Customized static operator design has enabled widespread application of Evolutionary Algorithms (EAs), but their search performance is transient during iterations and prone to degradation. Dynamic operators aim to address this but typically rely on predefined designs and localized parameter control during the search process, lacking adaptive optimization throughout evolution. To overcome these limitations, this work leverages Large Language Models (LLMs) to perceive evolutionary dynamics and enable operator-level meta-evolution. The proposed framework, LLMs for Evolutionary Optimization (LLM4EO), comprises three components: knowledge-transfer-based operator design, evolution perception and analysis, and adaptive operator evolution. Firstly, initialization of operators is performed by transferring the strengths of classical operators via LLMs. Then, search preferences and potential limitations of operators are analyzed by integrating fitness performance and evolutionary features, accompanied by corresponding suggestions for improvement. Upon stagnation of population evolution, gene selection priorities of operators are dynamically optimized via improvement prompting strategies. This approach achieves co-evolution of populations and operators in the search, introducing a novel paradigm for enhancing the efficiency and adaptability of EAs. Finally, a series of validations on multiple benchmark datasets of the flexible job shop scheduling problem demonstrate that LLM4EO accelerates population evolution and outperforms both mainstream evolutionary programming and traditional EAs.

翻译：定制化静态算子设计促进了进化算法（EAs）的广泛应用，但其搜索性能在迭代过程中具有瞬时性且易出现退化。动态算子旨在解决此问题，但通常依赖于预定义的设计和搜索过程中的局部参数控制，缺乏贯穿进化过程的自适应优化能力。为克服这些局限，本研究利用大语言模型（LLMs）感知进化动态并实现算子层面的元进化。所提出的框架——面向进化优化的大语言模型（LLM4EO）包含三个组成部分：基于知识迁移的算子设计、进化感知与分析、自适应算子进化。首先，通过LLMs迁移经典算子的优势完成算子的初始化。随后，通过融合适应度性能与进化特征分析算子的搜索偏好与潜在局限，并生成相应的改进建议。当种群进化陷入停滞时，通过改进提示策略动态优化算子的基因选择优先级。该方法实现了搜索过程中种群与算子的协同进化，为提升EAs的效率与适应性引入了新范式。最后，在柔性作业车间调度问题的多个基准数据集上进行系列验证，结果表明LLM4EO能够加速种群进化，其性能优于主流进化规划方法及传统进化算法。