{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T01:00:06Z","timestamp":1779152406364,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:00:00Z","timestamp":1744156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62106098"],"award-info":[{"award-number":["62106098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272210"],"award-info":[{"award-number":["62272210"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["B240207057.423180"],"award-info":[{"award-number":["B240207057.423180"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2020B121201001"],"award-info":[{"award-number":["2020B121201001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62106098"],"award-info":[{"award-number":["62106098"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62272210"],"award-info":[{"award-number":["62272210"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["B240207057.423180"],"award-info":[{"award-number":["B240207057.423180"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2020B121201001"],"award-info":[{"award-number":["2020B121201001"]}]},{"name":"Guangdong Provincial Key Laboratory","award":["62106098"],"award-info":[{"award-number":["62106098"]}]},{"name":"Guangdong Provincial Key Laboratory","award":["62272210"],"award-info":[{"award-number":["62272210"]}]},{"name":"Guangdong Provincial Key Laboratory","award":["B240207057.423180"],"award-info":[{"award-number":["B240207057.423180"]}]},{"name":"Guangdong Provincial Key Laboratory","award":["2020B121201001"],"award-info":[{"award-number":["2020B121201001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>With the escalating environmental crisis, electric vehicles have emerged as a key solution for emission reductions in logistics due to their low-carbon attributes, prompting significant attention and extensive research on the electric vehicle routing problem (EVRP). However, existing studies often overlook charging infrastructure (CI) capacity constraints and fail to fully exploit the synergistic potential of heterogeneous energy replenishment infrastructures (HERIs). This paper addresses the EVRP with HERIs under various capacity constraints (EVRP-HERI-CC), proposing a mixed-integer programming (MIP) model and a hybrid ant colony optimization (HACO) algorithm integrated with a variable neighborhood search (VNS) mechanism. Extensive numerical experiments demonstrate HACO\u2019s effective integration of problem-specific characteristics. The algorithm resolves charging conflicts via dynamic rescheduling while optimizing charging-battery swapping decisions under an on-demand energy replenishment strategy, achieving global cost minimization. Through small-scale instance experiments, we have verified the computational complexity of the problem and demonstrated HACO\u2019s superior performance compared to the Gurobi solver. Furthermore, comparative studies with other advanced heuristic algorithms confirm HACO\u2019s effectiveness in solving the EVRP-HERI-CC. Sensitivity analysis reveals that appropriate CI capacity configurations achieve economic efficiency while maximizing resource utilization, further validating the engineering value of HERI networks.<\/jats:p>","DOI":"10.3390\/a18040216","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T12:05:56Z","timestamp":1744200356000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Electric Vehicle Routing Problem with Heterogeneous Energy Replenishment Infrastructures Under Capacity Constraints"],"prefix":"10.3390","volume":"18","author":[{"given":"Bowen","family":"Song","sequence":"first","affiliation":[{"name":"Department of Management Science and Information Management, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Management Science and Information Management, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"key":"ref_1","unstructured":"European Commission (2019). 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