IFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems

IFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems | 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 IFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems Min-Rong Chen, Liu-Qing Yang, Guo-Qiang Zeng, Kang-Di Lu, Yi-Yuan Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-190790/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results. Software Engineering Firefly algorithm extremal optimization probability choice strategy adaptive step size continuous optimization problems Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 24 Nov, 2021 Reviewers invited by journal 24 Nov, 2021 Editor assigned by journal 08 Nov, 2021 First submitted to journal 07 Nov, 2021 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. 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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-190790","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":65640945,"identity":"c01d3551-1cd4-463d-b266-062ed9ce171a","order_by":0,"name":"Min-Rong Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYPCCAwwM7A1A2sCCGNXMUC08B0BaJEjRIpEAYhChhV+6/+jmipo7cuaSz69u+FEgwcDf3p2AV4vknMNsN88ce2ZsOTun7GYP0GESZ85uwKvF4EYy283GhsOJG27npN3gAWoxkMglTkv9hptn0m7+IUVLgsEN9mO3ibIF6Bezmw3HDhtuOJPDdlvGQIKHoF/4pRuf3WyoOSxvcPz4s5tv/tjI8bf34teCFBE8BmASv3JULewPCKseBaNgFIyCEQkAMjJODnEQ1HcAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-9817-0267","institution":"South China Normal University","correspondingAuthor":true,"prefix":"","firstName":"Min-Rong","middleName":"","lastName":"Chen","suffix":""},{"id":65640946,"identity":"d7087c10-5d68-4720-9e91-2d261e47e071","order_by":1,"name":"Liu-Qing Yang","email":"","orcid":"","institution":"South China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Liu-Qing","middleName":"","lastName":"Yang","suffix":""},{"id":65640947,"identity":"3273eb58-8b41-44a8-9b7a-d838f399b0ba","order_by":2,"name":"Guo-Qiang Zeng","email":"","orcid":"","institution":"Wenzhou University","correspondingAuthor":false,"prefix":"","firstName":"Guo-Qiang","middleName":"","lastName":"Zeng","suffix":""},{"id":65640948,"identity":"e05b0e74-c493-460f-bdd8-46dc598183b5","order_by":3,"name":"Kang-Di Lu","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Kang-Di","middleName":"","lastName":"Lu","suffix":""},{"id":65640949,"identity":"7a45442a-cd1d-4578-ac4e-8d548e081146","order_by":4,"name":"Yi-Yuan Huang","email":"","orcid":"","institution":"South China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yi-Yuan","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2021-01-30 13:01:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-190790/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-190790/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":15984626,"identity":"1682b943-b256-4e49-99f0-6645ad55edeb","added_by":"auto","created_at":"2021-11-29 22:31:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":564549,"visible":true,"origin":"","legend":"","description":"","filename":"IFAEORevised2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-190790/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eIFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-190790/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Firefly algorithm, extremal optimization, probability choice strategy, adaptive step size, continuous optimization problems","lastPublishedDoi":"10.21203/rs.3.rs-190790/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-190790/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAs one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. 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