Nevertheless, as said before, being able to solve a model or not within reasonable time heavily depends on whether the solver at hand is able to identify and exploit the structure of the model. This is true for both free/academic solvers as well as commercial solvers.įortunately, models of practical problems that are of interest in industrial applications are most often of the latter type. On the other hand, there are models with millions of variables and constraints that can be routinely solved to optimality. You really can see the exponential complexity. ![]() And for such models each additional binary variable pretty much doubles the resulting runtime. If there is no useful structure in the model or if the solver is not able to identify and exploit the structure, then you will often see that the theoretical exponential growth in running time manifests itself in practice.įor example, there are models with just 50 binary variables and a handful of constraints that are pretty much unsolvable with today's state-of-the-art algorithms. While this may also be true for other areas like ML or data base operations, I think that in practice the algorithms that are applied there scale reasonably well with the size of the input data.įor MIP, the running time heavily depends on the structure of the model to be solved and on the capabilities of the solver to exploit this structure. The main issue of performance for mixed integer programming solvers is that all known algorithms for MIP have exponential worst-case running time. I agree with dhasson's points, but I would like to emphasize a certain aspect of performance (also addressed in Kuifje's answer) that I think is hard to understand in its full consequences for people that are not experts in operations research.įirst, let me state that I am only discussing mixed integer programming (MIP) here, which is just a small sub-area in the field of operations research, but I think is the main topic that Skander H.'s question is about. In any case, what I am going to say is my personal opinion and not necessarily aligned with my current or former employers or my former research group. For my PhD thesis I developed the academic solver SCIP, which is still actively maintained and developed by a large group of researchers, so I also know the academic side of the solver world. Hence, my opinion may be biased, but still I am trying to not turn my answer into a marketing and sales pitch. ![]() Disclaimer: I am currently working for a commercial solver company (Gurobi) and have worked before on another commercial solver (IBM CPLEX).
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