Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

Taoan Huang, Aaron M Ferber, Yuandong Tian, Bistra Dilkina, Benoit Steiner

Keywords: Integer Linear Programs, Large Neighborhood Search, Machine Learning for Combinatorial Optimizations

TL;DR: We use contrastive learning to learn state-of-the-art destroy heuristics that select variables to reoptimize for large neighborhood search to solve integer linear programs.

Abstract: Integer Linear Programs (ILPs) are powerful tools for modeling and solving many combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high-quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a more efficient one with contrastive learning.

Submission Number: 14