Automatic programming via large language models with population self-evolution for dynamic fuzzy job shop scheduling problem

Heuristic dispatching rules (HDRs) are widely used for solving the dynamic fuzzy job shop scheduling problem (DFJSSP). However, their performance is highly sensitive to specific scenarios and often necessitates expert customization. To overcome this, automated design methods like genetic programming (GP) and gene expression programming (GEP) have been proposed. Despite their success, these methods face challenges, such as high randomness in the search process. Recently, the combination of large language models (LLMs) with evolutionary algorithms has opened new possibilities for prompt engineering and automated algorithm design. To improve the ability of LLMs in automatic HDR design, this paper introduces a novel population self-evolutionary (SeEvo) framework, which draws inspiration from the self-reflective design strategies employed by human experts. Notably, this framework employs a novel teacher-student learning mechanism, allowing the LLM (student) to generate robust HDRs. Guided by a teacher model with complete knowledge of actual processing times, the student learns to infer fuzzy uncertainties from historical deviations, enabling it to effectively anticipate and adapt to fuzzy impacts. Experimental results demonstrate that SeEvo significantly outperforms GP, GEP, deep reinforcement learning (DRL) methods, and more than ten commonly used HDRs from the literature, particularly in previously unseen and dynamic scenarios.