Divergence-guided Particle Swarm Optimization

Divergence-guided Particle Swarm Optimization | 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 Divergence-guided Particle Swarm Optimization Kleyton da Costa, Bernardo Modenesi, Ivan F.M. Menezes, Helio Vieira Lopes This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9431774/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Particle Swarm Optimization (PSO) is susceptible to premature convergence when the swarm collapses around the global best, particularly on multimodal landscapes in higher dimensions. We propose Divergence-guided PSO (DPSO), which augments the velocity update with a modulation term that repels particles whose personal bests have converged near the global best. The repulsion is gated by a Gaussian similarity kernel, which we prove is equivalent to an exponentially decaying function of the KL divergence between Gaussian-embedded personal and global bests, connecting the mechanism to the family of f-divergences and providing a principled basis for kernel design. Experiments on 36 benchmark functions (15 unimodal, 21 multimodal) across dimensions D ∈ {10, 30, 50}, each with 30 independent runs, show that DPSO frequently outperforms standard PSO on multimodal problems, with improvements of 2-8× on functions such as Pinter, Ackley, and Levy, and up to 5× reduction in run-to-run variance. On unimodal landscapes the modulation term is counterproductive, confirming that DPSO targets the exploration-exploitation trade-off rather than offering a universal improvement. The method adds one hyperparameter, incurs 15-25% wall-clock overhead, and does not increase the asymptotic per-iteration complexity of PSO. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 18 May, 2026 Reviewers agreed at journal 18 May, 2026 Reviewers agreed at journal 17 May, 2026 Reviews received at journal 17 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers agreed at journal 14 May, 2026 Reviewers invited by journal 14 May, 2026 Editor assigned by journal 12 May, 2026 Submission checks completed at journal 26 Apr, 2026 First submitted to journal 15 Apr, 2026 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. 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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-9431774","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":640655104,"identity":"2fbb122f-4462-4232-a2bf-b09a2658aad2","order_by":0,"name":"Kleyton da Costa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIie2RMYvCMBiGUz75XMJlTYj6GwoFcdIfc9Cpm0vFwaHgeuv9ksyVgC4F14IOVwVnHTzOzbRF3BLchMszvLzD+4SEEOLxvCG8++zBjwn64VTARN52CGsFX1GQN+lSRAZreU73JNzq0+yajHtIoDqUFkUCxjwvTiQs4+Gurz7NxTCKEosyADrkq6Um4pviTigwCkVpV9hvq3wVOBVq4VakObZRGEkwuCjtVkSG0agoNGU8jmSgNhTB8Ra+yaoyTfUAma4uNzWfsG5WHW2KoVN/B60btGmfN5PzowV/7rXH4/H8Q+7kNT6Q1GON3AAAAABJRU5ErkJggg==","orcid":"","institution":"Pontifical Catholic University of Rio de Janeiro","correspondingAuthor":true,"prefix":"","firstName":"Kleyton","middleName":"da","lastName":"Costa","suffix":""},{"id":640655105,"identity":"e404011e-458c-4604-92ad-197f35048685","order_by":1,"name":"Bernardo Modenesi","email":"","orcid":"","institution":"University of Utah","correspondingAuthor":false,"prefix":"","firstName":"Bernardo","middleName":"","lastName":"Modenesi","suffix":""},{"id":640655106,"identity":"6b9b9b11-f058-4f51-a7f1-9db4e0afb1a8","order_by":2,"name":"Ivan F.M. 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