Learning to Control Local Search for Combinatorial Optimization

TL;DR

This paper introduces NeuroLS, a deep learning-based controller for local search in combinatorial optimization, which learns to select the best algorithmic aspects dynamically, outperforming existing methods.

Contribution

The paper formalizes local search aspect selection as an MDP and designs a graph neural network policy, creating a novel learned controller called NeuroLS.

Findings

NeuroLS outperforms traditional local search controllers.

NeuroLS surpasses recent machine learning approaches.

The approach effectively automates local search configuration.

Abstract

Combinatorial optimization problems are encountered in many practical contexts such as logistics and production, but exact solutions are particularly difficult to find and usually NP-hard for considerable problem sizes. To compute approximate solutions, a zoo of generic as well as problem-specific variants of local search is commonly used. However, which variant to apply to which particular problem is difficult to decide even for experts. In this paper we identify three independent algorithmic aspects of such local search algorithms and formalize their sequential selection over an optimization process as Markov Decision Process (MDP). We design a deep graph neural network as policy model for this MDP, yielding a learned controller for local search called NeuroLS. Ample experimental evidence shows that NeuroLS is able to outperform both, well-known general purpose local search controllers from Operations Research as well as latest machine learning-based approaches.