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Open Access

ARTICLE

A Cross-Domain Meta-Reinforcement Learning Method for the Permutation Flow Shop Scheduling Problem with Sequence-Dependent Setup Times

Bo Wei, Hongfeng Wang*
College of Information Science and Engineering, Northeastern University, Shenyang, China
* Corresponding Author: Hongfeng Wang. Email: email

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.088577

Received 06 July 2026; Accepted 02 September 2026; Published online 17 September 2026

Abstract

The Permutation Flow Shop Scheduling Problem (PFSP) is one of the most classic combinatorial optimization problems in manufacturing systems, with wide applications in semiconductor fabrication, textile processing, and steelmaking. The Permutation Flow Shop Scheduling Problem with Sequence-Dependent Setup Times (PFSP-SDST) is more representative of real-world production, where machine changeovers depend on the sequence of jobs. However, SDST destroys the optimal substructure of standard PFSP, substantially increasing solution difficulty. To address this challenge, we propose a meta-reinforcement learning method based on Model-Agnostic Meta-Learning (MAML) and Evolution Strategy (ES). Meta-training is conducted only on standard PFSP instances to learn general policy initialization parameters, enabling the model to generalize to new SDST instances with only simple fine-tuning at test time without requiring any SDST information during the training phase. Architecturally, a multi-head self-attention encoder captures complex inter-job relationships and a pointer network decoder autoregressively constructs scheduling sequences, with neighborhood search further improving solution quality. Experimental results on the PFSP-SDST benchmark dataset demonstrate that the proposed method achieves an average ARPD of 3.27 across four SDST types and twelve instance scales. It outperforms seven state-of-the-art comparison algorithms across all SDST types and time budgets, achieving a 49.5% reduction against the average ARPD of 6.48 across all baselines, validating its cross-domain generalization capability from standard PFSP to PFSP-SDST.

Keywords

Permutation Flow Shop Scheduling; Sequence-Dependent Setup Times; meta-reinforcement learning; Model-Agnostic Meta-Learning; Evolution Strategy; attention mechanism; cross-domain generalization

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