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

2026-01-25

AI Summary

This work proposes E2OC, a novel framework for multi-objective evolutionary algorithms that addresses the challenge of modeling dynamic couplings among multiple neighborhood search operators—a task traditionally reliant on expert-designed heuristics and inadequately handled by existing large language model (LLM)-based approaches. E2OC formulates multi-operator optimization as a Markov decision process, explicitly capturing inter-operator dependencies for the first time. By integrating a co-evolutionary mechanism with an operator rotation strategy, it jointly optimizes both high-level design policies and executable code. Leveraging Monte Carlo tree search for progressive exploration and LLM-driven heuristic generation, E2OC consistently outperforms state-of-the-art methods across varying numbers of objectives and problem scales, demonstrating superior generalization and sustained optimization capability.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Multi-Objective Combinatorial Optimization
• Neighborhood Search Operators
• Operator Interdependence
• Automated Heuristic Design
• Markov Decision Process

Innovation

• Multi-Objective Evolutionary Algorithms
• Large Language Models
• Operator Co-evolution
• Monte Carlo Tree Search
• Automated Heuristic Design