Originally posted by: A.Omidi

Hello support team,

I was trying to write a chance constraint using Java in CPLEX but, I have some issues on it. I don't have any experience to deal with this form of constraints.

The constraint is as follows:

prob[sum(j, a(j)*x(j)) <= b] >= beta;

I was wondering if, is there any efficient way to write this using CPLEX in the Java?

Regards   

Hi,

could

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

that is in OPL help you ?

regards

Originally posted by: A.Omidi

Dear Alex,

Thanks for your replay. It is so useful. 

I try to write you mentioned model 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
                        List<IloRange> constraints = new ArrayList<IloRange>();
                        IloLinearNumExpr num_expr = cplex.linearNumExpr();
                        for (int a1 = 0; a1 < 6; a1++) {
                                for (int a2 = 0; a2 < 6; a2++) {
                                        num_expr.addTerm(a1, x);
                                        num_expr.addTerm(a2, y);
                                }
                        }

                        cplex.addGe(num_expr, 3);
                        constraints.add(cplex.addGe(num_expr, (0.5/(1/36))));

When I run the model it has some errors.

Would you please, say that how can I write such probability constraint using Java?

Regards

Hi,

you issue seems to be to translate

1/36*sum(a1,a2 in 1..6) (a1*x + a2*y >= 3)>=1-alpha;

from OPL to java concert.

For indicator constraints you could have a look at https://www.ibm.com/support/knowledgecenter/SSSA5P_12.9.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/indicator_constr/02_indicators_defn.html

and see the example Fixnet.java where you will see

// Add logical constraints that require x[i]==0 if f[i] is 0.
         for (int i = 0; i < orig.length; ++i)
            cplex.add(cplex.ifThen(cplex.eq(f[i], 0.0), cplex.eq(x[i], 0.0)));

In your case instead of cplex.ifThen you could use  IloCplexModeler.eq

regards

Originally posted by: A.Omidi

Dear Alex,

Thanks for your comment. I correct my code using you mentioned and run it. The code 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 (I was wondering, you advise me if I'm wrong about that).

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

Regards