Originally posted by: gkirlik

Dear All,

I want to enumerate all alternative optimal solutions of a binary integer linear programming problem (myModel.lp). Hence, I use populate method with the recommended parameters. This function generates one optimal solution for the given problem. Then, I add two new constraints to the model. First one is cx=cx^* where x^* is the optimal solution of the model, and the second one is to cut-off x*. If x* is the unique optimal solution for this problem, then the new problem should be infeasible. However, model returns another solution. It seems something goes wrong here. How can I handle this situation?

PS: I have attached source code and model file to this message. I am using Cplex 12.4 (c++) on 64bit Linux OS.

Best regards,
Gokhan
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Your model actually has two alternate optimal solutions. I think the problem is

cplex.setParam(IloCplex::SolnPoolAGap, 0.0);

This requires the objective function values of both solutions to be exactly equal and does not allow for any numerical round-off.
Since the objective function in your case is always integral I tried

cplex.setParam(IloCplex::SolnPoolAGap, 0.5);

and that gives me both optimal solutions.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: gkirlik

I appreciated for your concern. Your solution works, and it makes sense. The problem is pure binary integer model and coefficients are integer. Hence, setting the absolute gap at 0.5 still guarantees the optimality.

Best Regards,
Gokhan
#CPLEXOptimizers
#DecisionOptimization