Learning to Use Local Cuts

TL;DR

This paper introduces a machine learning approach to decide when to generate local cuts in MIP solvers, improving their efficiency on diverse problem sets.

Contribution

It presents a regression forest model to predict the benefit of local cuts, optimizing their use within a branch-and-bound solver.

Findings

Machine learning improves cut selection in MIP solving.

Enhanced solver performance on public and industry MIP instances.

Practical implementation benefits real-world applications.

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.