Multi-agent large language models as evolutionary optimizers for scheduling optimization

Scheduling optimization is critical for improving efficiency and resource utilization across industries. However, the complexity of scheduling problems—arising from diverse constraints, intricate task dependencies, and resource conflicts—poses significant challenges. Traditional approaches often require manually designed models and algorithms tailored to specific scenarios, which demand significant domain expertise and limit adaptability in highly complex environments. This paper proposes the Multi-Agent LLMs-driven Evolutionary Framework for Scheduling Optimization (MAEF), a novel approach that addresses these limitations through a feedback-driven iterative optimization process. MAEF employs multiple Large Language Model (LLM) agents, each with specialized roles, to automate tasks such as problem definition, initial population generation, evolutionary optimization, and result evaluation. A key innovation of MAEF is its feedback loop: an evaluation agent continuously assesses intermediate solutions, providing real-time guidance to optimization agents for dynamic refinement and ensuring convergence to high-quality solutions. By integrating natural language processing capabilities with evolutionary strategies, MAEF reduces reliance on domain-specific expertise and manual intervention. Experiments conducted on four representative scheduling problems—Single Machine Scheduling, Flow Shop Scheduling, Job Shop Scheduling, and Resource-Constrained Project Scheduling—demonstrate that MAEF outperforms traditional heuristic and meta-heuristic methods in scalability, user-friendliness, and solution quality. These results highlight MAEF's potential as a generalized, automated optimizer for scheduling problems, offering a significant advancement in scheduling optimization frameworks.