An Efficient Hybrid Particle Swarm Optimization and Firefly Algorithm

An Efficient Hybrid Particle Swarm Optimization and Firefly Algorithm | 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 An Efficient Hybrid Particle Swarm Optimization and Firefly Algorithm Rui Liu, Lisheng Wei, Pinggai Zhang, Baoling Hu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3602864/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 Typically, particle swarm optimization (PSO) is known for its robust global exploration, but it often falls into the “local trap”. Compared to PSO, the firefly algorithm (FFA) might offer superior local exploitation, but it often lacks speed characteristics and struggles to expand beyond local searches. To harness the strengths of both algorithms, an efficient hybrid particle swarm optimization and firefly algorithm (HPSOFF) is proposed, in which particle swarm optimization with nonlinear inertia weight and attenuation factor (PSO-NIWAF) and firefly algorithm with dynamic population (FFA-DP) are jointly executed to avoid their limitations. Firstly, the mechanism of stochastic parameter mapping (SPM) is employed to obtain uniformly distributed particles, which can promote the optimization speed of the algorithm. Then, the strategy of nonlinear inertia weight and attenuation factor (NIWAF) is introduced into the PSO to bolster its global exploration. In the later stage of the algorithm, a dynamic population strategy is introduced into the FFA to adaptively construct a temporary population. By ranking the fitness values of all particles in the temporary population, superior solutions can be identified to ensure precise local exploitation. Finally, the proposed HPSOFF is adopted to test the CEC2005 benchmark functions as well as famous engineering applications. The experimental results demonstrate that the proposed HPSOFF has significant advantages among these state-of-the-art algorithms. Hybrid algorithm PSO Nonlinear inertia weight FFA Dynamic population 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-3602864","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":586351734,"identity":"d7d1bcd0-70e2-416a-8e8c-82ee30ee0667","order_by":0,"name":"Rui Liu","email":"","orcid":"","institution":"Anhui Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"Liu","suffix":""},{"id":586351735,"identity":"48e02e45-36d7-41a7-a920-d8fb4700ca41","order_by":1,"name":"Lisheng Wei","email":"","orcid":"","institution":"Anhui Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Lisheng","middleName":"","lastName":"Wei","suffix":""},{"id":586351736,"identity":"61a3ba1d-1c96-4704-bc8f-75ca992391d6","order_by":2,"name":"Pinggai Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYDACCSTywAcgwcfAwEy8loMzgCw2IrVAADMPMVrkZzc/e/h1h0WevP/ih4dtKg7XsbE3HzZgqLGJxqWFcc4xc2PZMxLFhjeeGRzOOXNYgo3nWHICw7G03AYcWpglEsykJdskEjfOOGBwOLcNqEUix/gAY8NhnFrYJNK/QbUc/3DYkhgtPBI5ZpIfgVrm8/cYHGaEaknAp0VCIqdMmvGMROIGCZ6Cgz1n0iXbgH4xSMDjF/kZ6dskf+6oS5zff3zzhx8V1vz8wBCT+FBjg1MLOAh4gbIGNxKQhBKwq4QDxp9ALfL9BwgoGwWjYBSMghELAIcyWfJXXwzIAAAAAElFTkSuQmCC","orcid":"","institution":"Chaohu University","correspondingAuthor":true,"prefix":"","firstName":"Pinggai","middleName":"","lastName":"Zhang","suffix":""},{"id":586351737,"identity":"9ec2ca92-a528-43cc-b19e-170478a70797","order_by":3,"name":"Baoling Hu","email":"","orcid":"","institution":"Chaohu University","correspondingAuthor":false,"prefix":"","firstName":"Baoling","middleName":"","lastName":"Hu","suffix":""}],"badges":[],"createdAt":"2023-11-13 03:31:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3602864/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3602864/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102295771,"identity":"f6d1f44e-e27a-4e5e-a36b-dc805756367f","added_by":"auto","created_at":"2026-02-10 10:14:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1458676,"visible":true,"origin":"","legend":"","description":"","filename":"HPSOFF20231113.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3602864/v1_covered_50f9a49a-d5b9-4d0b-a882-e853ed5d39a4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Efficient Hybrid Particle Swarm Optimization and Firefly Algorithm","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Hybrid algorithm, PSO, Nonlinear inertia weight, FFA, Dynamic population","lastPublishedDoi":"10.21203/rs.3.rs-3602864/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3602864/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Typically, particle swarm optimization (PSO) is known for its robust global exploration, but it often falls into the “local trap”. Compared to PSO, the firefly algorithm (FFA) might offer superior local exploitation, but it often lacks speed characteristics and struggles to expand beyond local searches. To harness the strengths of both algorithms, an efficient hybrid particle swarm optimization and firefly algorithm (HPSOFF) is proposed, in which particle swarm optimization with nonlinear inertia weight and attenuation factor (PSO-NIWAF) and firefly algorithm with dynamic population (FFA-DP) are jointly executed to avoid their limitations. Firstly, the mechanism of stochastic parameter mapping (SPM) is employed to obtain uniformly distributed particles, which can promote the optimization speed of the algorithm. Then, the strategy of nonlinear inertia weight and attenuation factor (NIWAF) is introduced into the PSO to bolster its global exploration. In the later stage of the algorithm, a dynamic population strategy is introduced into the FFA to adaptively construct a temporary population. By ranking the fitness values of all particles in the temporary population, superior solutions can be identified to ensure precise local exploitation. Finally, the proposed HPSOFF is adopted to test the CEC2005 benchmark functions as well as famous engineering applications. The experimental results demonstrate that the proposed HPSOFF has significant advantages among these state-of-the-art algorithms.","manuscriptTitle":"An Efficient Hybrid Particle Swarm Optimization and Firefly Algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-06 06:26:08","doi":"10.21203/rs.3.rs-3602864/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":"29dad14f-8e8f-456d-b771-6c81fb72f33d","owner":[],"postedDate":"February 6th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-06T06:26:08+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-06 06:26:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3602864","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3602864","identity":"rs-3602864","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}