Learning to Remove Cuts in Integer Linear Programming

TL;DR

This paper introduces a novel approach to integer linear programming that involves learning when to remove previously added cuts, leading to improved efficiency over traditional cut addition methods.

Contribution

It proposes a learnable cut removal strategy within cutting plane methods for ILPs, which is a new concept compared to existing approaches.

Findings

Cut removal policies outperform traditional cut addition methods.

Simple models effectively learn to remove cuts, improving ILP solving.

Significant performance gains demonstrated in combinatorial optimization settings.

Abstract

Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional optimal solution while not affecting the optimal integer solution. In this work, we explore a novel approach within cutting plane methods: instead of only adding new cuts, we also consider the removal of previous cuts introduced at any of the preceding iterations of the method under a learnable parametric criteria. We demonstrate that in fundamental combinatorial optimization settings such cut removal policies can lead to significant improvements over both human-based and machine learning-guided cut addition policies even when implemented with simple models.