An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem

An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem | 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 Article An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem Chenxin Dong, Hui Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7373477/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 16 You are reading this latest preprint version Abstract The coordinated optimization of production and transportation ensures that enterprises can lower the total cost of the supply chain while providing high-quality products to consumers, thereby increasing company profits. The integrated distributed no-wait flow-shop scheduling and vehicle routing problem (DNFSVRP) is considered for a make-to-order (MTO) manufacturer. A mathematical model with the objective of minimizing the maximum delivery time is established. For the DNFSVRP, three vectors are designed to represent the solution encoding and an improved artificial bee colony (IABC) algorithm with problem-specific knowledge is proposed. Firstly, an ECT-2-machine method is introduced to generate high-quality initial solutions. Secondly, in the employed bee phase, eight neighborhood structures are designed to expand the search space. Moreover, in the onlooker bee phase, a path relinking strategy is adopted to fully utilize the information of the best solution and accelerate the convergence speed of the algorithm. Furthermore, in the scout bee phase, a destrucction and reconstruction operation based on problem-specific knowledge is designed to effectively balance the breadth and depth of the search. Finally, five sets of comparative experiments are conducted, and the results demonstrate the effectiveness of the IABC algorithm in addressing the DNFSVRP. Physical sciences/Engineering Physical sciences/Mathematics and computing make-to-order manufacturer vehicle routing problem problem-specific destruction and reconstruction strategy path-relinking strategy Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 16 Dec, 2025 Reviews received at journal 11 Dec, 2025 Reviewers agreed at journal 08 Dec, 2025 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 07 Dec, 2025 Reviewers agreed at journal 07 Dec, 2025 Reviewers agreed at journal 05 Dec, 2025 Reviewers agreed at journal 05 Dec, 2025 Reviewers agreed at journal 05 Dec, 2025 Reviewers agreed at journal 05 Dec, 2025 Reviewers agreed at journal 05 Dec, 2025 Reviewers invited by journal 05 Dec, 2025 Editor assigned by journal 05 Dec, 2025 Editor invited by journal 04 Dec, 2025 Submission checks completed at journal 08 Sep, 2025 First submitted to journal 08 Sep, 2025 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-7373477","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":556913311,"identity":"8777c54b-fda2-4436-b647-c258ed957c0b","order_by":0,"name":"Chenxin Dong","email":"","orcid":"","institution":"Qingdao Hengxing University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Chenxin","middleName":"","lastName":"Dong","suffix":""},{"id":556913312,"identity":"89c45865-0b2c-440f-9ce3-020c76f7e177","order_by":1,"name":"Hui Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYBACfv7mww8SKiR4GNubD0DFEvBrkZxxLM3gwxkbOeaeYzClBLQYHMgxkJzZlmbMPiPHgDgtDAcOGBjznDmc2Ntz5pt04Y7DDPzsQL0/d+DWwdjckPCYp+Jw4sz23m3SM88cZpDseWPA2HsGtxZmoDVgWzb2nN0mzdt2mMHgRo4BM2Mbbi1sDIkNIJWJ+2/kPANrsSekhYchmQHsfcYZOWwQWyQIaJGQOMYGDmTGnmPG1rxt6TwSZ54VHOzFo8X+fP9nWFQ+vM3bZi3H35688cFPPFqQAYsE2KVAcIA4DcDQ+0CsylEwCkbBKBhZAAButFkVT7CSrQAAAABJRU5ErkJggg==","orcid":"","institution":"Yunnan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Hui","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-08-14 11:38:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7373477/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7373477/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-34976-3","type":"published","date":"2026-01-05T15:58:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97897214,"identity":"0c171d5d-7408-4b2d-bc97-c4cea6c308f5","added_by":"auto","created_at":"2025-12-10 15:37:34","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1117679,"visible":true,"origin":"","legend":"","description":"","filename":"SRDongsubmit.docx","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/2884901832c63b1ee5618a48.docx"},{"id":97757677,"identity":"009b3f18-401a-455b-8af9-0af89a057533","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4121,"visible":true,"origin":"","legend":"","description":"","filename":"3d2de3eb204942a5a33b8bbc0c99c62d.json","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/af6f0f7a492f74cac1848ede.json"},{"id":97897034,"identity":"44aa8f59-1f75-452b-a884-8db8bc60ee19","added_by":"auto","created_at":"2025-12-10 15:37:22","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":153403,"visible":true,"origin":"","legend":"","description":"","filename":"3d2de3eb204942a5a33b8bbc0c99c62d1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/d8006ce74943e93b95f2a4b9.xml"},{"id":97757680,"identity":"a2ad62f1-a96c-4fdf-91c7-91ce55dac4b8","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":563176,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/ea18c23042d714486f297698.emf"},{"id":97757678,"identity":"6dd97258-55bf-4aa1-9a99-6d7265e04b5a","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":79764,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/5a279ddbdac2cad437ca5dfc.emf"},{"id":97896533,"identity":"487fa56b-5d9c-4aff-801e-7938df0ff452","added_by":"auto","created_at":"2025-12-10 