{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T17:31:42Z","timestamp":1792171902088,"version":"4.4.0"},"reference-count":33,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>With the rapid expansion of rural e-commerce, widely dispersed demand and limited road infrastructure have made conventional truck-based first-mile pickup and last-mile delivery increasingly unsustainable, creating an urgent need for alternative logistics models. We introduce a bus-assisted heterogeneous-drone scheme that treats fixed-route rural buses as mobile hubs while dispatching drones with complementary ranges and payloads for door-to-door service. A mixed-integer programming model captures bus schedules, drone heterogeneity, time-window constraints, and battery limits. To solve this model efficiently, we develop a two-stage framework\u2014bus-stop clustering followed by an Improved Black-Kite Algorithm (IBKA). IBKA incorporates four enhancements: opposition-based learning, adaptive attack probability, random boundary shrinkage, and a Differential Evolution hybrid operator. Numerical experiments on adapted Solomon instances show the proposed method outperforms Gurobi, a standard Genetic Algorithm (GA), an Eel and Grouper Optimizer (EGO), and the original Black-Kite Algorithm (BKA) in terms of cost, stability, and convergence. On average, IBKA reduces total delivery cost by 5% relative to GA, 9% relative to EGO, and 13% relative to BKA, and enhances stability by 23%, 55%, and 23%, respectively. Sensitivity tests highlight the pivotal influence of drone payload and bus headway. A real-world study on the Xunyang\u2013Tongqianguan line in Shaanxi Province further demonstrates substantial cost savings and operational advantages over both truck-only and homogeneous-drone delivery modes, underscoring the practical value of bus\u2013drone collaboration for rural logistics.<\/jats:p>","DOI":"10.1371\/journal.pone.0344897","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T17:23:42Z","timestamp":1775669022000},"page":"e0344897","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Rural first-mile pickup and last-mile delivery: A bus-assisted heterogeneous-drone model"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5651-7397","authenticated-orcid":true,"given":"Song","family":"Jin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunpeng","family":"Gong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingyu","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"pone.0344897.ref001","doi-asserted-by":"crossref","first-page":"101871","DOI":"10.1016\/j.seps.2024.101871","article-title":"A cooperative vehicle routing problem with delivery options for simultaneous pickup and delivery services in rural areas","volume":"93","author":"R Zhang","year":"2024","journal-title":"Socioecon Plan Sci"},{"key":"pone.0344897.ref002","doi-asserted-by":"crossref","first-page":"102024","DOI":"10.1016\/j.tre.2020.102024","article-title":"A cooperative rich vehicle routing problem in the last-mile logistics industry in rural areas","volume":"141","author":"F Yang","year":"2020","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"pone.0344897.ref003","unstructured":"China Internet Network Information Center (CNNIC). The 55th Statistical Report on China\u2019s Internet Development. 2025. https:\/\/cnnic.cn\/n4\/2025\/0117\/c208-11228.html"},{"key":"pone.0344897.ref004","unstructured":"Ministry of Commerce of the People\u2019s Republic of China MOFCOM. 2024 China E-Commerce Development Report. 2024. https:\/\/dzswgf.mofcom.gov.cn\/news\/5\/2025\/3\/1741656544282.html"},{"key":"pone.0344897.ref005","doi-asserted-by":"crossref","first-page":"109849","DOI":"10.1016\/j.cie.2023.109849","article-title":"Cooperative trucks and drones for rural last-mile delivery with steep roads","volume":"187","author":"J Xiao","year":"2024","journal-title":"Comput Ind Eng"},{"key":"pone.0344897.ref006","doi-asserted-by":"crossref","first-page":"8351","DOI":"10.3390\/en15228351","article-title":"Rural E-customers\u2019 preferences for last mile delivery: Evidence from Poland","volume":"15","author":"M Markowska","year":"2022","journal-title":"Energies"},{"key":"pone.0344897.ref007","doi-asserted-by":"crossref","first-page":"101665","DOI":"10.1016\/j.seps.2023.101665","article-title":"Feasibility on the integration of passenger and freight transportation