Cutting Plane Selection with Analytic Centers and Multiregression

TL;DR

This paper introduces new distance-based measures using analytic centers and multiregression techniques to improve the selection of cutting planes in mixed-integer programming, leading to more efficient solver performance.

Contribution

It proposes novel distance measures based on analytic centers and a multiregression approach to predict and enhance cut selection in mixed-integer programming.

Findings

Analytic center-based measures reduce branch-and-bound nodes.

Multiregression improves performance over individual measures.

Methods outperform existing literature in solver efficiency.

Abstract

Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.