Reducing the vehicle routing problem complexity by mapping and sequencing clusters of high-density deliveries in urban regions

Reducing the vehicle routing problem complexity by mapping and sequencing clusters of high-density deliveries in urban regions | 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 Reducing the vehicle routing problem complexity by mapping and sequencing clusters of high-density deliveries in urban regions Weslley Moura, António Grilo, Paulo Novais This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7411695/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 urban logistics, a massive number of parcels need to be delivered on a daily basis to individual customer's doors. This is known as last-mile delivery, and logistics companies commonly use Vehicle Routing Problem (VRP) solutions to create intelligent route plans to support the execution of their work. Route planning can be optimized for different cost functions, such as cost-based optimization, time-based optimization, CO2 emission optimization, service-level optimization, workload-balancing optimization, and more. In this work, we propose a Kernel Density Estimation (KDE) task on past deliveries to identify central and peripheral areas. Then, a density-based clustering method is used to segment dense delivery regions within peripheral areas. These dense regions are further sequenced in order to simplify the VRP optimization space. The method was tested on real-world datasets containing thousands of deliveries from some of the largest Brazilian cities, and initial results suggest a transportation cost reduction of around 7 percent compared to other traditional user demand segmentation methods. Density-Based Clustering Kernel Density Estimation Vehicle Route Problem Last Mile Urban Logistics 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-7411695","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511230292,"identity":"2a3ad6e7-998e-4fd4-a1d7-6a001a9cfd0c","order_by":0,"name":"Weslley Moura","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYHACxgMPYMwPQMzGToSeAwkwzTNAWphJ0cLMAyYJKDc43v7gQELF4Wh+idyHn21+bZPnY2Zg/PAxB4+WM2cMDiScOZw7c0a6sXRu323DNmYGZsmZ23BrMbuRw3Agse1w7oYbaQzSuT23GYFa2Jh58Wm5//zBgcR/YC3Mvy17btsT1nKDweBAYgNYC5s0w4/biQS12J/JAfrlWHruzJ5nbJa9DbeT25gZm/H6RbL9+MMHH2qsc/vZ05hv/Phz23Z+e/PBDx/xaIGCZgjF2AYmGwiqB4I6KP2HGMWjYBSMglEw0gAAGJdZdPOCYskAAAAASUVORK5CYII=","orcid":"","institution":"University of Minho","correspondingAuthor":true,"prefix":"","firstName":"Weslley","middleName":"","lastName":"Moura","suffix":""},{"id":511230293,"identity":"932bef1c-2fa7-47b5-933f-c84457bcf103","order_by":1,"name":"António Grilo","email":"","orcid":"","institution":"Universidade Nova de Lisboa","correspondingAuthor":false,"prefix":"","firstName":"António","middleName":"","lastName":"Grilo","suffix":""},{"id":511230294,"identity":"b42667de-ba41-4091-bdc9-c9ac6939fd94","order_by":2,"name":"Paulo Novais","email":"","orcid":"","institution":"University of Minho","correspondingAuthor":false,"prefix":"","firstName":"Paulo","middleName":"","lastName":"Novais","suffix":""}],"badges":[],"createdAt":"2025-08-19 20:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7411695/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7411695/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95205247,"identity":"e1cd7f6e-2291-4c08-8d74-38517f391b2e","added_by":"auto","created_at":"2025-11-05 13:08:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":643402,"visible":true,"origin":"","legend":"","description":"","filename":"jdsaweslleymoura.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7411695/v1_covered_efcbb5b2-ded5-45af-ae46-a4b9b2bf6711.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Reducing the vehicle routing problem complexity by mapping and sequencing clusters of high-density deliveries in urban regions","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":"Density-Based Clustering, Kernel Density Estimation, Vehicle Route Problem, Last Mile Urban Logistics","lastPublishedDoi":"10.21203/rs.3.rs-7411695/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7411695/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In urban logistics, a massive number of parcels need to be delivered on a daily basis to individual customer's doors. 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