Dimensionality reduction for binary quadratic programming problems

Dimensionality reduction for binary quadratic programming problems | 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 Dimensionality reduction for binary quadratic programming problems Rabih Battikh, Bilal Hammoud, Hassan Alabboud, Danny El Kass, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7273186/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 paper addresses the constrained binary quadratic problem (QP). This problem consists in minimizing a quadratic function a binary variables (0-1 variables) with linear constraints. Accordingly, in this work, We have generalized reliable fixing criteria (F 0 ) and (F 1 ) for the (QP) problem. The purpose of these fixing criteria is to facilitate the resolution of the initial problem (QP) where through these criteria we can decrease the dimension of the (QP) problem when it is possible and sometimes we can solve this problem completely by using a repeat loop based on these criteria (QPFA algorithm). Numerical results are presented to consolidate the demonstrated theoretical results and prove efficiency and performance in terms of speed, quality and robustness of our work. Mathematics Subject Classification: 90C20 , 90C27 , 90C10 Binary constrained quadratic programming Fixing criteria 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-7273186","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":494429237,"identity":"b6b59c3b-88a2-4924-ad15-507f2c009131","order_by":0,"name":"Rabih Battikh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYFACHhAhYWDA3gPh8hGl5UACUAvPGSADyGUjUguDgYFEDlgLA0Et5g28Bz9//GFhbC759uDjjzl2MmwMzA8f3cCjReYAX7IE0GFmlrPzkg0ObksGOozN2DgHjxYJBh4DkBYbg9s5ZhIHtzEDtfCwSRPQYvwDrOXmGZCWeqK0mIEdZnCDB6TlMDFa+NIszqRJGBucyTE2OLvtOA8bM0G/8B6+UWFTZ7jh+BnDB5Xbqu352ZsfPsanhUH+AboIMz7lo2AUjIJRMAqIAgAd/EGwyHnVvQAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Rabih","middleName":"","lastName":"Battikh","suffix":""},{"id":494429238,"identity":"a20d4347-91ac-40b5-b57e-f9389362d0fb","order_by":1,"name":"Bilal Hammoud","email":"","orcid":"","institution":"Beirut Arab University","correspondingAuthor":false,"prefix":"","firstName":"Bilal","middleName":"","lastName":"Hammoud","suffix":""},{"id":494429239,"identity":"f466abd4-a7dc-4d74-9cdf-bcc7742cc072","order_by":2,"name":"Hassan Alabboud","email":"","orcid":"","institution":"Lebanese University","correspondingAuthor":false,"prefix":"","firstName":"Hassan","middleName":"","lastName":"Alabboud","suffix":""},{"id":494429240,"identity":"c0bc6fb4-ef27-4045-8010-626068850fe0","order_by":3,"name":"Danny El Kass","email":"","orcid":"","institution":"Lebanese University","correspondingAuthor":false,"prefix":"","firstName":"Danny","middleName":"El","lastName":"Kass","suffix":""},{"id":494429241,"identity":"666c66a4-f4bd-4071-a741-0c5a6aa6d2f5","order_by":4,"name":"Adnan Yassine","email":"","orcid":"","institution":"Normandie Univ, Univ. 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This problem consists in minimizing a quadratic function a binary variables (0-1 variables) with linear constraints. Accordingly, in this work, We have generalized reliable fixing criteria (F\u003csub\u003e0\u003c/sub\u003e) and (F\u003csub\u003e1\u003c/sub\u003e) for the (QP) problem. The purpose of these fixing criteria is to facilitate the resolution of the initial problem (QP) where through these criteria we can decrease the dimension of the (QP) problem when it is possible and sometimes we can solve this problem completely by using a repeat loop based on these criteria (QPFA algorithm). Numerical results are presented to consolidate the demonstrated theoretical results and prove efficiency and performance in terms of speed, quality and robustness of our work.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification: 90C20 , 90C27 , 90C10\u003c/p\u003e","manuscriptTitle":"Dimensionality reduction for binary quadratic programming problems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-05 02:52:08","doi":"10.21203/rs.3.rs-7273186/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":"64b1fe8a-ce3d-4e63-a9cd-e72213cee250","owner":[],"postedDate":"August 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-06T15:09:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-05 02:52:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7273186","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7273186","identity":"rs-7273186","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}