15:36:44","extension":"emf","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":79680,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/ca301a25214b16e2962c0094.emf"},{"id":97897819,"identity":"372cde7f-1b24-4c53-a08a-d0a804e2910d","added_by":"auto","created_at":"2025-12-10 15:38:18","extension":"emf","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":261676,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/1aa1109735ed087995c0875f.emf"},{"id":97896621,"identity":"042f4575-0a08-4853-b636-0101f3f09ad7","added_by":"auto","created_at":"2025-12-10 15:36:48","extension":"emf","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64996,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/4e1401e33fff627c61adbbad.emf"},{"id":97757690,"identity":"225f654a-f72c-418c-baa1-6d2a08fbdd6c","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64008,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/58db8362256ee4394f78fd33.emf"},{"id":97757683,"identity":"32a776c3-4e3d-4dcd-a354-392769c106ff","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64996,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/5aad857a454456708ef51d0f.emf"},{"id":97757692,"identity":"599c05e1-1942-49f9-aacc-deba862bd41b","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":66164,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/8327148a05d89e158dd3daf9.emf"},{"id":97757686,"identity":"5b72841b-e00f-4e45-9a1a-fad4c1d58a93","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":62940,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/d6253380dbd56a4e86de8d72.emf"},{"id":97757688,"identity":"2c18b35a-a990-4691-8b72-2edfe8987c11","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64044,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage18.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/3de2dd43a2f2c929aa84553c.emf"},{"id":97757687,"identity":"2d9194d8-15e8-488a-af2c-4441d3f08026","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":62544,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage19.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/84707a49470585bae30b077c.emf"},{"id":97757695,"identity":"acc639cd-ffc3-458f-9fca-bdb51dbd047a","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":218212,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/2bd9a61d0f764a21752772cf.emf"},{"id":97757694,"identity":"3f5049da-bbba-45fc-8231-a8b085030276","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":75728,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage20.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/e2dd0d9953fd802e47de32f5.emf"},{"id":97757711,"identity":"1216a372-d0b8-4527-b727-c65aaa6c7c1c","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"emf","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":118188,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage21.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/8a3963bfc5140fcf954266e5.emf"},{"id":97757701,"identity":"38fa779f-dcca-462a-8e91-f5f83de2c637","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"emf","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":81344,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage22.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/70de1b88bd1cd2f7efb6d27b.emf"},{"id":97757698,"identity":"2ae7713c-a336-4755-b68a-5c4953e94732","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"emf","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59112,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/9f385a28df265490be029752.emf"},{"id":97894759,"identity":"155440c2-fdc8-4978-9d44-eb1836c2e6ff","added_by":"auto","created_at":"2025-12-10 15:33:00","extension":"emf","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":53472,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/8f56e6ea853ba10072e487a4.emf"},{"id":97757693,"identity":"8d2fca12-f6d2-4d34-97ca-dbcf8d267852","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"emf","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55448,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/eb07016e4b297748b27b3f03.emf"},{"id":97894920,"identity":"85d93ad4-55dd-419d-8916-9b1e280ae5d1","added_by":"auto","created_at":"2025-12-10 15:33:14","extension":"emf","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":83440,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/8545cfca2d9d318378a906e4.emf"},{"id":97757721,"identity":"eaef896a-e404-48b4-aaaa-e26a4b4e5fd7","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"emf","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55332,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/6aa93eac23c3bee50dab0879.emf"},{"id":97897016,"identity":"bd61610e-ee7d-4f1c-a7cf-b50241bb70c9","added_by":"auto","created_at":"2025-12-10 