{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T06:13:35Z","timestamp":1768284815055,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,8]],"date-time":"2025-06-08T00:00:00Z","timestamp":1749340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2024A1515010206"],"award-info":[{"award-number":["2024A1515010206"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Dynamic scheduling in hybrid flexible job shops (HFJSs) presents a critical challenge in modern manufacturing systems, particularly under dynamic and uncertain conditions. These systems often exhibit inherent structural and behavioral symmetry, such as uniform machine\u2013job relationships and repeatable event response patterns. To leverage this, we propose a time Petri nets (TPNs) model that integrates time and logic constraints, capturing symmetric processing and setup behaviors across machines as well as dynamic job and machine events. A transition select coding mechanism is introduced, where each transition node is assigned a normalized priority value in the range [0, 1], preserving scheduling consistency and symmetry during decision-making. Furthermore, we develop a symmetry-aware time Petri nets-based improved genetic algorithm (TPGA) to solve both static and dynamic scheduling problems in HFJSs. Experimental evaluations show that TPGA significantly outperforms classical dispatching rules such as Shortest Job First (SJF) and Highest Response Ratio Next (HRN), achieving makespan reductions of 23%, 10%, and 13% in process, discrete, and hybrid manufacturing scenarios, respectively. These results highlight the potential of exploiting symmetry in system modeling and optimization for enhanced scheduling performance.<\/jats:p>","DOI":"10.3390\/sym17060907","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T09:13:01Z","timestamp":1749460381000},"page":"907","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Symmetry-Aware Dynamic Scheduling Optimization in Hybrid Manufacturing Flexible Job Shops Using a Time Petri Nets Improved Genetic Algorithm"],"prefix":"10.3390","volume":"17","author":[{"given":"Xuanye","family":"Lin","sequence":"first","affiliation":[{"name":"Future Tech College, South China University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenxiong","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shujun","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juntao","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4489-2517","authenticated-orcid":false,"given":"Deping","family":"Li","sequence":"additional","affiliation":[{"name":"School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai 519070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6425","DOI":"10.1109\/TII.2019.2938572","article-title":"Digital-twin-based job shop scheduling toward smart manufacturing","volume":"15","author":"Fang","year":"2019","journal-title":"IEEE Trans. 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