Originally posted by: Aaron.Sun

For a linear program which has multiple optimal solutions, how can I get an optimal solution at extreme points using Cplex?

For example, A and B are two optimal solutions of a problem. When I use primopt (I think it means primal simplex) to solve it, the Cplex delivers convex combination of A and B. Why? What should I do, if I want the Cplex always return optimal solutions at extreme points.

Thanks,

Aaron

Originally posted by: T_O

If you are using primal or dual simplex or barrier with crossover, CPLEX should return a basic solution which corresponds to a vertex of the polyhedron. Are you sure that A and B are optimal and the solution is a convex combination of A and B? Can you give an example?

Also consider that strange things can sometimes happen. Consider a feasible set that is a straight unbounded line. Let the objective be 0 (or tangential to the line). Then any point on that line is optimal. On the other hand, it is not obvious which points on that line are "vertices" belonging to basic solutions (of course, such a basic solution exists).

Best regards,
Thomas

Originally posted by: Aaron.Sun

Thank you, T_O.

It is a very large model. Since it is a network problem, I know A and B are optimal for sure. But as you said, I also doubt that the CPLEX solution is not a convex combination of A and B. I will check it, even though it may be a tough job.

Thank you again.

Aaron