Dear friends and professors, I have a question. In fact, this is a question asked by a reviewer, and I have to address his/her concern.
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?
His/her concern: "The model is really complex with thousands of constraints. I have difficulty in imaging that the exact method needs few seconds..."
I want to express my appreciation for your efforts in advance. In addition, I want to thank you for the privilege of your time.
Dear Amirhossein,
I suggest you to see links and attached files in topics.
- Using more processors does not necessarily lead to reduced run times ...
www.thequestforoptimality.com/using-more-processors-does-not-...
- Soft Computing in Industrial Applications: Proceedings of the 17th ...
https://books.google.dz/books?isbn=3319009303
- Could We Use a Million Cores to Solve an Integer Program?
coral.ie.lehigh.edu/~ted/files/papers/Million11.pdf
- Using mixed-integer programming to solve power grid blackout ...
www.corc.ieor.columbia.edu/reports/techreports/tr-2005-07.pdf
Best regards
I contacted with the GAMS support team. Their explanation regarding this issue is as follows:
For nowadays standards, the size of your model is not exorbitant. Furthermore, size is not the only criterion that determines whether a model is difficult or not. Of course, there are much smaller MIPs that take way longer to solve but the other way round, there are also larger ones that may solve even faster.
The time taken to solve a MILP depends not only on the size, but also on the gap between the LP bound and the optimum, and the proportion of the basic feasible LP solutions that are fractional. I have encountered MILPs with tens of thousands of variables that solve in a minute, and ones with only a few hundred variables that take hours.
Of course the answer the GAMS team have been sent you is quite reliable. In my main topic, which is minimizing the cyclic time in a robotic cell, I have less than 100 variables and about 500 constraints, very smaller than your problem, but the CPLEX can not solve the problem in less than 72 hours. For this reason I had to develop Metaheuristic algorithms to solve the problem.
From my experience, integer programming solvers, such as CPLEX, work really well and indeed fast if the optimization problem is either very highly constrained, and thus few branching lead to the optimal integer solution, or the very opposite when the problem is constrained relatively sparsely, allowing the solver heuristic to find good feasible solution quickly, consequently removing most of the live nodes within the binary tree. So you really need to check yourself as this is certainly problem-specific - was the solution found by heuristic? Did most of the branching led to the infeasible branches? What is the value of the root relaxation objective compared to the optimal solution? How does it improve? Also, presolve contained in CPLEX may reformulate your MILP in a better way, e.g., it may contain fewer binary variables (again, it depends on the problem and how you formulated it).
The answers you have been provided all seem very sound. A bigger issue for you and everyone who submits papers is... Why does a Referee make such a STUPID statement and now you feel challenged to waste your time and address it? Is your paper about the solution times for IP problems? I did not perceive that and it sounded like you are using an IP model for a particular purpose. This person is obviously refereeing a paper and DOES NOT know the basics of IP. He seems to not understand that when GAMS/CPLEX provides an optimal solution that it is indeed optimal and does not really need to be questioned re: whether it is actually optimal. And you did not write the software so you really do not know exactly how CPLEX did anything. First, as indicated by GAMS, the size of your problem is not really large. Second, anyone who works in IP knows that the difficulty of the problems is not associated only with size of the model. Apparently this Referee is NOT QUALIFIED to review a paper with IP models if they do not understand the basics of IP models. Yet, this person is one of probably two Referees who are ultimately controlling the acceptance of your paper. I grow really tired of LAZY-ass Editors and Assoc. Editors who send papers to only 2 often unqualified Referees, don't examine it themselves, and then take the opinions of the 2 unqualified Referees without hesitation to make it simple and efficient for processing. And, the 2 Referees are too often NOT qualified as your Referee appears to be. I had a Referee a couple of years ago who examined an IP model of ours and indicated that he/she did not understand our IP model because he/she did not understand portfolio optimization. However, portfolio optimization was not yet presented in the paper when that statement was made. And, why would the Referee have that paper if he/she did not understand portfolio optimization when it was part of the title of the paper? Yet, that person was 1 of 2 ultimately in charge of the paper. We all need to initiate change in how this Refereeing process is done. It has changed very little in 50 years. We are being like lambs just accepting the poor opinions of only 2 often unqualified persons.
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