Bayesian network structure learning by  opposition-based learning

Bayesian network structure learning by opposition-based learning | 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 Article Bayesian network structure learning by opposition-based learning Baodan Sun, Xinyi Zhang, Junhui Jiang, Jianguang Gong, Dan Lin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5870291/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 May, 2025 Read the published version in Scientific Reports → Version 1 posted 8 You are reading this latest preprint version Abstract As a classical basic model for causal inference, Bayesian networks are of vital importance both in artificial intelligence with uncertainty and interpretability. The significant status of Bayesian networks in these research orientations depends on its topological structure, namely directed acyclic graphs(DAGs). Bayesian network structure learning is a well-known NP-hard problem, and its computation accuracy is still worth being further studied. In this paper, we propose a new Bayesian network structure learning algorithm, OP-PSO-DE, which combines Particle Swarm Optimization(PSO) and Differential Evolution(DE) to search for the optimal structure. Since the computation complexity of BN structure learning increases exponentially with the number of nodes, the proposed algorithm incorporates opposition-based learning to narrow the search space of heuristic algorithms, which can effectively accelerate the searching process. Experimental results show that the proposed algorithm achieves better performances than other state-of-the-art structure learning algorithms when the sample size is 500. The source code of the paper can be found at this link: https://github.com/sunbaodan-hrbeu/paper_code . Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Information technology Opposition-based learning Differential evolution Particle swarm optimization Structure learning Bayesian networks Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 27 May, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 29 Apr, 2025 Reviews received at journal 25 Apr, 2025 Reviews received at journal 17 Apr, 2025 Reviewers agreed at journal 15 Apr, 2025 Reviewers agreed at journal 15 Apr, 2025 Reviewers invited by journal 21 Mar, 2025 Submission checks completed at journal 19 Mar, 2025 First submitted to journal 09 Mar, 2025 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-5870291","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":448191876,"identity":"e6791456-83cb-430d-98c3-ff668136d09b","order_by":0,"name":"Baodan Sun","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Baodan","middleName":"","lastName":"Sun","suffix":""},{"id":448191877,"identity":"e54bb465-e761-4d54-a252-0f50a1e50fc5","order_by":1,"name":"Xinyi Zhang","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Xinyi","middleName":"","lastName":"Zhang","suffix":""},{"id":448191878,"identity":"bd514be8-fa2c-4a95-a4e3-626c991fc5ee","order_by":2,"name":"Junhui Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYBACxhkMCQeAtJwBAw9EoIFYLcbEa2GQgFCJG4jWwjy74eGBnztq07dLnz34mIfBRnbDAeZnD/A6bM6BhIO9Z47n7uzLSzbmYUgz3nCAzdwAv18SEg7wth3L3XCGx0yah+Fw4oYDPGwShLQc/Nt2LN3gDI/5bx6G/8RpOczbVpMA1GLGzMNwgEgtsm0HDDec4UuWnGOQbDzzMJsZXi2GM3KSP75tq5M3OMN78MObCjvZvuPNz/BraeBJAFKHoVxQUDHjUw8E8gzsB4BUHQFlo2AUjIJRMKIBAOlkT0eiCxZpAAAAAElFTkSuQmCC","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":true,"prefix":"","firstName":"Junhui","middleName":"","lastName":"Jiang","suffix":""},{"id":448191879,"identity":"0a46fb3d-542d-4ba8-b47d-4b7866f69056","order_by":3,"name":"Jianguang Gong","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Jianguang","middleName":"","lastName":"Gong","suffix":""},{"id":448191880,"identity":"e1d7d263-eb80-4f2c-970f-d5ffa20dee0d","order_by":4,"name":"Dan Lin","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Dan","middleName":"","lastName":"Lin","suffix":""}],"badges":[],"createdAt":"2025-01-21 05:23:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5870291/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5870291/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-03267-2","type":"published","date":"2025-05-27T15:57:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83783009,"identity":"37868e48-7e23-4102-a108-d509f4af8d92","added_by":"auto","created_at":"2025-06-02 16:09:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":397727,"visible":true,"origin":"","legend":"","description":"","filename":"newopsub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5870291/v1_covered_6c5d5e99-576c-47eb-b8d1-43bc68f8605a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bayesian network structure learning by opposition-based learning","fulltext":[],"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":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Opposition-based learning, Differential evolution, Particle swarm optimization, Structure learning, Bayesian networks","lastPublishedDoi":"10.21203/rs.3.rs-5870291/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5870291/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"As a classical basic model for causal inference, Bayesian networks are of vital importance both in artificial intelligence with uncertainty and interpretability. 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