γ - Competitveness. An Approach to Multi-Objective Optimization with High Computation Costs in Lipschitz Functions

γ - Competitveness. An Approach to Multi-Objective Optimization with High Computation Costs in Lipschitz Functions | 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 γ - Competitveness. An Approach to Multi-Objective Optimization with High Computation Costs in Lipschitz Functions Ilgam Latypov, Yuriy Dorn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5189949/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Jan, 2025 Read the published version in Operations Research Forum → Version 1 posted 9 You are reading this latest preprint version Abstract In practical engineering and optimization, solving multi-objective optimization (MOO) problems typically involves scalarization methods that convert a multiobjective problem into a single-objective one. While effective, these methods often incur significant computational costs due to iterative calculations and are further complicated by the need for hyperparameter tuning. In this paper, we introduce an extension of the concept of competitive solutions and propose the Scalarization With Competitiveness Method (SWCM) for multicriteria problems. This method is highly interpretable and eliminates the need for hyperparameter tuning. Additionally, we offer a solution for cases where the objective functions are Lipschitz continuous and can only be computed once, termed Competitiveness Approximation on Lipschitz Functions (CAoLF). This approach is particularly useful when computational resources are limited or recomputation is not feasible. Through computational experiments on the minimum-cost concurrent flow problem, we demonstrate the efficiency and scalability of the proposed method, underscoring its potential for addressing computational challenges in MOO across various applications. multi-objective optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Jan, 2025 Read the published version in Operations Research Forum → Version 1 posted Editorial decision: Revision requested 03 Dec, 2024 Reviews received at journal 03 Dec, 2024 Reviews received at journal 01 Dec, 2024 Reviewers agreed at journal 09 Oct, 2024 Reviewers agreed at journal 07 Oct, 2024 Reviewers invited by journal 05 Oct, 2024 Editor assigned by journal 04 Oct, 2024 Submission checks completed at journal 01 Oct, 2024 First submitted to journal 01 Oct, 2024 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-5189949","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":385873193,"identity":"a65a1e40-ee27-43ae-a321-2f58c915c58a","order_by":0,"name":"Ilgam Latypov","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIie2PsQqDMBRFXxDiYu3qZH8hIBQ3f8X8RHGMCOnYWfoTTp0jDi6ls6JDQXBu6eLQoamVjsax0BwI3IR3uC8AGs0PgsFgn2TGDMJlCmIg3snKFyrwVZyF82ADih933rqk7uLbFU4BEaveUSyWODnvPdLQRBY1NBPmVqUwqRQ0PVL2VkIiMFa2DKOS5skglWCJwseWgyODVFCmVAzE/fOl99YW5X4of5QW2PDnlM0+Kapo17rYLLt6iJrALjmq5hQw5EFYTDcyvah5CuWIRqPR/DEv9H9J8HxR+2EAAAAASUVORK5CYII=","orcid":"","institution":"Institute for Artificial Intelligence, Lomonosov Moscow State University, Moscow, Russian Federation","correspondingAuthor":true,"prefix":"","firstName":"Ilgam","middleName":"","lastName":"Latypov","suffix":""},{"id":385873194,"identity":"e2f9de11-a457-4377-ba7a-ac2da264d34e","order_by":1,"name":"Yuriy Dorn","email":"","orcid":"","institution":"Institute for Artificial Intelligence, Lomonosov Moscow State University, Moscow, Russian Federation","correspondingAuthor":false,"prefix":"","firstName":"Yuriy","middleName":"","lastName":"Dorn","suffix":""}],"badges":[],"createdAt":"2024-10-01 23:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5189949/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5189949/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s43069-024-00411-y","type":"published","date":"2025-01-14T15:57:17+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":74284561,"identity":"98ab885f-a32b-409a-9d30-9b59aaebff4f","added_by":"auto","created_at":"2025-01-20 16:08:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":365501,"visible":true,"origin":"","legend":"","description":"","filename":"Lipchitzpaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5189949/v1_covered_6c698663-e64f-4c31-bc7f-a128828544c5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eγ - Competitveness. 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While effective, these methods often incur significant computational costs due to iterative calculations and are further complicated by the need for hyperparameter tuning.\u003c/p\u003e\n\u003cp\u003eIn this paper, we introduce an extension of the concept of competitive solutions and propose the Scalarization With Competitiveness Method (SWCM) for multicriteria problems. This method is highly interpretable and eliminates the need for hyperparameter tuning. Additionally, we offer a solution for cases where the objective functions are Lipschitz continuous and can only be computed once, termed Competitiveness Approximation on Lipschitz Functions (CAoLF). 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