SPL-LNS: Sampling-Enhanced Large Neighborhood Search for Solving Integer Linear Programs

TL;DR

This paper introduces SPL-LNS, a sampling-enhanced neural Large Neighborhood Search method that improves solution quality and efficiency for Integer Linear Programs by escaping local optima and utilizing a novel training approach.

Contribution

It formulates LNS as a stochastic process and develops SPL-LNS with locally-informed proposals and a hindsight relabeling training method, advancing neural LNS capabilities.

Findings

SPL-LNS outperforms previous neural LNS methods on various ILP problems.

The sampling approach effectively escapes local optima.

The hindsight relabeling method improves training efficiency.

Abstract

Large Neighborhood Search (LNS) is a common heuristic in combinatorial optimization that iteratively searches over a large neighborhood of the current solution for a better one. Recently, neural network-based LNS solvers have achieved great success in solving Integer Linear Programs (ILPs) by learning to greedily predict the locally optimal solution for the next neighborhood proposal. However, this greedy approach raises two key concerns: (1) to what extent this greedy proposal suffers from local optima, and (2) how can we effectively improve its sample efficiency in the long run. To address these questions, this paper first formulates LNS as a stochastic process, and then introduces SPL-LNS, a sampling-enhanced neural LNS solver that leverages locally-informed proposals to escape local optima. We also develop a novel hindsight relabeling method to efficiently train SPL-LNS on self-generated data. Experimental results demonstrate that SPL-LNS substantially surpasses prior neural LNS solvers for various ILP problems of different sizes.