Variable Search Stepsize for Randomized Local Search in Multi-Objective Combinatorial Optimization

TL;DR

This paper introduces VS-RLS, a variable stepsize randomized local search method for multi-objective combinatorial optimization, which adaptively balances exploration and exploitation, outperforming fixed-steps methods and some MOEAs.

Contribution

The paper proposes a novel variable stepsize local search technique that dynamically adjusts search granularity, improving solution quality in MOCOPs over fixed-steps approaches.

Findings

VS-RLS outperforms fixed-steps local search in diverse MOCOPs.

VS-RLS is competitive with or better than some MOEAs.

Adaptive stepsize enhances exploration and convergence.

Abstract

Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs). Combinatorial problems differ significantly from continuous ones in terms of problem structure and landscape. Recent studies have shown that on MOCOPs multi-objective evolutionary algorithms (MOEAs) can even be outperformed by simple randomised local search. Starting with a randomly sampled solution in search space, randomised local search iteratively draws a random solution (from an archive) to perform local variation within its neighbourhood. However, in most existing methods, the local variation relies on a fixed neighbourhood, which limits exploration and makes the search easy to get trapped in local optima. In this paper, we present a simple yet effective local search method, called variable stepsize randomized local search (VS-RLS), which adjusts the stepsize during the search. VS-RLS transitions gradually from a broad, exploratory search in the early phases to a more focused, fine-grained search as the search progresses. We demonstrate the effectiveness and generalizability of VS-RLS through extensive evaluations against local search and MOEAs methods on diverse MOCOPs.