Chaotic games driven grey wolf optimization: optimal performance design and comprehensive analysis

Chaotic games driven grey wolf optimization: optimal performance design and comprehensive analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Chaotic games driven grey wolf optimization: optimal performance design and comprehensive analysis Chenhua Tang, Changcheng Huang, Yi Chen, Ali Asghar Heidari, Huiling Chen, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3883489/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Introduction : Meta-heuristics have attracted much attention due to their compatibility with other algorithms and excellent optimization ability. Gray wolf optimization (GWO) is also a meta-heuristic algorithm. GWO mainly tries to find the optimal solution by simulating the hierarchical structure and hunting behavior of gray wolves. GWO has the advantages of a relatively simple algorithm structure and fewer parameter Settings. Therefore, it is used in many fields, such as engineering and forecasting. Objectives GWO may have problems in harmonic convergence or be trapped into local optima for some complex tasks. An improved variant of basic GWO is proposed in this paper to efficiently alleviate this deficiency. Preferentially, chaos game optimization (CGO) is introduced into the conventional method to expand its neighborhood searching capabilities. Based on this strategy, we called the improved GWO as CGGWO. Methods To confirm the effectiveness and optimization ability of the CGGWO algorithm, CGGWO is compared with a set of meta-heuristics, including 7 basic meta-heuristics, 7 state-of-the-art meta-heuristics, and 5 enhanced GWO variants. The benchmark functions for comparison are IEEE CEC 2017. The dimensions( D ) of the benchmark test function are 10, 30, 50, and 100. Moreover, CGGWO is applied to five practical engineering problems and two real-world benchmarks from IEEE CEC 2011. Non-parametric statistical Wilcoxon signed-rank and the Friedman tests are performed to monitor the performance of the proposed method. Results In benchmark function testing, CGGWO can find better solutions in most functions. In the Wilcoxon signed-rank and the Friedman tests, the P-value of CGGWO is mostly less than 5%. Among the five engineering problems, the feasible solution found by CGGWO is also the best compared with other methods. Conclusions In the benchmark function test, CGGWO has a better convergence effect than other methods and finds a better solution. From the results of the Wilcoxon signed-rank and the Friedman tests, we can see that the CGGWO results are statistically significant. In engineering problems, CGGWO can find feasible solutions. Grey wolf optimizer Meta-heuristic search algorithms Chaos game optimization Engineering problems Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3883489","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":268500287,"identity":"928f89ef-e72b-4f8f-ac3c-655e28d19c48","order_by":0,"name":"Chenhua Tang","email":"","orcid":"","institution":"Wenzhou University","correspondingAuthor":false,"prefix":"","firstName":"Chenhua","middleName":"","lastName":"Tang","suffix":""},{"id":268500288,"identity":"7a7a1224-b532-47cd-90fd-6110fd1271bc","order_by":1,"name":"Changcheng Huang","email":"","orcid":"","institution":"Wenzhou University","correspondingAuthor":false,"prefix":"","firstName":"Changcheng","middleName":"","lastName":"Huang","suffix":""},{"id":268500289,"identity":"8c08d744-1560-4bb3-b92a-5191315b545a","order_by":2,"name":"Yi Chen","email":"","orcid":"","institution":"Wenzhou University","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Chen","suffix":""},{"id":268500290,"identity":"fe570730-9f35-492e-bdcc-71152354be1d","order_by":3,"name":"Ali Asghar Heidari","email":"","orcid":"","institution":"University of Tehran","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"Asghar","lastName":"Heidari","suffix":""},{"id":268500291,"identity":"686608d2-5ac2-41df-aef0-4f3976a05a4a","order_by":4,"name":"Huiling Chen","email":"","orcid":"","institution":"Wenzhou University","correspondingAuthor":false,"prefix":"","firstName":"Huiling","middleName":"","lastName":"Chen","suffix":""},{"id":268500292,"identity":"342d51ce-0def-4e74-96d6-7d08f008dfc9","order_by":5,"name":"Guoxi