L2P-MIP: Learning to Presolve for Mixed Integer Programming

Modern solvers for solving mixed integer programming (MIP) often rely on the branch-and-bound (B&B) algorithm which could be of high time complexity, and presolving techniques are well designed to simplify the instance as pre-processing before B&B. However, such presolvers in existing literature or open-source solvers are mostly set by default agnostic to specific input instances, and few studies have been reported on tailoring presolving settings. In this paper, we aim to dive into this open question and show that the MIP solver can be indeed largely improved when switching the default instance-agnostic presolving into instance-specific presolving. Specifically, we propose a combination of supervised learning and classic heuristics to achieve efficient presolving adjusting, avoiding tedious reinforcement learning. Notably, our approach is orthogonal from many recent efforts in incorporating learning modules into the B&B framework after the presolving stage, and to our best knowledge, this is the first work for introducing learning to presolve in MIP solvers. Experiments on multiple real-world datasets show that well-trained neural networks can infer proper presolving for arbitrary incoming MIP instances in less than 0.5s, which is neglectable compared with the solving time often hours or days.