An LLM-Driven Multi-Agent Evolution Framework for Solver Code Generation in Job Shop Scheduling

Developing high-quality and reliable solver code for the job shop scheduling problem (JSSP) remains a challenging and expertise-intensive task because generated code must stay executable, produce feasible schedules, and achieve strong scheduling results. This paper proposes a large language model (LLM)-driven multi-agent evolution framework for scheduling solver code generation, where LLMs act as hyper-heuristics for program-space search under external evaluation. The framework forms a closed-loop process with three collaborating agents. A seed heuristic generation agent uses a structured constraint template and a shared solver skeleton to synthesize, screen, and diversify seed programs to construct a competitive initial code pool. An evolutionary operator agent updates the pool through program-space crossover and best-so-far mutation. A code reflection agent analyzes solver code and maintains trajectory-aware reflective memory to generate structured guidance for later revision. Experiments on standard JSSP benchmarks show that the framework outperforms representative metaheuristics across heterogeneous instance families and scales while reaching best-known reference quality on a subset of instances. Ablation results further confirm the contributions of the initialization design and the reflection-guided revision mechanism. More broadly, the proposed framework helps reduce manual heuristic design effort and offers a practical approach to production scheduling optimization in intelligent manufacturing environments.