Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework

TL;DR

This paper introduces BaMCTS, a Monte Carlo Tree Search framework that effectively finds backdoors in mixed integer linear programs, improving over existing sampling methods and aiding in understanding problem structure.

Contribution

The paper presents BaMCTS, a novel MCTS-based algorithm for identifying backdoors in MIPs, integrated with CPLEX, outperforming previous sampling approaches.

Findings

BaMCTS finds backdoors more frequently than baselines.

BaMCTS is more efficient in identifying backdoors.

The method enhances understanding of MIP structural properties.

Abstract

In Mixed Integer Linear Programming (MIP), a (strong) backdoor is a "small" subset of an instance's integer variables with the following property: in a branch-and-bound procedure, the instance can be solved to global optimality by branching only on the variables in the backdoor. Constructing datasets of pre-computed backdoors for widely used MIP benchmark sets or particular problem families can enable new questions around novel structural properties of a MIP, or explain why a problem that is hard in theory can be solved efficiently in practice. Existing algorithms for finding backdoors rely on sampling candidate variable subsets in various ways, an approach which has demonstrated the existence of backdoors for some instances from MIPLIB2003 and MIPLIB2010. However, these algorithms fall short of consistently succeeding at the task due to an imbalance between exploration and exploitation. We propose BaMCTS, a Monte Carlo Tree Search framework for finding backdoors to MIPs. Extensive algorithmic engineering, hybridization with traditional MIP concepts, and close integration with the CPLEX solver have enabled our method to outperform baselines on MIPLIB2017 instances, finding backdoors more frequently and more efficiently.