Comparison between CPLEX and Gurobi

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Gurobi and CPLEX are solvers that have been very popular in recent years. CPLEX is easier for academics in terms of the license. It is also said to be very high in performance. But Gurobi is claimed to be the fastest solver in recent years, with continuous improvements. However, it is said that its performance decreases when the number of constraints increases.

In terms of speed and performance, which solver is generally recommended specifically for large-scale problems with the quadratic objective function, which have not too many constraints?

Will their use within Python affect their performance?

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2 Answers

Math programming is inherently hard and there will likely always be instances where one solver is faster than another. Often, problems are solved quickly just because some heuristic was "lucky".

Also, the size of a problem alone is not a reliable measure for its difficulty. There are tiny instances that are still unsolved while we can solve instances with millions of constraints in a very short amount of time.

When you're looking for the best performance, you should analyze the solver's behavior by inspecting the log file and then try to adjust parameters accordingly. If you have the opportunity to test out different solvers you should just go for it to have even more options available. You should be careful about recommendations for either of the established, state-of-the-art solvers - especially without hands-on computational experiments.

You also need to consider the difficulty of the modeling environment/language and how much time you might need to finish the modeling part.

To answer your question concerning Gurobi's Python interface: this is a very performant and popular tool for all kinds of applications and is most likely not going to impact the overall solving time. In the majority of cases, the actual solving time is still the dominant factor while the model construction time is negligible.

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As mattmilten already said, if you compare the performance of the major commercial solvers on a range of problems you will find instances where one is clearly better than the others. However that will depend on many details that might seem irrelevant. We did a side-by-side comparison on our own collection of problem instances (saved as MPS files) that were all generated from the same C++ code on different sub-problems of a large optimisation problem. So they were essentially just different sets of data in the same model and we still found big variations across the solvers. It really does depend on the details of your specific problem.

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