Liang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIie2PMUvEMBTHWw46FW6NU79CihAdavs1BJcXAnVRcHQ4jojgfYUb/QJCJsHtHYVOYtbALbnF+UZdxDSHbk1XwfyGlxd4v/zzkiQS+avADXF1hsi/Ktekdzit0EHJuLVZOyhyWknoUPLj0madvweV4lz0xNLT4mT+yAjkun5adS5lUV2MKaVpBXUfK1/WtiVAtuL5lTulb6/lmLK+Kq1TUmWwJ0C3gqFTUtmFFIpOaZTZPBCAN8H0LqwU5JDClb6fUUCsmZlIofm730Uok6WWSwHMuBQI7FKsRH/0cbs8U1rvN5+ybpi+3Nn9ohpPwZ+OgD+4n4SRcZ/y+9b8IDeB4UgkEvmnfAMbIWnRi926kwAAAABJRU5ErkJggg==","orcid":"","institution":"Wenzhou Polytechnic","correspondingAuthor":true,"prefix":"","firstName":"Guoxi","middleName":"","lastName":"Liang","suffix":""}],"badges":[],"createdAt":"2024-01-21 04:17:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3883489/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3883489/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73133398,"identity":"1ad721fd-a307-43ad-8a7a-820fbcbbebbd","added_by":"auto","created_at":"2025-01-07 05:31:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1793464,"visible":true,"origin":"","legend":"","description":"","filename":"chenghuaCGGWO1213enhancedrevfinal010711.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3883489/v1_covered_f03dba13-07dd-4cfe-a564-0f7a32a9ac41.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Chaotic games driven grey wolf optimization: optimal performance design and comprehensive analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Grey wolf optimizer, Meta-heuristic search algorithms, Chaos game optimization, Engineering problems","lastPublishedDoi":"10.21203/rs.3.rs-3883489/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3883489/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eIntroduction\u003c/h2\u003e \u003cp\u003e: Meta-heuristics have attracted much attention due to their compatibility with other algorithms and excellent optimization ability. Gray wolf optimization (GWO) is also a meta-heuristic algorithm. GWO mainly tries to find the optimal solution by simulating the hierarchical structure and hunting behavior of gray wolves. GWO has the advantages of a relatively simple algorithm structure and fewer parameter Settings. Therefore, it is used in many fields, such as engineering and forecasting.\u003c/p\u003e\u003ch2\u003eObjectives\u003c/h2\u003e \u003cp\u003eGWO may have problems in harmonic convergence or be trapped into local optima for some complex tasks. An improved variant of basic GWO is proposed in this paper to efficiently alleviate this deficiency. Preferentially, chaos game optimization (CGO) is introduced into the conventional method to expand its neighborhood searching capabilities. Based on this strategy, we called the improved GWO as CGGWO.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eTo confirm the effectiveness and optimization ability of the CGGWO algorithm, CGGWO is compared with a set of meta-heuristics, including 7 basic meta-heuristics, 7 state-of-the-art meta-heuristics, and 5 enhanced GWO variants. The benchmark functions for comparison are IEEE CEC 2017. The dimensions(\u003cem\u003eD\u003c/em\u003e) of the benchmark test function are 10, 30, 50, and 100. Moreover, CGGWO is applied to five practical engineering problems and two real-world benchmarks from IEEE CEC 2011. Non-parametric statistical Wilcoxon signed-rank and the Friedman tests are performed to monitor the performance of the proposed method.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eIn benchmark function testing, CGGWO can find better solutions in most functions. In the Wilcoxon signed-rank and the Friedman tests, the P-value of CGGWO is mostly less than 5%. Among the five engineering problems, the feasible solution found by CGGWO is also the best compared with other methods.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eIn the benchmark function test, CGGWO has a better convergence effect than other methods and finds a better solution. From the results of the Wilcoxon signed-rank and the Friedman tests, we can see that the CGGWO results are statistically significant. In engineering problems, CGGWO can find feasible solutions.\u003c/p\u003e","manuscriptTitle":"Chaotic games driven grey wolf optimization: optimal performance design and comprehensive analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-23 16:55:18","doi":"10.21203/rs.3.rs-3883489/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"431696f2-bf67-4b68-bf8f-4e8598ace5ea","owner":[],"postedDate":"January 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-07T05:23:12+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-23 16:55:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3883489","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3883489","identity":"rs-3883489","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}