An Automatic Decomposition Algorithm for Solving Stochastic Mixed-Integer Programs Based on Progressive Hedging Algorithm

An Automatic Decomposition Algorithm for Solving Stochastic Mixed-Integer Programs Based on Progressive Hedging Algorithm | 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 An Automatic Decomposition Algorithm for Solving Stochastic Mixed-Integer Programs Based on Progressive Hedging Algorithm Sheng-I Chen, Yu-Ting Tseng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6276218/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 study focuses on stochastic mixed-integer programming problems and proposes an automatic decomposition algorithm that is capable of detecting the problem structure and then determining the best way to separate the original problem into sub-problems. We utilize the hypergraph to capture the relationship between decision variables and constraints according to the nonzero elements in the left-hand-side matrix of the original problem. The proposed decomposition method is shown to be terminated in finite iterations. Additionally, the decomposed problem is solved using the progressive hedging algorithm, with various configurations adjusted to enhance runtime. Computational experiments use public instances of two-stage stochastic integer programs. The result shows that most linked variables are continuous as the number of decomposed sub-problems decreases. This improves the convergence of the progressive hedging algorithm, yielding optimal or near-optimal solutions even for very large-scale instances that cannot be solved by commercial solvers. Automatic decomposition algorithm Hypergraphs Stochastic mixed-integer programs Progressive hedging algorithm 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-6276218","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":444554477,"identity":"f8ef661d-6bb8-4aea-894c-c39093aec465","order_by":0,"name":"Sheng-I Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYDACZgY2IGkD5bERryUNoYWHCE0gLYdJ0CLfzvzswccd5/MMjp8xYPhQdpjBXiIBvxaDw2zmhjPP3C42OJNjwDjj3GEGHoJamHnYpHnbbiduuMFjwMzbBtQiTUCLfDNQy9+2cxAtf4nRwnAYqIWx7QBECyMxWoB+MZPsbUtOnHkmreBgz7l0Hp77Dwg4rP/wM4mfbXaJfccPb3zwo8xajr3nAAGHwYACUCFILTExCbOugXi1o2AUjIJRMMIAAPr3P5Ahgg2iAAAAAElFTkSuQmCC","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":true,"prefix":"","firstName":"Sheng-I","middleName":"","lastName":"Chen","suffix":""},{"id":444554478,"identity":"5ab50a7b-fd68-433d-be57-79178089d229","order_by":1,"name":"Yu-Ting Tseng","email":"","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":false,"prefix":"","firstName":"Yu-Ting","middleName":"","lastName":"Tseng","suffix":""}],"badges":[],"createdAt":"2025-03-21 09:38:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6276218/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6276218/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96604768,"identity":"4fcadfa8-70cc-42ec-81fb-6eae2f89a12a","added_by":"auto","created_at":"2025-11-24 09:14:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":744001,"visible":true,"origin":"","legend":"","description":"","filename":"ADASNLatexFormat.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6276218/v1_covered_7b93fc3f-505d-4cba-88a9-b6ee643862db.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Automatic Decomposition Algorithm for Solving Stochastic Mixed-Integer Programs Based on Progressive Hedging Algorithm","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":"Automatic decomposition algorithm, Hypergraphs, Stochastic mixed-integer programs, Progressive hedging algorithm","lastPublishedDoi":"10.21203/rs.3.rs-6276218/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6276218/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study focuses on stochastic mixed-integer programming problems and proposes an automatic decomposition algorithm that is capable of detecting the problem structure and then determining the best way to separate the original problem into sub-problems. 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