in rural areas: A service mode and an optimization model","volume":"88","author":"T Yang","year":"2023","journal-title":"Socioecon Plan Sci"},{"key":"pone.0344897.ref008","doi-asserted-by":"crossref","first-page":"103069","DOI":"10.1016\/j.tre.2023.103069","article-title":"Optimization of a rural bus service integrated with e-commerce deliveries guided by a new sustainable policy in China","volume":"172","author":"D He","year":"2023","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"pone.0344897.ref009","doi-asserted-by":"crossref","first-page":"123472","DOI":"10.1016\/j.eswa.2024.123472","article-title":"Ensemble multi-objective optimization approach for heterogeneous drone delivery problem","volume":"249","author":"X Wen","year":"2024","journal-title":"Expert Systems with Applications"},{"key":"pone.0344897.ref010","first-page":"104355","article-title":"Optimization of urban\u2013rural bus services with shared passenger-freight transport: Formulation and a case study","volume":"192","author":"X Bing","year":"2025","journal-title":"Transportation Research Part A: Policy and Practice"},{"key":"pone.0344897.ref011","doi-asserted-by":"crossref","first-page":"104231","DOI":"10.1016\/j.tre.2025.104231","article-title":"To ride or to fly: Optimal freight-on-transit operations using drones","volume":"201","author":"J Osorio","year":"2025","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"6","key":"pone.0344897.ref012","doi-asserted-by":"crossref","first-page":"9312","DOI":"10.1109\/JIOT.2023.3323704","article-title":"Multidrone parcel delivery via public vehicles: a joint optimization approach","volume":"11","author":"T Deng","year":"2024","journal-title":"IEEE Internet Things J"},{"key":"pone.0344897.ref013","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.tranpol.2025.01.016","article-title":"Truck-drone joint delivery network for rural area: Optimization and implications","volume":"163","author":"J Lu","year":"2025","journal-title":"Transport Policy"},{"key":"pone.0344897.ref014","doi-asserted-by":"crossref","first-page":"100679","DOI":"10.1016\/j.rtbm.2021.100679","article-title":"Freight on urban public transportation: A systematic literature review","volume":"45","author":"R Elbert","year":"2022","journal-title":"Research in Transportation Business & Management"},{"key":"pone.0344897.ref015","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.trb.2015.07.016","article-title":"Planning and operating a shared goods and passengers on-demand rapid transit system for sustainable city-logistics","volume":"81","author":"E Fatnassi","year":"2015","journal-title":"Transportation Research Part B: Methodological"},{"key":"pone.0344897.ref016","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1287\/trsc.2017.0798","article-title":"Branch-and-price for the pickup and delivery problem with time windows and scheduled lines","volume":"52","author":"V Ghilas","year":"2018","journal-title":"Transp Sci"},{"issue":"3","key":"pone.0344897.ref017","doi-asserted-by":"crossref","first-page":"758","DOI":"10.3390\/su11030758","article-title":"Path Optimization Model for Intra-City Express Delivery in Combination with Subway System and Ground Transportation","volume":"11","author":"L Zhao","year":"2019","journal-title":"Sustainability"},{"key":"pone.0344897.ref018","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1016\/j.trpro.2024.12.247","article-title":"A conceptual framework for integrating urban freight deliveries with public transportation and crowdsourcing","volume":"82","author":"F Zingler","year":"2025","journal-title":"Transportation Research Procedia"},{"key":"pone.0344897.ref019","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.trc.2015.03.005","article-title":"The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery","volume":"54","author":"CC Murray","year":"2015","journal-title":"Transportation Research Part C: Emerging Technologies"},{"key":"pone.0344897.ref020","first-page":"655","article-title":"Routing of carrier-vehicle systems with dedicated last-stretch delivery vehicle and fixed carrier route","volume":"25","author":"MS Bin Othman","year":"2017","journal-title":"J Inf Process"},{"issue":"4","key":"pone.0344897.ref021","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1002\/net.21847","article-title":"Drone delivery from trucks: Drone scheduling for given truck routes","volume":"72","author":"N Boysen","year":"2018","journal-title":"Networks"},{"key":"pone.0344897.ref022","doi-asserted-by":"crossref","unstructured":"Lasla N, Ghazzai H, Menouar H, Massoud Y. Exploiting Land Transport to Improve the UAV\u2019s Performances for Longer Mission Coverage in Smart Cities. In: 2019 IEEE 89th Vehicular Technology Conference (VTC2019-Spring). 