Originally posted by: A.Omidi

Dear community team,

I was trying to solve a MIP model that contains a chance constraint. An OPL example is:

https://www.ibm.com/developerworks/community/forums/html/topic?id=662dda0c-f72b-44ef-9da3-9f12022ea6b0&ps=25

I try to write the mentioned model (OPL) in Java and I have some issues on it.  The model is as follows:

                        // variables
                        IloNumVar x = cplex.numVar(0, Double.MAX_VALUE, "x");
                        IloNumVar y = cplex.numVar(0, Double.MAX_VALUE, "y");

                        // expressions
                        IloLinearNumExpr objective = cplex.linearNumExpr();
                        objective.addTerm(5, x);
                        objective.addTerm(6, y);

                        // define objective
                        cplex.addMinimize(objective);

                        // define constraints                   
                        double alfa = 0.5;      
                        double[] a1 = new double[] {1,2,3,4,5,6};
                        double[] a2 = new double[] {1,2,3,4,5,6};
                        IloLinearNumExpr logic = cplex.linearNumExpr();
                        for (int i = 0; i < a1.length; i++) {
                                logic.addTerm(a1[i], x);
                                logic.addTerm(a2[i], y);
                                IloLinearNumExpr num_expr = cplex.linearNumExpr();
                                cplex.add(cplex.ifThen(cplex.ge(logic, 3), cplex.ge(num_expr, (1-alfa)/(1/36))));
                        }

When it's solved log file is:

Found incumbent of value 0.000000 after 0.00 sec. (0.00 ticks)

Root node processing (before b&c):
  Real time             =    0.00 sec. (0.00 ticks)
Parallel b&c, 4 threads:
  Real time             =    0.00 sec. (0.00 ticks)
  Sync time (average)   =    0.00 sec.
  Wait time (average)   =    0.00 sec.
                          ------------
Total (root+branch&cut) =    0.00 sec. (0.00 ticks)
obj = 0.0
x   = 0.0
y   = 0.0

I think the probabilistic model is a little bit different from the logical constraints model. In if-clause, in my model, I do not have a parameter and it is an expression. I added an IloLinearNumExpr "num_expr " to add the result to the if-clause but, it did not work.

Would you please, say that how can I interpret such expressions using "add method"?

Regards

Originally posted by: EdKlotz

Generally speaking, when you get unexpected results that you think relate to a constraint in the model, you should call the exportModel function to write our model out to an LP file.   Then look at the relevant constraint.   Now it's a bit trickier with IloIfThen, but it will can help you figure out what is happening.

Looking at your code, I see two issues.

• The first one is general.   You have:

                                IloLinearNumExpr num_expr = cplex.linearNumExpr();

                               cplex.add(cplex.ifThen(cplex.ge(logic, 3), cplex.ge(num_expr, (1-alfa)/(1/36))));

                               So num_expr is empty at this point, which means this constraint evaluates to

                               If a1[i]x + a2[i]y >= 3 Then 0 >= b                                       where b is positive given that your alpha is  .05.

                               Since 0 >= b can never be true, this is equivalent to a1[i]x + a2[i]y <= 3, and the solution you got of x = y = 0.0 satisfies that.for each pass in your for loop.

• The second issue is specific to what you are actually trying to express.   The OPL statement is using logical cardinality to add up the number of times a sequence of constraints is satisfied.   The add method adds individual constraints.   So you need to build up a sum of logical conditions, then express your final constraint in terms of your logical conditions.   Have a look at the Logical Constraints for Counting and Logical Constraints as Binary Variables in the User manual.   Based on that, I think you want to create an array of binary variables to count the number of times a1[i]x + a2[i]y >= 3 in your for loop.   Associated a different binary for each (a1,a2) pair.   Then after your loop, and one more constraint that the sum of those binaries is >= 36*(1 - alpha).