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.

翻译：邻域搜索算子是影响多目标进化算法性能的关键因素，其设计高度依赖专家经验。尽管近期基于大语言模型的自动化启发式设计方法取得了显著进展，但这些方法主要独立优化单一启发式策略或组件，缺乏对算子间动态耦合关系的显式探索与利用。本文将多目标进化算法中的多算子优化问题建模为马尔可夫决策过程，通过序贯决策实现互依赖算子的协同改进。为此，我们提出面向多目标进化算法的算子组合演化框架，实现设计策略与可执行代码的协同进化。该框架采用蒙特卡洛树搜索渐进式探索算子设计策略组合，并引入算子轮换机制以识别有效的算子配置，同时支持集成主流自动化启发式设计方法作为底层设计器。在不同目标函数与问题规模的自动化启发式设计任务上的实验结果表明，该框架在各项指标上均优于当前最先进的自动化启发式设计方法及其他多启发式协同设计框架，展现出优异的泛化能力与持续优化性能。