{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:38:47Z","timestamp":1760060327883,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T00:00:00Z","timestamp":1755734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFB4700602","2022YFB4700601","22086429092517"],"award-info":[{"award-number":["2022YFB4700602","2022YFB4700601","22086429092517"]}]},{"name":"Ministry of education industry\u2013university cooperative education project","award":["2022YFB4700602","2022YFB4700601","22086429092517"],"award-info":[{"award-number":["2022YFB4700602","2022YFB4700601","22086429092517"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As the global manufacturing industry\u2019s transformation accelerates toward being intelligent, \u201cunmanned\u201d, and low-carbon, manufacturing workshops face conflicts between production schedules and transportation tasks, leading to low efficiency and resource waste. This paper presents a multi-agent collaborative scheduling optimization method based on a hybrid game\u2013genetic framework to address issues like high AGV (Automated Guided Vehicle) idle rates, excessive energy consumption, and uncoordinated equipment scheduling. The method establishes a trinity system integrating distributed decision-making, dynamic coordination, and environment awareness. In this system, the multi-agent decision-making and collaboration process exhibits significant symmetry characteristics. All agents (machine agents, mobile agents, etc.) follow unified optimization criteria and interaction rules, forming a dynamically balanced symmetric scheduling framework in resource competition and collaboration, which ensures fairness and consistency among different agents in task allocation, path planning, and other links. An improved best-response dynamic algorithm is employed in the decision-making layer to solve the multi-agent Nash equilibrium, while the genetic optimization layer enhances the global search capability by encoding scheduling schemes and adjusting crossover\/mutation probabilities using dynamic competition factors. The coordination pivot layer updates constraints in real time based on environmental sensing, forming a closed-loop optimization mechanism. Experimental results show that, compared with the traditional genetic algorithm (TGA) and particle swarm optimization (PSO), the proposed method reduces the maximum completion time by 54.5% and 44.4% in simple scenarios and 57.1% in complex scenarios, the AGV idling rate by 68.3% in simple scenarios and 67.5%\/77.6% in complex scenarios, and total energy consumption by 15.7%\/10.9% in simple scenarios and 25%\/18.2% in complex scenarios. This validates the method\u2019s effectiveness in improving resource utilization and energy efficiency, providing a new technical path for intelligent scheduling in manufacturing workshops. Meanwhile, its symmetric multi-agent collaborative framework also offers a reference for the application of symmetry in complex manufacturing system optimization.<\/jats:p>","DOI":"10.3390\/sym17081368","type":"journal-article","created":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T14:46:04Z","timestamp":1755787564000},"page":"1368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on a Multi-Agent Job Shop Scheduling Method Based on Improved Game Evolution"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3821-3461","authenticated-orcid":false,"given":"Wei","family":"Xie","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Harbin Institute of Technology at WeiHai, Weihai 264209, China"}]},{"given":"Bin","family":"Du","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Harbin Institute of Technology at WeiHai, Weihai 264209, China"}]},{"given":"Jiachen","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Harbin Institute of Technology at WeiHai, Weihai 264209, China"}]},{"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Ocean Engineering, Harbin Institute of Technology at WeiHai, Weihai 264209, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7046-7388","authenticated-orcid":false,"given":"Xiangle","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Harbin Institute of Technology at WeiHai, Weihai 264209, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,21]]},"reference":[{"key":"ref_1","first-page":"1539","article-title":"Integrated Scheduling of Flexible Job-Shop Considering Heterogeneous AGVs","volume":"31","author":"Li","year":"2024","journal-title":"Comput. 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