{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T02:31:57Z","timestamp":1775788317163,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,19]],"date-time":"2018-08-19T00:00:00Z","timestamp":1534636800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Railway Corporation","award":["2015X004-C"],"award-info":[{"award-number":["2015X004-C"]}]},{"name":"National Railway Administration of the People\u2019s Republic of China","award":["KF2017-015"],"award-info":[{"award-number":["KF2017-015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Electric multiple unit (EMU) trains\u2019 high-level maintenance planning is a discrete problem in mathematics. The high-level maintenance process of the EMU trains consumes plenty of time. When the process is undertaken during peak periods of the passenger flow, the transportation demand may not be fully satisfied due to the insufficient supply of trains. In contrast, if the process is undergone in advance, extra costs will be incurred. Based on the practical requirements of high-level maintenance, a 0\u20131 programming model is proposed. To simplify the description of the model, candidate sets of delivery dates, i.e., time windows, are generated according to the historical data and maintenance regulations. The constraints of the model include maintenance regulations, the passenger transportation demand, and capacities of workshop. The objective function is to minimize the mileage losses of all EMU trains. Moreover, a modified particle swarm algorithm is developed for solving the problem. Finally, a real-world case study of Shanghai Railway is conducted to demonstrate the proposed method. Computational results indicate that the (approximate) optimal solution can be obtained successfully by our method and the proposed method significantly reduces the solution time to 500 s.<\/jats:p>","DOI":"10.3390\/sym10080349","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T11:23:06Z","timestamp":1534764186000},"page":"349","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Optimizing the High-Level Maintenance Planning Problem of the Electric Multiple Unit Train Using a Modified Particle Swarm Optimization Algorithm"],"prefix":"10.3390","volume":"10","author":[{"given":"Jianping","family":"Wu","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9286-0873","authenticated-orcid":false,"given":"Boliang","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Computing Technology, China Academy of Railway Sciences, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Vehicles, China Railway Shanghai Bureau Group Co., Ltd., Shanghai 200071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongkai","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Computing Technology, China Academy of Railway Sciences, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,19]]},"reference":[{"key":"ref_1","unstructured":"China Railway (2013). 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