Learning to Use Local Cuts

Timo Berthold; Matteo Francobaldi; Gregor Hendel

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arXiv · 2206.11618

Learning to Use Local Cuts

Timo Berthold·Matteo Francobaldi·Gregor Hendel

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Abstract

An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, given that they tend to slow down the solution time of the relaxation. One of the most crucial questions is: Should cuts only be generated globally at the root or also locally at nodes of the tree? We address this question by a machine learning approach for which we train a regression forest to predict the speed-up (or slow-down) provided by using local cuts. We demonstrate with an open implementation that this helps to improve the performance of the FICO Xpress MIP solver on a public test set of general MIP instances. We further report on the impact of a practical implementation inside Xpress on a large, diverse set of real-world industry MIPs.

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Timo Berthold, Matteo Francobaldi, Gregor Hendel. 2022-06-23. Learning to Use Local Cuts. https://arxiv.org/abs/2206.11618

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