A Two-stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment under Multiple Uncertainty within Urban Agglomerations

A Two-stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment under Multiple Uncertainty within Urban Agglomerations | 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 Two-stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment under Multiple Uncertainty within Urban Agglomerations Yingzi Feng, Honglu Cao, Jiandong Zhao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6510003/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 In order to maximize passenger travel satisfaction, this paper proposes a two-stage model for intercity multimodal timetable coordination optimization under uncertainty. At the first stage, a robust spatio-temporal graph is built to allocate intermodal passenger flows in order to determine passengers' route selection results to minimize the total travel cost. At the same time, explicit capacity constraints and transfer behaviors are considered in order to be more realistic. In addition, passengers can take multiple transportation modes (High-speed Rail, Ordinary Rail, Motor Car and Coach) in a single trip. Then, the results of the first stage are substituted into the second stage of the interval multi-objective timetable optimization model to obtain departure times and parking patterns based on uncertain parking and travel times. It is able to achieve the maximum reduction of passenger travelling time and waiting time within the minimum timetable adjustment, which further improve the integration level of transportation services. To ensure the diversity and convergence of model solving on the basis of retaining uncertain information, we propose an integrated algorithm PSO-IMOEA-MC involving Particle Swarm Optimization algorithm (PSO) and Interval Many-objective Evolutionary Algorithm combined with Monte Carlo (IMOEA-MC). Finally, the effectiveness of the proposed two-stage model and algorithm is verified by taking the intercity networks of Beijing-Zhangjiakou, Chengdu-Chongqing, and Guangzhou-Qingyuan city clusters as examples. The results demonstrate the performance of the method in finding high-level solutions that retain more uncertainty. Two-stage Uncertainty Timetable optimization Multimodal transportation Passenger flow allocation Many-objective evolutionary algorithm 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. 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-6510003","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":472966287,"identity":"7f2040ea-29e1-464f-9e2b-9bda8f516b1d","order_by":0,"name":"Yingzi Feng","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yingzi","middleName":"","lastName":"Feng","suffix":""},{"id":472966288,"identity":"7a41fc19-c764-401d-9b2f-3254c6240d17","order_by":1,"name":"Honglu Cao","email":"","orcid":"","institution":"Beijing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Honglu","middleName":"","lastName":"Cao","suffix":""},{"id":472966289,"identity":"b4c95d42-ead4-48e6-8948-d27f3bb24619","order_by":2,"name":"Jiandong Zhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYDACCRBms0lgbADx2IjXkpbA2EaSFga2wwkQ1cRokZ/d/PCBRdn5POb5PQYMH8oOM/DPbsCvhXHOMWMDiXO3ixnbeAwYZ5w7zCBx5wB+LcwSCWYSkm23ExuBWph52w4zGEgk4NfCJpH+DajlHETLX2K08EjkgGw5ANHCSIwWCYmcYqBfkoF+SSs42HMunUfiBgEt8jPSNz6WKLPLM2w+vPHBjzJrOf4ZBLSAADMobgwbGBgOgFxKWD0QMH4AWUeU0lEwCkbBKBiRAAAjFT5Y1I3pugAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-8402-0380","institution":"Beijing Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Jiandong","middleName":"","lastName":"Zhao","suffix":""}],"badges":[],"createdAt":"2025-04-23 07:36:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6510003/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6510003/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89609453,"identity":"337f09d0-59c6-45e7-8ff3-e0bc5b16852a","added_by":"auto","created_at":"2025-08-21 22:32:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1349893,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6510003/v1_covered_7aee407d-56a0-4bb0-9930-f22f8b10b44e.pdf"}],"financialInterests":"","formattedTitle":"A Two-stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment under Multiple Uncertainty within Urban Agglomerations","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":"Two-stage, Uncertainty, Timetable optimization, Multimodal transportation, Passenger flow allocation, Many-objective evolutionary algorithm","lastPublishedDoi":"10.21203/rs.3.rs-6510003/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6510003/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In order to maximize passenger travel satisfaction, this paper proposes a two-stage model for intercity multimodal timetable coordination optimization under uncertainty. At the first stage, a robust spatio-temporal graph is built to allocate intermodal passenger flows in order to determine passengers' route selection results to minimize the total travel cost. At the same time, explicit capacity constraints and transfer behaviors are considered in order to be more realistic. In addition, passengers can take multiple transportation modes (High-speed Rail, Ordinary Rail, Motor Car and Coach) in a single trip. Then, the results of the first stage are substituted into the second stage of the interval multi-objective timetable optimization model to obtain departure times and parking patterns based on uncertain parking and travel times. It is able to achieve the maximum reduction of passenger travelling time and waiting time within the minimum timetable adjustment, which further improve the integration level of transportation services. To ensure the diversity and convergence of model solving on the basis of retaining uncertain information, we propose an integrated algorithm PSO-IMOEA-MC involving Particle Swarm Optimization algorithm (PSO) and Interval Many-objective Evolutionary Algorithm combined with Monte Carlo (IMOEA-MC). Finally, the effectiveness of the proposed two-stage model and algorithm is verified by taking the intercity networks of Beijing-Zhangjiakou, Chengdu-Chongqing, and Guangzhou-Qingyuan city clusters as examples. The results demonstrate the performance of the method in finding high-level solutions that retain more uncertainty.","manuscriptTitle":"A Two-stage Model for Optimizing Intercity Multimodal Timetables and Passenger Flow Assignment under Multiple Uncertainty within Urban Agglomerations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-20 03:12:08","doi":"10.21203/rs.3.rs-6510003/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":"a3e1077e-436d-413d-a980-427a87e3e5d0","owner":[],"postedDate":"June 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-21T22:24:32+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-20 03:12:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6510003","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6510003","identity":"rs-6510003","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}