Modern MIP solvers consist of many subroutines that take care of different aspects of the solution process: presolving, cut generation, cut selection, primal heuristics, and so forth. For a given MIP, the solver has to make online decisions on which of multiple alternative instantiations of a subroutine to employ or how to combine them. While it is often hard to beat hand-crafted rules, the use of machine learning models for making those decisions has become more prominent in recent years. In this presentation, we will discuss
four projects in which we used ML to improve the performance of the solvers Xpress and SCIP on general MIP benchmarks. Two topics relate to cutting planes, while the other two are concerned with numerical stability.
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