2019. https:\/\/doi.org\/10.1109\/vtcspring.2019.8746387","DOI":"10.1109\/VTCSpring.2019.8746387"},{"key":"pone.0344897.ref023","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1007\/s10846-020-01223-y","article-title":"A new parcel delivery system with drones and a public train","volume":"100","author":"H Huang","year":"2020","journal-title":"J Intell Robot Syst"},{"issue":"3","key":"pone.0344897.ref024","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1109\/TTE.2020.3011682","article-title":"Round trip routing for energy-efficient drone delivery based on a public transportation network","volume":"6","author":"H Huang","year":"2020","journal-title":"IEEE Trans Transp Electrific"},{"issue":"8","key":"pone.0344897.ref025","doi-asserted-by":"crossref","first-page":"4941","DOI":"10.1109\/TITS.2020.2983491","article-title":"Reliable path planning for drone delivery using a stochastic time-dependent public transportation network","volume":"22","author":"H Huang","year":"2021","journal-title":"IEEE Trans Intell Transport Syst"},{"key":"pone.0344897.ref026","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1613\/jair.1.12450","article-title":"Efficient large-scale multi-drone delivery using transit networks","volume":"70","author":"S Choudhury","year":"2021","journal-title":"J Artif Intell Res"},{"key":"pone.0344897.ref027","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s10462-024-10723-4","article-title":"Black-winged kite algorithm: A nature-inspired meta-heuristic for solving benchmark functions and engineering problems","volume":"57","author":"J Wang","year":"2024","journal-title":"Artif Intell Rev"},{"key":"pone.0344897.ref028","doi-asserted-by":"crossref","first-page":"128375","DOI":"10.1016\/j.eswa.2025.128375","article-title":"Optimal arrangement of shaded photovoltaic array using new modified black-winged kite algorithm","volume":"289","author":"A Fathy","year":"2025","journal-title":"Expert Systems with Applications"},{"key":"pone.0344897.ref029","doi-asserted-by":"crossref","first-page":"113558","DOI":"10.1016\/j.knosys.2025.113558","article-title":"A modified black-winged kite optimizer based on chaotic maps for global optimization of real-world applications","volume":"318","author":"H Mansouri","year":"2025","journal-title":"Knowledge-Based Systems"},{"issue":"6","key":"pone.0344897.ref030","doi-asserted-by":"crossref","first-page":"4049","DOI":"10.1007\/s11831-022-09730-x","article-title":"Hybrid meta-heuristic algorithms for optimal sizing of hybrid renewable energy system: a review of the state-of-the-art","volume":"29","author":"A Bouaouda","year":"2022","journal-title":"Arch Comput Methods Eng"},{"key":"pone.0344897.ref031","unstructured":"SF Express. Ark UAV logistics system overview. http:\/\/piw-mr-web.inn.sf-express.com\/uav. Accessed 2025 June 1."},{"key":"pone.0344897.ref032","doi-asserted-by":"crossref","first-page":"109179","DOI":"10.1016\/j.cie.2023.109179","article-title":"Optimal delivery route planning for a fleet of heterogeneous drones: A rescheduling-based genetic algorithm approach","volume":"179","author":"X Wang","year":"2023","journal-title":"Comput Ind Eng"},{"issue":"9","key":"pone.0344897.ref033","doi-asserted-by":"crossref","first-page":"12745","DOI":"10.1007\/s10586-024-04545-w","article-title":"Eel and grouper optimizer: a nature-inspired optimization algorithm","volume":"27","author":"A Mohammadzadeh","year":"2024","journal-title":"Cluster Comput"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0344897","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T17:23:49Z","timestamp":1775669029000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0344897"}},"subtitle":[],"editor":[{"given":"Vincent","family":"Yu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,4,8]]},"references-count":33,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4,8]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0344897","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,8]]}}}