15:37:20","extension":"emf","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59812,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/a195d46c38474949715375de.emf"},{"id":97757720,"identity":"af682a67-72d4-4ab5-b0cc-57bf24e92544","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"emf","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":58892,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.emf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/8275abaa15041f96c51e862f.emf"},{"id":97757705,"identity":"6c4d0b9e-84f0-414e-8c14-868fce4ef3e0","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":30068,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/ee0a243531fbc8077d1729b4.png"},{"id":97757710,"identity":"1b0a947c-7473-448a-a481-9f007a61274e","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9905,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/78a354b02b8d7d1b547663cd.png"},{"id":97757704,"identity":"c72b6633-31a3-4aca-bcd1-1493536fbb47","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9909,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/55f33c877c48d0a0cb57a037.png"},{"id":97757716,"identity":"d58ddb2f-9a29-41a5-ab0b-fcfb631f4de4","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":17456,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/4b474dcb8afecdb30df4bbd7.png"},{"id":97757709,"identity":"102660bf-f4b2-4c53-a8e4-cd3f728e7d13","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7966,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/23a608d2beaa3761b1c5a241.png"},{"id":97757697,"identity":"656f5381-6362-4c45-a1bd-0e108483ddf4","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3223,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/4d326939bf3e3d33e9c5ac65.png"},{"id":97896638,"identity":"4fa7d98e-371f-48fd-bdcb-40529e79c974","added_by":"auto","created_at":"2025-12-10 15:36:49","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8953,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/d428e3f4758999c45b978729.png"},{"id":97894907,"identity":"39f5599d-8b45-4456-a3c3-a48510d55c48","added_by":"auto","created_at":"2025-12-10 15:33:12","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3450,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/a525329d89fc42fbd5b48e90.png"},{"id":97757717,"identity":"cfbd9165-90f0-4c81-b782-7e0f9b36142f","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9732,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/b7a79fc040649811c37b04e3.png"},{"id":97757719,"identity":"453c01d8-2c6e-4042-87ec-ea380defcd73","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3292,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/967e002489c1ea3edbd4e6aa.png"},{"id":97894811,"identity":"1fba403e-f519-4f77-8042-601bcbaf6197","added_by":"auto","created_at":"2025-12-10 15:33:03","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":14701,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/0f3c1f61fc853d7d0081c6aa.png"},{"id":97757703,"identity":"5bc4f151-b9a5-43d5-9194-da07ed3a302e","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":31266,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/1620e17f426a65ae380bda8e.png"},{"id":97757713,"identity":"f250cdc1-dbb6-4a8c-ac36-63124834272a","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3533,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/c4c6f78e6a8b04c4b1dedc40.png"},{"id":97757696,"identity":"4f1a91cd-5d53-47a2-a37c-560e781ebaea","added_by":"auto","created_at":"2025-12-09 04:45:23","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8799,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage21.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/97ebe1c01cb3bc24e88caf0e.png"},{"id":97897291,"identity":"a8c2d663-b434-4000-aecf-f1a996be4195","added_by":"auto","created_at":"2025-12-10 15:37:43","extension":"png","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4412,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage22.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/80b17394c94a5215c853b691.png"},{"id":97757700,"identity":"c5c9c7dd-1e75-47f2-a6bb-df4c11f54b71","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":21437,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/a41a2eb9e95a8861c1f02022.png"},{"id":97897023,"identity":"63d9730b-d34a-4cb1-a96b-be058276c11c","added_by":"auto","created_at":"2025-12-10 15:37:21","extension":"png","order_by":41,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5145,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/d326fbc63504b90d0fa6dfa1.png"},{"id":97757707,"identity":"5babfa1b-2b14-432f-b722-d05ab004a15a","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":42,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5125,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/793b84e5797a427288f788b9.png"},{"id":97757724,"identity":"beddba84-7c4f-4d2d-b478-8e3c98966291","added_by":"auto","created_at":"2025-12-09 04:45:25","extension":"png","order_by":43,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9571,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/701df22214380e4bfbc666d0.png"},{"id":97757723,"identity":"27af5393-6933-4c45-8a6a-0876cb0bbcfd","added_by":"auto","created_at":"2025-12-09 04:45:25","extension":"png","order_by":44,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5108,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/e8321365b3a476f2fc26fc63.png"},{"id":97757706,"identity":"18cb9b94-e4c6-45c1-b80e-c864241ad8bd","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":45,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":7036,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/4cf31da0025c7cea7dded9e3.png"},{"id":97757702,"identity":"998d9969-b3b7-43d2-b398-d6f02146196a","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"png","order_by":46,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":8509,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/bde6bc65f609492bfc558dde.png"},{"id":97757712,"identity":"bace70d7-b328-4b80-8135-b0b426b518f7","added_by":"auto","created_at":"2025-12-09 