Create wumpus_faster_edition.mzn

wumpus_faster_edition.mzn

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+% This is a working edition of wumpus problem of workshop_08 at week 4 of the Modeling Discrete Optimization of coursera 
+% Done by: Ahmed Hassan, <[email protected]>, 7.9.2016
+int: n; % number of nodes
+set of int: NODE = 1..n;
+int: m; % number of edges
+set of int: EDGE = 1..m;
+array[EDGE] of NODE: from;
+array[EDGE] of NODE: to;
+int: maxsteps; % maximum number of steps
+set of int: TIME = 0..maxsteps;
+
+NODE: start;
+NODE: gold;
+
+set of int: ACTION = 0..n+1;
+ACTION: donothing = 0; % do nothing action = 0
+ACTION: pickup = n+1;  % action n+1 is pickup gold
+                       % otherwise its move to node i
+
+%% decisions
+var 1..maxsteps: steps;  % number of actions required
+array[1..maxsteps] of var ACTION: act;
+
+%% auxiliaries to hold state
+array[TIME] of var NODE: position;
+array[TIME] of var bool: holding;
+
+
+
+int: wumpus = 99; % forbiden point 
+constraint forall(t in TIME)(position[t] != wumpus); 
+
+
+
+
+solve :: int_search([steps], input_order, indomain_min, complete)
+      minimize steps;
+% solve minimize steps;
+
+
+output ["Actions are : Starting at "  ++ show(start) ++ " , "]++[ if fix(act[t]) = donothing then 
+            "do_nothing"
+         else if fix(act[t]) = pickup then
+            "pickup_gold"
+         else "move_to " ++ show(act[t]) endif endif
+         ++ " , "
+       | t in 1..fix(maxsteps) ] ++ ["\n ACTIONS = " ++ show(act)]  ++ ["\n POSITIONS = " ++ show(position)]  ++ ["\n hold_status = " ++ show(holding)]  ++ ["\n Steps = " ++ show(steps)];
+
+
+predicate valid(var int: current_position, var int: next_position) = exists(i in EDGE)(from[i] == current_position /\ to[i] == next_position);
+
+predicate action(var int: current_position, var bool: current_holding,var ACTION: next_action,var int: next_position, var bool: next_holding) = 
+((valid(current_position,next_position) /\ next_action == next_position) \/ (current_position == next_position /\ next_action in { pickup, donothing})) 
+/\ (current_holding <= next_holding)
+/\ (current_position == gold /\ not(current_holding)  <-> next_action == pickup); 
+
+constraint forall(i in 0..maxsteps-1)(action(position[i], holding[i], act[i+1], position[i+1], holding[i+1]));
+
+constraint position[0] = start;
+constraint position[steps] = start /\ holding[steps];
+constraint exists(i in 1..maxsteps-1)(act[i] = pickup);
+constraint steps = sum(i in 1..maxsteps )(if act[i] != 0 then 1 else 0 endif);
+constraint forall(i in 1..maxsteps-1)(act[i] == 0 -> act[i+1] == 0 );