraint Generation: Introduction
+==================================================
 
 .. contents:: Table of Contents
     :local:
@@ -8,6 +8,10 @@ Introduction to the Column-and-Constraint Generation
 Introduction
 ------------
 
+.. warning::
+
+    This tutorial is still under construction.
+
 Robust Bilevel Optimization with Wait-and-See Lower Level
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 

docs/tutorials/robust-optimization/two-stage/index.rst

@@ -1,14 +1,11 @@
 .. _robust_single:
 
-Adjustable Robust Optimization (Two-stage)
+Two-stage Robust Optimization (Adjustable)
 ==========================================
 
-
-
 .. toctree::
-    :maxdepth: 3
+    :maxdepth: 1
     :glob:
 
     modeling
     ccg
-    column-and-constraint-generation/index

docs/tutorials/robust-optimization/two-stage/modeling.rst

@@ -3,6 +3,10 @@
 Modeling Adjustable Robust Problems
 ===================================
 
+.. warning::
+
+    This tutorial is still under construction.
+
 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.

examples/robust/ccg-wait-and-see-follower.data.txt

@@ -0,0 +1,16 @@
+5	5
+28	109
+60	144
+42	103
+0	31
+42	154
+63
+59
+35
+49
+65
+0.98	0.58	0.37	0.84	1.08	
+0.78	0.58	0.48	0.51	0.54	
+0.9	0.61	0.41	0.64	0.73	
+0.27	0.46	0.64	0.16	0.14	
+0.18	0.34	0.57	0.1	0.27	

examples/robust/ccg-wait-and-see-follower.example.cpp

@@ -88,7 +88,7 @@ int main(int t_argc, const char** t_argv) {
     for (const auto& ctr : second_stage_constraints) {
         bilevel_description.make_lower_level(ctr);
     }
-    bilevel_description.set_lower_level_obj(model.get_obj_expr());
+    bilevel_description.set_lower_level_obj(-model.get_obj_expr());
 
     /**************************/
     /* Create Uncertainty Set */

lib/src/robust/optimizers/column-and-constraint-generation/Formulation.cpp

@@ -19,7 +19,6 @@ idol::CCG::Formulation::Formulation(const idol::Model &t_parent, const idol::Rob
     parse_constraints();
     copy_bilevel_description(t_bilevel_description, m_bilevel_description_separation);
 
-    // if is wait-and-see follower, copy annotation, make sure master solver is a bilevel solver
     if (is_wait_and_see_follower()) {
         auto& env = m_parent.env();
         m_bilevel_description_master = std::make_optional<::idol::Bilevel::Description>(env);