LLM-Assisted Non-Dominated Sorting Genetic Algorithm for Solving Distributed Heterogeneous No-Wait Permutation Flowshop Scheduling

In distributed manufacturing systems, minimizing completion time and improving resource utilization are critical for enhancing operational efficiency. Conventional scheduling models for centralized flowshops struggle to capture the complexity of distributed heterogeneous systems, while existing studies often overlook the combined challenges of heterogeneous factories, no-wait constraints, and sequence-dependent setup times (SDST). This study focuses on the distributed heterogeneous no-wait permutation flowshop scheduling problem with SDST (DHNPFSP-SDST), which is proven NP-hard via polynomial reduction to the classic permutation flowshop scheduling problem (PFSP). We first establish a bi-objective optimization model to simultaneously minimize makespan and total machine non-working time, serving as a standard experimental foundation. The core innovation is a large language model-assisted non-dominated sorting genetic algorithm (LLM-NSGAII), Through a structured prompt framework, LLM-NSGAII leverages LLM’s zero-shot in-context learning to dynamically orchestrate selection, crossover, and mutation operations—replacing the fixed operators of traditional NSGAII. Experiments on extended benchmarks show that when compared with mainstream, multi-objective algorithms demonstrate competitiveness across most instances and provide a proof of concept for integrating LLMs with evolutionary algorithms, opening new avenues for algorithmic optimization.