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

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.

Automated heuristic design has recently advanced through large language models that synthesize algorithmic components to solve multi-objective optimization problems. However, existing methods typically optimize individual heuristics in isolation, ignoring the complex, dynamic coupling relationships required for multiple operators to cooperate effectively. To bridge this gap, this paper introduces the Evolution of Operator Combination (E2OC) framework, which treats multi-operator optimization as a sequential decision-making process modeled via a Markov decision process. By integrating Monte Carlo Tree Search to explore the language space of high-level design strategies and employing a coordinate-rotation mechanism for local code refinement, E2OC achieves a dual-loop co-evolution of semantic design thoughts and executable operator code. Experimental evaluations across various problem scales demonstrate that E2OC consistently delivers superior multi-objective optimization performance and achieves exceptional cross-scale generalization, enabling robust, low-cost training on small instances for direct deployment on massive real-world challenges.