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They control agents\u2019 behavior in a multiagent system (MAS) and need to evolve to cope with changing environments. Mutation oriented norm evolution is a strategies for allowing norms to evolve. However, this strategy simply adds some possible trigger condition constraints on the norms, which means that some agents are unable to perform actions. To address this problem, this paper presents a new strategy for norm evolution based on an improved crossover operator. First, this paper presents a power-set approach to improve the integrity of norm evolution. This approach can help ensure that all possible combinations of norms are considered during the analysis, providing a deeper understanding of how norms interact and evolve within a norm set. Then, to improve the efficiency of norm evolution, a trade-off between efficiency and completeness is proposed. This approach reduces the search space and improves efficiency, as not every power set combination needs to be searched; it also ensures completeness. Finally, the crossover operator in this strategy is improved based on the trade-off approach. Specifically, the triggers and expectations of one mutated norm enrich the triggers and expectations of other norms. All of these factors enrich the normative conditions through the trade-off approach. A MAS can take immediate action to adapt to new requirements or problems encountered, and quickly make normative changes and learn to respond appropriately to a new situation. The MAS is able to more clearly understand and learn about causality in the environment during norm evolution, and understand the connection between behavior and outcomes. The proposed strategy is applied to a case study of an unmanned vehicle system. The experimental results show that the trade-off approach has greater completeness and effectiveness in norm evolution. This strategy achieves a more complete and effective autonomous norm evolution. It helps the system achieve its goals better and reach better performance in terms of adaptability, helping it to function better in complex multiagent environments.<\/jats:p>","DOI":"10.1007\/s40747-024-01470-8","type":"journal-article","created":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T02:01:38Z","timestamp":1716948098000},"page":"6081-6102","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Crossover in mutation oriented norm evolution"],"prefix":"10.1007","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3122-0527","authenticated-orcid":false,"given":"Bingyu","family":"Lv","sequence":"first","affiliation":[]},{"given":"Xianchang","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Rui","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,29]]},"reference":[{"key":"1470_CR1","doi-asserted-by":"publisher","first-page":"116370","DOI":"10.1016\/j.eswa.2021.116370","volume":"192","author":"A Abu-Monshar","year":"2022","unstructured":"Abu-Monshar A, Al-Bazi A, Palade V (2022) An agent-based optimisation approach for vehicle routing problem with unique vehicle location and depot. 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