Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic Optimization

Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic 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 Article Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic Optimization Renchong Zhang, Chunyan Pan, Renmao Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3826405/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 In this paper, for a general type of multi-objective probabilistic optimization problem without any prior noisy information, which has an extensive engineering application background and needs to be solved urgently, we propose a small-population immune algorithm with adaptive sampling to solve. In the design. First, we design a small-population immune algorithm framework inspired by the response mechanism of adaptive immunity. Second, we design an adaptive sampling scheme that adaptively allocates an appropriate number of samples for each sub-objective function of all individuals in the population to estimate the objective function value. Third, based on the objective function estimates, the dominance levels of all individuals in the population and the crowding distances of individuals in each dominance level are determined. Fourth, the clone size, mutation rate, crossover distribution index, and mutation distribution index of an individual are designed to be adaptively determined based on the number of iterations, dominance level, and crowding distance. Cloning, crossover, and mutation operators are implemented for each individual, using simulated binary crossover and polynomial mutation to enhance co-evolution and facilitate information sharing and exchange among all individuals. Fifth, based on the dominance level and crowding distance, the population update strategies are designed to adaptively update the memory set with high-quality individuals and generate a new generation population with good diversity. Finally, based on three theoretical problems and two engineering problems, as well as six representative comparative algorithms, the experimental results show that the proposed algorithm is an optimizer with good competitiveness and application potential, and has few parameters, less sample consumption, strong noise suppression ability, and high search efficiency. 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-3826405","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":264727548,"identity":"c63ea744-bdd1-4156-92d5-882ed749508a","order_by":0,"name":"Renchong Zhang","email":"","orcid":"","institution":"Guizhou University of Commerce","correspondingAuthor":false,"prefix":"","firstName":"Renchong","middleName":"","lastName":"Zhang","suffix":""},{"id":264727549,"identity":"9fc479ff-7272-47cc-84ea-9497e00a0ffd","order_by":1,"name":"Chunyan Pan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYDACCTiL+eCDDxUScvIkaGFLNpxxxsLYsIF4LTxqwpxtFYkMBwjo4J/dY/aYp+ZOHpDBxsw4TyKBsYH54aMb+Cy5c8bcmOfYs2KJO2ePPS7cJpHHzsBmbJyDR4uBRI6ZNA/b4cSGG3npxjO3SRQzNvCwSRPW8u9w4vwbQAbvHInEhgPEaOFtO5y4AaylgQgtEjfSyiTn9h0uNryRBgzkYxLGhs0E/MI/I3mbxJtvh/PkbiQDo7KmTk6evfnhY3xaQICJh4EhAcFlJqAcBBh/oGgZBaNgFIyCUYAGAEKZTPEGo/hqAAAAAElFTkSuQmCC","orcid":"","institution":"Qiannan Normal University for Nationalities","correspondingAuthor":true,"prefix":"","firstName":"Chunyan","middleName":"","lastName":"Pan","suffix":""},{"id":264727550,"identity":"94fb8676-4006-4bd4-a962-2dbfcd4013ab","order_by":2,"name":"Renmao Zhang","email":"","orcid":"","institution":"Central South University","correspondingAuthor":false,"prefix":"","firstName":"Renmao","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2023-12-31 18:44:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3826405/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3826405/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57592100,"identity":"4d565529-bd56-402d-b943-76a6c452abe2","added_by":"auto","created_at":"2024-06-03 05:42:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12574756,"visible":true,"origin":"","legend":"","description":"","filename":"AdaptiveSamplingImmuneAlgorithmforMultiObjectiveProbabilisticOptimization.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3826405/v1_covered_544635fe-8d48-48e2-89a1-3e7cbd6f0ff4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic Optimization","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":"","lastPublishedDoi":"10.21203/rs.3.rs-3826405/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3826405/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, for a general type of multi-objective probabilistic optimization problem without any prior noisy information, which has an extensive engineering application background and needs to be solved urgently, we propose a small-population immune algorithm with adaptive sampling to solve. 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Cloning, crossover, and mutation operators are implemented for each individual, using simulated binary crossover and polynomial mutation to enhance co-evolution and facilitate information sharing and exchange among all individuals. Fifth, based on the dominance level and crowding distance, the population update strategies are designed to adaptively update the memory set with high-quality individuals and generate a new generation population with good diversity. 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