{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:44:50Z","timestamp":1760031890279,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T00:00:00Z","timestamp":1742774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"],"award-info":[{"award-number":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Applied Basic Research Project of Liaoning Province","award":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"],"award-info":[{"award-number":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"]}]},{"name":"Dalian Key Field Innovation Team Project","award":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"],"award-info":[{"award-number":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"]}]},{"name":"Science and Technology Major Project of the Xinjiang Uygur Autonomous Region","award":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"],"award-info":[{"award-number":["62073056","61876029","2023JH2\/101300207","2021RT14","2022A01001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Cyber-physical systems need more intelligent decision-making methods. To address this issue with respect to incomplete process models and inefficient scheduling, we have previously proposed a new method called Petri-nets-adaptive ant colony optimization (PN-AACO). This method targets small-scale job shops with shared resource limits. These shops require symmetric job designs for resource sharing but have asymmetric job processing times. PN-AACO uses Petri net symmetry at edge nodes but faces a problem. Its marking\u2013transition pheromone index mechanism causes state space explosion from Petri nets. This leads to a decrease in the computational speed of the algorithm in the face of an increase in scale or state, which results in a longer overall manufacturing process time that impacts productivity. Thus, we propose the improved PN-AACO (iPN-AACO). The improved method uses transition\u2013transition pheromone recording to control pheromone amounts. It also adds pheromone-based initial selection and best-known-paths-based probability rules. Tests show this approach speeds up computations up to 92% in more-states models while keeping scheduling effective.<\/jats:p>","DOI":"10.3390\/sym17040487","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T13:48:20Z","timestamp":1742824100000},"page":"487","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improvement of Scheduling Optimization of Cyber-Physical Systems Based on Petri Net and Intelligent Algorithm"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8856-2723","authenticated-orcid":false,"given":"Yuhai","family":"Yang","sequence":"first","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"}]},{"given":"Xiaodong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5775-1222","authenticated-orcid":false,"given":"Wei","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1007\/s12555-022-0415-y","article-title":"Modeling and Analysis of Cyber-physical Systems Based on Petri Net","volume":"21","author":"Yang","year":"2023","journal-title":"Int. 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[Master\u2019s Thesis, Xidian University]."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/487\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:59:26Z","timestamp":1760029166000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/487"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,24]]},"references-count":25,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["sym17040487"],"URL":"https:\/\/doi.org\/10.3390\/sym17040487","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,24]]}}}