Surrogate-Assisted Global Optimization Using Structured Low-Discrepancy Sampling and Neural Network

Surrogate-Assisted Global Optimization Using Structured Low-Discrepancy Sampling and Neural Network | 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 Surrogate-Assisted Global Optimization Using Structured Low-Discrepancy Sampling and Neural Network N. Cheggaga, F. Hannane, F. Adli, L. Ouzeri, A. Benallel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8621745/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 Surrogate-assisted optimization is an effective strategy for solving global optimization problems involving expensive and highly multimodal objective functions, but its performance strongly depends on the structure of the experimental design and the reliability of the surrogate model. This paper proposes a structured surrogate-assisted optimization framework that integrates hybrid low-discrepancy sampling, informed neural network surrogate modeling, and adaptive evolutionary optimization under limited evaluation budgets. The initial training dataset is generated using a hybrid Latin Hypercube-Sobol sampling strategy, ensuring both stratified marginal distributions and low global discrepancy. To improve scalability, an informed surrogate modeling approach is adopted, combining analytical trend decomposition with trigonometric feature encoding to reduce the effective complexity of the learning task. The surrogate is embedded within a genetic algorithm and progressively refined through adaptive enrichment based on a small number of exact evaluations. The framework is evaluated on the multimodal Rastrigin benchmark in two- and five-dimensional settings. Results demonstrate high surrogate accuracy, stable optimization behavior, and effective mitigation of surrogate-induced artifacts, highlighting the benefits of structured sampling and informed surrogate modeling for efficient global optimization. Applied Mathematics Operations Research Surrogate-assisted optimization Neural networks LHS-Sobol sampling Low-discrepancy sequences Genetic algorithms Rastrigin function Full Text Additional Declarations The authors declare no competing interests. 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-8621745","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575802969,"identity":"99f068e7-6bb7-48e8-9858-98fa4ba7f23d","order_by":0,"name":"N. Cheggaga","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"N.","middleName":"","lastName":"Cheggaga","suffix":""},{"id":575802970,"identity":"0122ad55-b692-49b8-8f60-c813d5684ddd","order_by":1,"name":"F. 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Université Saad Dahleb","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":"Surrogate-assisted optimization, Neural networks, LHS-Sobol sampling, Low-discrepancy sequences, Genetic algorithms, Rastrigin function","lastPublishedDoi":"10.21203/rs.3.rs-8621745/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8621745/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSurrogate-assisted optimization is an effective strategy for solving global optimization problems involving expensive and highly multimodal objective functions, but its performance strongly depends on the structure of the experimental design and the reliability of the surrogate model. This paper proposes a structured surrogate-assisted optimization framework that integrates hybrid low-discrepancy sampling, informed neural network surrogate modeling, and adaptive evolutionary optimization under limited evaluation budgets.\u003c/p\u003e \u003cp\u003eThe initial training dataset is generated using a hybrid Latin Hypercube-Sobol sampling strategy, ensuring both stratified marginal distributions and low global discrepancy. To improve scalability, an informed surrogate modeling approach is adopted, combining analytical trend decomposition with trigonometric feature encoding to reduce the effective complexity of the learning task. The surrogate is embedded within a genetic algorithm and progressively refined through adaptive enrichment based on a small number of exact evaluations.\u003c/p\u003e \u003cp\u003eThe framework is evaluated on the multimodal Rastrigin benchmark in two- and five-dimensional settings. Results demonstrate high surrogate accuracy, stable optimization behavior, and effective mitigation of surrogate-induced artifacts, highlighting the benefits of structured sampling and informed surrogate modeling for efficient global optimization.\u003c/p\u003e","manuscriptTitle":"Surrogate-Assisted Global Optimization Using Structured Low-Discrepancy Sampling and Neural Network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-19 05:47:53","doi":"10.21203/rs.3.rs-8621745/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":"18761815-bd20-4d6d-8369-6167c3e55d5d","owner":[],"postedDate":"January 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61270785,"name":"Applied Mathematics"},{"id":61270786,"name":"Operations Research"}],"tags":[],"updatedAt":"2026-01-19T05:47:53+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-19 05:47:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8621745","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8621745","identity":"rs-8621745","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}