A Decomposition and Dynamic Programming Aggregation Method for the Optimal Water Allocation of Reservoirs in Series

A Decomposition and Dynamic Programming Aggregation Method for the Optimal Water Allocation of Reservoirs in Series | 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 A Decomposition and Dynamic Programming Aggregation Method for the Optimal Water Allocation of Reservoirs in Series Zhihao Gong, Jilin Cheng, Haomiao Cheng, Yi Gong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-431229/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 Research on water allocation of multiple reservoirs with the purpose of reducing water spills and improving the local runoff utilization is a matter of great concern in humid areas with uneven temporal and spatial distributions of water resources. An optimization model for a system of reservoirs in series is developed to minimize water shortages. Several constraints restrict the objective function, including available water, operation rules and water rights for replenishment of the reservoirs with water. The model features multiple dimensions with a single coupling constraint of the large-scale system. A decomposition and dynamic programming aggregation method (DDPA) is proposed; the subsystem models and the aggregation model are both solved with the classical one-dimensional dynamic programming. Compared with the conventional decomposition-coordination method, the proposed method is concise but reliable because it can directly use the results of subsystems to form the one-dimensional dynamic programming aggregation model, avoiding the iterative calculations according to the coordinating function. Compared with the meta-heuristic algorithms, the proposed method is more efficient because it is independent of any algorithm parameter. The proposed method may provide a new reference for solving similar multi-reservoir optimization models. Civil Engineering reservoirs in series joint operation multidimensional dynamic programming decomposition aggregation meta-heuristic algorithm Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text 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. 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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-431229","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":30517783,"identity":"a5a4a8ac-8cfe-4e08-a9f5-0c108ddfedc8","order_by":0,"name":"Zhihao Gong","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhihao","middleName":"","lastName":"Gong","suffix":""},{"id":30517784,"identity":"dd846b2c-da6e-4dd2-a345-5f13b1a606e9","order_by":1,"name":"Jilin Cheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYBACxnYGNhAtB+GyEaOlGaLMmHgtDMwQZYkNRGthbmZ+9uDjjtr0DefPGDB8KDvMwD+7gZDD2MwNZ545nrvhwBkDxhnnDjNI3DlASAsPmzRv27HcDQd7DJh52w4zGEgkEKHlb9uxdIPDPAbMf4nWwthWk2BwDKiFkTgtbGaSvW0HgP5hKzjYcy6dR+IGAS2G7c3PJH621cnznT+88cGPMms5/hmEtDSAqcMMCgcYGICIgQe/eiCQh1B1DPINBNWOglEwCkbBSAUAcC9BjN3sQSkAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-8624-9223","institution":"Yangzhou University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jilin","middleName":"","lastName":"Cheng","suffix":""},{"id":30517785,"identity":"e1ee33a9-d615-403c-ab8e-4a6cd9b116fa","order_by":2,"name":"Haomiao Cheng","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Haomiao","middleName":"","lastName":"Cheng","suffix":""},{"id":30517786,"identity":"a578a532-ab9d-4ccf-8e5d-aaf98c736596","order_by":3,"name":"Yi Gong","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Gong","suffix":""}],"badges":[],"createdAt":"2021-04-17 01:33:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-431229/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-431229/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":9958951,"identity":"373b178f-d45d-4205-82ef-6151237f174b","added_by":"auto","created_at":"2021-06-03 20:29:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":51043,"visible":true,"origin":"","legend":"A system of reservoirs in series\nNote: (a) a system of reservoirs in series; (b) a subsystem of a reservoir; (c) a subsystem of a reservoir and a pumping station","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1/6026e49a79a82e0437d39db6.png"},{"id":9959155,"identity":"7b521afc-5307-4efc-a631-8b36ed5380f1","added_by":"auto","created_at":"2021-06-03 20:32:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":84983,"visible":true,"origin":"","legend":"Flow chart of DDPA\nNote: d is a certain increment; the aggregation model is optimized in reverse order so that Yi+1 is a known quantity when Vi is calculated according to Equation (6); M is a positive number, which is large enough.","description":"","filename":"fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1/594ad5333f8b6e58afc6bcc7.png"},{"id":9959154,"identity":"90e2d22a-c130-47ba-8161-5398edb28289","added_by":"auto","created_at":"2021-06-03 20:32:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":134988,"visible":true,"origin":"","legend":"Location of the system\nNote: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.","description":"","filename":"fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1/fc501faa26ad0f5ac1553f16.png"},{"id":9958950,"identity":"424f1c55-310e-4579-b557-0f3cecbdf370","added_by":"auto","created_at":"2021-06-03 20:29:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":679227,"visible":true,"origin":"","legend":"The objective function values obtained with GA and PSO\n(a) Genetic algorithm\n(b) Particle swarm optimization algorithm \nNotes: Each objective function value under different combinations of parameters is the minimum value among five runs.\n\n","description":"","filename":"fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1/efc481ad32156dcf92e8b0f1.png"},{"id":13640012,"identity":"7c584e97-1bb1-447e-a2fe-590ed5d552d6","added_by":"auto","created_at":"2021-09-17 08:58:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":863593,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1_covered.pdf"},{"id":9959156,"identity":"8af2a7f7-be0c-447c-b67f-907fc5df89a7","added_by":"auto","created_at":"2021-06-03 20:32:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":860116,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-431229/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eA Decomposition and Dynamic Programming Aggregation Method for the Optimal Water Allocation of Reservoirs in Series\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-431229/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"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":"reservoirs in series, joint operation, multidimensional dynamic programming, decomposition, aggregation, meta-heuristic algorithm","lastPublishedDoi":"10.21203/rs.3.rs-431229/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-431229/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eResearch on water allocation of multiple reservoirs with the purpose of reducing water spills and improving the local runoff utilization is a matter of great concern in humid areas with uneven temporal and spatial distributions of water resources. An optimization model for a system of reservoirs in series is developed to minimize water shortages. Several constraints restrict the objective function, including available water, operation rules and water rights for replenishment of the reservoirs with water. The model features multiple dimensions with a single coupling constraint of the large-scale system. A decomposition and dynamic programming aggregation method (DDPA) is proposed; the subsystem models and the aggregation model are both solved with the classical one-dimensional dynamic programming. Compared with the conventional decomposition-coordination method, the proposed method is concise but reliable because it can directly use the results of subsystems to form the one-dimensional dynamic programming aggregation model, avoiding the iterative calculations according to the coordinating function. Compared with the meta-heuristic algorithms, the proposed method is more efficient because it is independent of any algorithm parameter. The proposed method may provide a new reference for solving similar multi-reservoir optimization models.\u003c/p\u003e","manuscriptTitle":"A Decomposition and Dynamic Programming Aggregation Method for the Optimal Water Allocation of Reservoirs in Series","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-06-03 20:29:15","doi":"10.21203/rs.3.rs-431229/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":"bb6c9fe8-933c-4393-ad3b-d1d473c425a8","owner":[],"postedDate":"June 3rd, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":4774648,"name":"Civil Engineering"}],"tags":[],"updatedAt":"2021-08-18T04:06:03+00:00","versionOfRecord":[],"versionCreatedAt":"2021-06-03 20:29:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-431229","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-431229","identity":"rs-431229","version":["v1"]},"buildId":"-HB7Z8yhvgn0wM9Nzuekk","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}