20.500.12556/DKUM-97384 A new solution to distributed permutation flow shop scheduling problem based on NASH Q-Learning Aiming at Distributed Permutation Flow-shop Scheduling Problems (DPFSPs), this study took the minimization of the maximum completion time of the workpieces to be processed in all production tasks as the goal, and took the multi-agent Reinforcement Learning (RL) method as the main frame of the solution model, then, combining with the NASH equilibrium theory and the RL method, it proposed a NASH Q-Learning algorithm for Distributed Flow-shop Scheduling Problem (DFSP) based on Mean Field (MF). In the RL part, this study designed a two-layer online learning mode in which the sample collection and the training improvement proceed alternately, the outer layer collects samples, when the collected samples meet the requirement of batch size, it enters to the inner layer loop, which uses the Q-learning model-free batch processing mode to proceed, and adopts neural network to approximate the value function to adapt to large-scale problems. By comparing the Average Relative Percentage Deviation (ARPD) index of the benchmark test questions, the calculation results of the proposed algorithm outperformed other similar algorithms, which proved the feasibility and efficiency of the proposed algorithm. flow shop scheduling distributed scheduling permutation flow shop NASH Q-learning mean field (MF) razporejanje pretoka dela v delavnici porazdeljeno razporejanje trgovina s permutacijskim tokom NASH Q-učenje povprečno polje true false true Chair of Production Engineering (CPE), University of Maribor Faculty of Mechanical Engineering Angleški jezik Slovenski jezik https://apem-journal.org/ Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Članek v reviji 2026-03-03 08:22:30 2026-03-03 08:22:31 2026-03-04 03:14:27 0000-00-00 00:00:00 2021 0 0 str. 269-284 no. 3 Vol. 16 Sept. 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-07-29 2021-09-26 2021-10-31 331.103:678.02 270030595 10.14743/apem2021.3.399 1854-6250 APEM16-3_269-284.pdf APEM16-3_269-284.pdf 1 0BDA68EC782622F0B61A2F38F178CF66 87c8335e7ad844885a8de2378a6775f6b97277dfb8fbd661ebef2756cee05998 6556c054-16d2-11f1-9bb8-00155d580e1a https://dk.um.si/Dokument.php?lang=slv&id=204182 https://apem-journal.org/Archives/2021/APEM16-3_269-284.pdf 0 6b93aeb6-16d2-11f1-9bb8-00155d580e1a https://dk.um.si/Dokument.php?lang=slv&id=204183 Fakulteta za strojništvo Advances in production engineering & management 0 0 0