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Does anyone know what the state of the art industry solvers do for these problems? I had dabbled a bit in ml approaches to combinatorial optimization with great interest a few years back, but I don't think any of these rl based methods ended up being used in production.

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The state of the art solvers are the proprietary ones like Gurobi, FICO, Cplex, Mosek, etc. A major contributor to the proprietary "sauce" is in the heuristics they use. For example, all solvers will have a "presolve" phase which attempts to eliminate redundant constraints/variables. There may be some ML they are using behind the scenes to derive these heuristics, I'm not sure, although I know it is a major research area.

Otherwise, the basic underlying algorithms are all the same, as in the textbook: branch-and-bound and so on.

I know about only one such library, and works great for toy problems: PuLP [0][1].

[0]: https://coin-or.github.io/pulp/

[1]: https://pypi.org/project/PuLP/

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