Originally posted by: Devin063

Greetings,

I am working on a linear programming problem with 49 decision variables and 120 constraints.

I found that barrier (interior point) algorithm and dual simplex algorithm of CPLEX, gave different optimal decision vector and same objectives.

Is the reason multiple optimal solutions? Can anyone give me some hints on how to refine my problem to get a definite solution?

Thank you!

Did you run barrier with or without crossover?

And what do you mean by definite solution? If your problem has multiple optimal solutions then which one do you want to get?

Originally posted by: Devin063

Hi Daniel

I think I did not select which barrier algorithm I used. So it should be default one.

For definite solution, I mean I would like to know what I can do, to covert this problem with multiple solutions to a one with only one solution.

Thank you

In any case, barrier will give you a solution on the optimal face and a subsequent crossover step will cross over to a solution that is a vertex. Simplex algorithms will always give you a vertex solution. If there are multiple optimal solutions then it is quite expected that different algorithms find different solutions/vertices. In order to avoid that you have to make the optimal solution unique in some way.

But is it really a problem that different algorithms find different solution vectors? Since the objective value is the same, these solutions are all optimal.
 

Originally posted by: Devin063

I think you are right. I got two optimal solutions; one from interior point method, one from dual simplex method.