Augmented Lagrangian Weighted Chebyshev Method for Constrained Multiobjective Optimization

Augmented Lagrangian Weighted Chebyshev Method for Constrained Multiobjective 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 Augmented Lagrangian Weighted Chebyshev Method for Constrained Multiobjective Optimization Augustin Kaboré, Appolinaire Tougma, Kounhinir Somé This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7982083/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 This document focuses primarily on addressing multi-objective optimization issues using an augmented Lagrange method to derive a set of non-dominated solutions. The proposed technique involves transforming the initial multiobjective optimization problem into a scalar parametric problem via the weighted Chebyshev approach. This transformed function is then applied within the augmented Lagrange framework. By adhering to well-defined assumptions, the algorithm’s initial output consists of feasible sequences that satisfy problem constraints. Moreover, the document establishes that any limit point of these sequences represents a Pareto optimal solution, indicating an optimal trade-off among diverse objectives. To practically execute the proposed algorithm, a dedicated secondary algorithm is introduced to solve the sub-problem within the primary algorithm. The second algorithm incorporates the Steepest Descent method and a Max-type non-monotone line search technique. The document presents results that validate the correct configuration of the linear search method in the second algorithm. Additionally, while adhering to rigorous assumptions, it is shown that any limit point produced by this second algorithm is a Pareto-critical point. To assess the method’s efficiency and performance, numerical validations are conducted by solving various test problems. The obtained numerical outcomes effectively demonstrate the algorithm’s competence in generating high-quality solutions for multiobjective optimization problems subject to constraints. Multiobjective optimization Penalty function Augmented Lagrangian Pareto front Weighted Chebyshev. 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. 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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-7982083","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":552952944,"identity":"227231c0-ae23-4e5c-bc82-9a82d8b20328","order_by":0,"name":"Augustin Kaboré","email":"","orcid":"","institution":"Université Norbert ZONGO","correspondingAuthor":false,"prefix":"","firstName":"Augustin","middleName":"","lastName":"Kaboré","suffix":""},{"id":552952945,"identity":"947a74e6-199c-4c30-9604-dc64bf951636","order_by":1,"name":"Appolinaire Tougma","email":"","orcid":"","institution":"Université Norbert ZONGO","correspondingAuthor":false,"prefix":"","firstName":"Appolinaire","middleName":"","lastName":"Tougma","suffix":""},{"id":552952946,"identity":"d3486cea-6318-4641-bb68-5699210ba870","order_by":2,"name":"Kounhinir Somé","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYFACNhAhwcMPohIKiNdiISPZANJiQLyWChuDAyCaGC3y7W2Jj3n+SPAYn1+d+OGBAYM8v9gB/FoMzhw7bMzbJsFjduPtZgmgwwxnzk4goEUivU2atwGk5ewGkJYEg9sEtMjPAGoBO2zG2c0/iNLCcCPtmDQPmwSPAX/vNuJsAfol2XAu0C8SN3i3WSQYSBD2CzDEDB+8+VNnz99/dvPNHxU28vzShBwGBxJglRLEKgcB/gOkqB4Fo2AUjIKRBABeAT7zZOQyEAAAAABJRU5ErkJggg==","orcid":"","institution":"Université Norbert ZONGO","correspondingAuthor":true,"prefix":"","firstName":"Kounhinir","middleName":"","lastName":"Somé","suffix":""}],"badges":[],"createdAt":"2025-10-29 16:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7982083/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7982083/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97109444,"identity":"2146c3dd-c9af-42ac-94e3-71171243518d","added_by":"auto","created_at":"2025-12-01 05:56:20","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5178,"visible":true,"origin":"","legend":"","description":"","filename":"e3ddbab322f44e96adf4912b4e7171e6.json","url":"https://assets-eu.researchsquare.com/files/rs-7982083/v1/08d8fdadd999d2106ae91777.json"},{"id":100369310,"identity":"20986b16-b98d-42e1-9cd3-4c4f09a6c741","added_by":"auto","created_at":"2026-01-16 07:58:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":544432,"visible":true,"origin":"","legend":"","description":"","filename":"snarticletemplate.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7982083/v1_covered_30ca1e7c-a567-4bad-b91f-5eb2f6fee55b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Augmented Lagrangian Weighted Chebyshev Method for Constrained Multiobjective 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":"Multiobjective optimization, Penalty function, Augmented Lagrangian, Pareto front, Weighted Chebyshev.","lastPublishedDoi":"10.21203/rs.3.rs-7982083/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7982083/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This document focuses primarily on addressing multi-objective optimization issues using an augmented Lagrange method to derive a set of non-dominated solutions. 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