20.500.12556/DKUM-96818 Flexible job-shop scheduling problem with parallel operations using reinforcement learning: an approach based on heterogeneous graph attention networks The Flexible Job-shop Scheduling Problem (FJSP) has received considerable scholarly attention as a classic problem. However, in practical industrial manufacturing scenarios, it is common for an operation to have multiple preceding parallel operations. This not only necessitates adhering to the sequential relationships inherent in FJSP but also requires ensuring that preceding operations are completed simultaneously whenever feasible. We term this scenario as the Flexible Job-shop Scheduling Problem with Parallel Operations (FJSP-PO), a pervasive challenge encountered across nearly every production line in real-world discrete manufacturing applications. Despite its prevalence, there is a noticeable scarcity of research on FJSP-PO in existing literature. Given the objective of synchronizing multiple preceding operations, FJSP-PO presents a broader solution space and more intricate optimization challenges compared to traditional FJSP. To address this, we propose an Attention Restart method based on Heterogeneous Graph Attention Networks (AR-HGAT). Leveraging a heterogeneous graph network structure and reinforcement learning, AR-HGAT learns the implicit features of operations and machines through node-level and semantic-level attention mechanisms. The AR mechanism is utilized to determine the optimal scheduling of operations at specific time slots. Compared to existing FJSP methods, our AR-HGAT approach demonstrates superior performance in terms of inference time and solution effectiveness. Furthermore, we conducted a comparative analysis using authentic operational data from companies and contrasted it with results obtained from an online tree search algorithm, thereby providing empirical validation of the effectiveness of the proposed AR-HGAT method. flexible scheduling flexible job-shop scheduling problem FJSP unified scheduling mode parallel operations reinforcement learning heterogeneous graph networks attention restart method based on heterogeneous graph attention networks AR-HGAT heterogeni grafi modeli razporejanja true false true Chair of Production Engineering (CPE), University of Maribor Faculty of Mechanical Engineering Angleški jezik Slovenski jezik https://apem-journal.org/ Članek v reviji 2026-01-29 08:49:03 2026-01-29 08:49:04 2026-03-20 07:03:49 0000-00-00 00:00:00 2024 0 0 str. 157-181 no. 2 Vol. 19 June 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-06-18 2024-06-29 2024-08-29 658.5 266563587 10.14743/apem2024.2.499 1854-6250 APEM19-2_157-181.pdf APEM19-2_157-181.pdf 1 DC80DC5FA78D2C576B34893C7A333B56 ec3804130774366d7989ed58d051f54ece0e6168070eab66fa6dabb5485ca182 36b57f25-fce7-11f0-a012-00155d00018d https://dk.um.si/Dokument.php?lang=slv&id=202751 https://apem-journal.org/Archives/2024/Abstract-APEM19-2_157-181.html 0 3c44e5c9-fce7-11f0-a012-00155d00018d https://dk.um.si/Dokument.php?lang=slv&id=202752 Fakulteta za strojništvo Advances in production engineering & management 0 0 0