Flexible Job Shop Scheduling Problems with setup and transportation times (FJSP-TS) involve assigning operations to machines and sequencing them under additional time constraints, making the problem highly complex and common in modern manufacturing systems. Discrete Particle Swarm Optimization (DPSO) is one of the mainstream meta-heuristic methods for solving such scheduling problems, and this paper proposes a hybrid optimization approach based on DPSO to enhance solution quality. To reduce the complexity of meta-heuristic search and improve solution accuracy, a decoupled framework is introduced: DPSO is employed to optimize the operation sequence globally, while a Multi-Agent System (MAS) handles machine sequence. Furthermore, to enhance the state representation and decision-making capability of Machine Agents, a Heterogeneous Graph Neural Network (HGNN) integrated with Multi-head Attention is utilized to efficiently extract comprehensive features from the scheduling environment. Experimental results on 30 benchmark instances demonstrate that the proposed method achieves notable performance improvements in key scheduling metrics. Our method reduces the average makespan by 5.7%, total setup time by 8.9%, and total transportation time by 4.8% compared to representative optimization approaches.
Chen et al. (2026) studied this question.