LLM4EO: Large Language Model for Evolutionary Optimization in Flexible Job Shop Scheduling

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.