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

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