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

2026-02-05

AI Summary

This work addresses the limitations of traditional stochastic local search in multi-objective combinatorial optimization, where fixed neighborhood structures often lead to premature convergence and insufficient exploration. To overcome this, the authors propose Variable-Step Stochastic Local Search (VS-RLS), a novel approach that dynamically adjusts step size and neighborhood range throughout the search process. Initially employing large steps to enhance global exploration, VS-RLS progressively reduces step size to enable fine-grained exploitation in later stages, thereby effectively balancing exploration and exploitation. As the first method to incorporate a dynamic variable-step mechanism into local search for multi-objective combinatorial optimization, VS-RLS significantly improves the ability to escape local optima and enhances solution set diversity. Experimental results demonstrate its superior performance over state-of-the-art local search and multi-objective evolutionary algorithms across multiple benchmark problems, highlighting its robustness and generalization capability.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

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.

Problem

• multi-objective combinatorial optimization
• randomized local search
• local optima
• search stepsize
• exploration

Innovation

• variable stepsize
• randomized local search
• multi-objective combinatorial optimization
• adaptive neighborhood
• local search