Learning Pseudo-Backdoors for Mixed Integer Programs

Abstract

AbstractWe propose a machine learning approach for quickly solving Mixed Integer Programs (MIPs) by learning to prioritize sets of branching variables at the root node which result in faster solution times, which we call pseudo-backdoors. Learning-based approaches have seen success in combinatorial optimization by flexibly leveraging common structures in a given distribution of problems. Our approach takes inspiration from the concept of strong backdoors, which are small sets of variables such that only branching on these variables yields an optimal integral solution and a proof of optimality. Our notion of pseudo-backdoors corresponds to a small set of variables such that prioritizing branching on them when possible leads to faster solve time. A key advantage of pseudo-backdoors over strong backdoors is that they retain the solver’s optimality guarantees and are amenable to data-driven identification. Our proposed method learns to estimate the relative solver speed of a candidate pseudo-backdoor and determine whether or not to use it. This pipeline can be used to identify high-quality pseudo-backdoors on unseen MIP instances for a given MIP distribution. We evaluate our method on five problem distributions and find that our approach can efficiently identify high-quality pseudo-backdoors. In addition, we compare our learned approach against Gurobi, a state-of-the-art MIP solver, demonstrating that our method can be used to improve solver performance.