04:45:24","extension":"xml","order_by":47,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":151698,"visible":true,"origin":"","legend":"","description":"","filename":"3d2de3eb204942a5a33b8bbc0c99c62d1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/33eaee286a7f33b4c766c055.xml"},{"id":97896489,"identity":"cbeb6cc1-79f4-4ebf-a8c2-f3595bf39709","added_by":"auto","created_at":"2025-12-10 15:36:38","extension":"html","order_by":48,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":169029,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1/52a0c613c5219699e6902bb1.html"},{"id":100069617,"identity":"bfbcb771-4855-4d24-b5e1-e461a613e7b9","added_by":"auto","created_at":"2026-01-12 16:15:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":735080,"visible":true,"origin":"","legend":"","description":"","filename":"SRDongsubmit.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7373477/v1_covered_c4d5097c-bbb8-46fd-b48f-96e386d10f23.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"make-to-order manufacturer, vehicle routing problem, problem-specific destruction and reconstruction strategy, path-relinking strategy","lastPublishedDoi":"10.21203/rs.3.rs-7373477/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7373477/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe coordinated optimization of production and transportation ensures that enterprises can lower the total cost of the supply chain while providing high-quality products to consumers, thereby increasing company profits. The integrated distributed no-wait flow-shop scheduling and vehicle routing problem (DNFSVRP) is considered for a make-to-order (MTO) manufacturer. A mathematical model with the objective of minimizing the maximum delivery time is established. For the DNFSVRP, three vectors are designed to represent the solution encoding and an improved artificial bee colony (IABC) algorithm with problem-specific knowledge is proposed. Firstly, an ECT-2-machine method is introduced to generate high-quality initial solutions. Secondly, in the employed bee phase, eight neighborhood structures are designed to expand the search space. Moreover, in the onlooker bee phase, a path relinking strategy is adopted to fully utilize the information of the best solution and accelerate the convergence speed of the algorithm. Furthermore, in the scout bee phase, a destrucction and reconstruction operation based on problem-specific knowledge is designed to effectively balance the breadth and depth of the search. Finally, five sets of comparative experiments are conducted, and the results demonstrate the effectiveness of the IABC algorithm in addressing the DNFSVRP.\u003c/p\u003e","manuscriptTitle":"An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-09 04:45:18","doi":"10.21203/rs.3.rs-7373477/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-16T12:42:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-11T09:58:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"250265493784853186162115768280789797490","date":"2025-12-08T10:40:33+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-07T17:10:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"112341149641627509334830477281453671180","date":"2025-12-07T12:43:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"241061586182011470793971376906078888428","date":"2025-12-07T09:57:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"139754028509439736755741966592802994947","date":"2025-12-06T03:12:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"190983639522502984393061722232008605211","date":"2025-12-05T11:48:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"214191993987519981229805832155863555161","date":"2025-12-05T10:35:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48730553420727878759116936245297688092","date":"2025-12-05T10:35:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"75542055781401813655836053275058487663","date":"2025-12-05T09:59:31+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-05T09:55:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-05T09:54:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-04T16:17:14+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-08T13:27:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-08T09:29:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"73ca979a-439d-4498-b5ae-be69d0aa15e5","owner":[],"postedDate":"December 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":59270125,"name":"Physical sciences/Engineering"},{"id":59270126,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-01-12T16:07:52+00:00","versionOfRecord":{"articleIdentity":"rs-7373477","link":"https://doi.org/10.1038/s41598-025-34976-3","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-05 15:58:04","publishedOnDateReadable":"January 5th, 2026"},"versionCreatedAt":"2025-12-09 04:45:18","video":"","vorDoi":"10.1038/s41598-025-34976-3","vorDoiUrl":"https://doi.org/10.1038/s41598-025-34976-3","workflowStages":[]},"version":"v1","identity":"rs-7373477","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7373477","identity":"rs-7373477","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}