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> That's a whole field of wonderful computer science / math that is mostly usable via a couple of extraordinarily expensive closed-source offerings.

Take a look at Google OR-Tools: https://developers.google.com/optimization/

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OR-Tools is a whole grab-bag of tools, most of which are wrappers around various solvers, including Gurobi and CPLEX. It seems like CP-SAT is under the OR-Tools umbrella, and CP-SAT may well be state-of-the-art for the specific sets of problems that it's well-suited for.

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