Evolving Interdependent Operators with Large Language Models for Multi-Objective Combinatorial Optimization

TL;DR

This paper introduces E2OC, a framework that uses Monte Carlo Tree Search to co-evolve interdependent neighborhood search operators in MOEAs, significantly improving multi-objective optimization performance.

Contribution

It formulates multi-operator optimization as a Markov decision process and develops E2OC for co-evolving operator strategies and codes, integrating AHD methods.

Findings

E2OC outperforms state-of-the-art AHD methods.

Demonstrates strong generalization across tasks.

Supports integration of mainstream AHD techniques.

Abstract

Neighborhood search operators are critical to the performance of Multi-Objective Evolutionary Algorithms (MOEAs) and rely heavily on expert design. Although recent LLM-based Automated Heuristic Design (AHD) methods have made notable progress, they primarily optimize individual heuristics or components independently, lacking explicit exploration and exploitation of dynamic coupling relationships between operators. In this paper, multi-operator optimization in MOEAs is formulated as a Markov decision process, enabling the improvement of interdependent operators through sequential decision-making. To address this, we propose the Evolution of Operator Combination (E2OC) framework for MOEAs, which achieves the co-evolution of design strategies and executable codes. E2OC employs Monte Carlo Tree Search to progressively search combinations of operator design strategies and adopts an operator rotation mechanism to identify effective operator configurations while supporting the integration of mainstream AHD methods as the underlying designer. Experimental results across AHD tasks with varying objectives and problem scales show that E2OC consistently outperforms state-of-the-art AHD and other multi-heuristic co-design frameworks, demonstrating strong generalization and sustained optimization capability.