A Meta-Cognitive LLM-guided Evolutionary Algorithm for Heterogeneous Hybrid Flow Shop Scheduling Problem with Energy Consumption

The heterogeneous hybrid flow shop scheduling problem (HHFSSP) in modern manufacturing is a critical NP-hard problem, for which an efficient solution is of great significance for enhancing production efficiency and resource utilization. This paper proposes a Meta-cognitive LLM-guided Evolutionary Algorithm (MC-LLM-EA) for the multi-objective HHFSSP aimed at optimizing makespan and total energy consumption (TEC). MC-LLM-EA employs a hybrid initialization mechanism that integrates random, makespan-oriented, and TEC-oriented approaches to ensure the quality and diversity of the initial population. An adaptive parameter adjustment (APA) strategy based on population diversity is designed to auto-control crossover and mutation rate. The core innovation lies in the meta-cognitive architecture coordinated by dual LLMs: the Evolutionary Prompt Reasoning LLM (EvoPrompt LLM) generates cognitive search strategies (CSS) based on evolutionary performance and population state, while the Code Morphogenesis LLM (CodeMorph LLM) produces executable search code based on CSS. This meta-cognitive mechanism enables the simultaneous evolution of both population and search operator during the optimization process. Experimental results demonstrate that the proposed algorithm outperforms NSGA-II, MOEA/D, and DQN-NSGA-III on both HV and IGD metrics. Among different LLM kernels, DeepSeek-V3 achieves superior performance in HHFSSP due to the targeted, specific, and context-aware cognitive search strategies it generates.