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CPU time for large-scale instances

Posted: Sun Dec 17, 2017 4:49 pm
by moosavi_69
Dear friends, I have a question. Note that this inquiry is a question asked by a reviewer and I have to fully address his concern.

His concern: "The model is really complex with thousands of constraints. I have difficulty in imaging that the exact method needs few seconds..."

Let me explain the problem a little bit more. I have coded a MIP model in the GAMS and applied the Cplex as an exact method to solve instances. I am able to solve a relatively large-scale instance with about 23,000 decision variables and 4,000 constraints in less than a minute. I would like to ask for your clarification that how it would be possible to solve such a large-scale instance in less than one minute? Is there any specific reason?

I want to express our appreciation for your efforts in advance. In addition, I want to thank you for the privilege of your time.

Re: CPU time for large-scale instances

Posted: Mon Dec 18, 2017 1:58 pm
by dirkse
Moosavi,

I would not call the problem size you mention - 23k vars and 4k constraints - large-scale. If this is an LP, there is nothing remarkable about solving such a problem in seconds. You say it is a MIP, but you don't say how many of these 23k vars are discrete. And even if many are discrete, that doesn't necessarily make the problem difficult.

The reviewer could be doubtful that the solvers really do the job correctly, or that the model is formulated correctly. The former case isn't such a hard problem: you could make sure you have the optimality tolerances optca and optcr at zero and try multiple MIP solvers to ensure they get the same solution or at least objective value. If you really want to be thorough, use the Examiner tool:

https://www.gams.com/latest/docs/S_EXAMINER.html

The reviewer could also doubt the model formulation. That is a different issue and is more specific to your application and less about GAMS and MIP solvers.

HTH,

-Steve

Re: CPU time for large-scale instances

Posted: Mon Dec 18, 2017 9:45 pm
by moosavi_69
Dear Steve,

I am grateful for your prompt attention. Following to your question regarding the decision variables, I have to tell you that variables in this problem are positive integer or binary. To be more precise, around 15,000 of them are binary variables and 8,000 of them are positive integer variables.

I want to appreciate your sincere answer (or even other experts) in advance, and thx for the privilege of your time.