Originally posted by: amindehghanian

I solve an MIP by CPLEX. In addition, I provide CPLEX with a warm-start solution which turns out to be optimal.

CPLEX accepts the warm-start solution, and solve the MIP by the preprocessing and probing.

When the problem is solved, I try to reach the optimality gap, and it gives the default number  1E+70 rather than 0!!! Could you please advise me about why this happens?

Many thanks,

What function do you use to query the gap? Could you show us the engine log output for this case? What is the status/CPLEX status after the solve?

What function do you use to query the gap? Could you show us the engine log output for this case? What is the status/CPLEX status after the solve?

Originally posted by: amindehghanian

Thanks for your answer, Daniel.

The solution status of CPLEX is 118. So, it means that the MIP is unbounded. But, this MIP must be bounded theoretically, and I am sure that there is no error in my code. Could the numerical instability lead to this issue?

Thanks,

Originally posted by: T_O

Numerical instability can of course lead to such situations, but if we assume that you have no numerical problems, there is an easy way to see if your model is unbounded: You have a feasible MIP start, so it is ok to check whether the linear relaxation is unbounded. If it is unbounded, you can query the ray of unboundedness and try to find your modelling issue.

Best regards,
Thomas

Originally posted by: amindehghanian

Thanks for your reply, Thomas!

When I solve the linear relaxation, the solution status is 5. This is inconsistent with the fact that the MIP is unbounded, right? Do you know why this happens?

Thanks,

Originally posted by: T_O

This sounds like numerical troubles. You could play around with the parameters (preprocessing, scaling, ...). Can you post a sav file of your model?

Are you using the interactive optimizer or some API? Can you post the problem statistics and condition number data?

Best regards,
Thomas

Originally posted by: amindehghanian

Thanks for you reply, Thomas.

I use the callable library. I do not have the problem statistics, but the variability in coefficients is high, and the constraint matrix is dense.

I could not upload the problem since its size is large (30 MB). I can email it to you if you want?  You answered my question, and I do not need to explore this problem anymore.

Thanks,

Originally posted by: T_O

If you don't want to investigate this problem anymore, then we don't need either :-)

If the orders of magnitude of the coefficients are very different, such strange things often happen. Sometimes, it is possible to avoid such problems, but in many cases, it isn't.

Best regards,
Thomas