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2021 May 19;8(3):370–389. doi: 10.1007/s42524-021-0157-1

A review on the electric vehicle routing problems: Variants and algorithms

Hu Qin 1, Xinxin Su 1,2, Teng Ren 3, Zhixing Luo 4,✉
PMCID: PMC8131175

Abstract

Over the past decade, electric vehicles (EVs) have been considered in a growing number of models and methods for vehicle routing problems (VRPs). This study presents a comprehensive survey of EV routing problems and their many variants. We only consider the problems in which each vehicle may visit multiple vertices and be recharged during the trip. The related literature can be roughly divided into nine classes: Electric traveling salesman problem, green VRP, electric VRP, mixed electric VRP, electric location routing problem, hybrid electric VRP, electric dial-a-ride problem, electric two-echelon VRP, and electric pickup and delivery problem. For each of these nine classes, we focus on reviewing the settings of problem variants and the algorithms used to obtain their solutions.

Keywords: electric vehicles, routing, recharging stations, exact algorithms, metaheuristics

Acknowledgements

This study was written in early 2020, when the first author was infected with COVID-19. Fortunately, he received timely free treatment and recovered in time to submit this review paper. We are grateful to the Chinese government and all the people who supported the first author.

Footnotes

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 71971090, 71571077, and 71531009).

References

  1. Affi M, Derbel H, Jarboui B. Variable neighborhood search algorithm for the green vehicle routing problem. International Journal of Industrial Engineering Computations. 2018;9(2):195–204. doi: 10.5267/j.ijiec.2017.6.004. [DOI] [Google Scholar]
  2. Afroditi A, Boile M, Theofanis S, Sdoukopoulos E, Margaritis D. Electric vehicle routing problem with industry constraints: Trends and insights for future research. Transportation Research Procedia. 2014;3:452–459. doi: 10.1016/j.trpro.2014.10.026. [DOI] [Google Scholar]
  3. Al-Kanj L, Nascimento J, Powell W B. Approximate dynamic programming for planning a ride-hailing system using autonomous fleets of electric vehicles. European Journal of Operational Research. 2020;284(3):1088–1106. doi: 10.1016/j.ejor.2020.01.033. [DOI] [Google Scholar]
  4. Andelmin J, Bartolini E. An exact algorithm for the green vehicle routing problem. Transportation Science. 2017;51(4):1288–1303. doi: 10.1287/trsc.2016.0734. [DOI] [Google Scholar]
  5. Andelmin J, Bartolini E. A multi-start local search heuristic for the green vehicle routing problem based on a multigraph reformulation. Computers & Operations Research. 2019;109:43–63. doi: 10.1016/j.cor.2019.04.018. [DOI] [Google Scholar]
  6. Archetti C, Speranza M G. Vehicle routing problems with split deliveries. International Transactions in Operational Research. 2012;19(1–2):3–22. doi: 10.1111/j.1475-3995.2011.00811.x. [DOI] [Google Scholar]
  7. Baldacci R, Christofides N, Mingozzi A. An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Mathematical Programming. 2008;115(2):351–385. doi: 10.1007/s10107-007-0178-5. [DOI] [Google Scholar]
  8. Baldacci R, Mingozzi A, Roberti R. New route relaxation and pricing strategies for the vehicle routing problem. Operations Research. 2011;59(5):1269–1283. doi: 10.1287/opre.1110.0975. [DOI] [Google Scholar]
  9. Baldacci R, Mingozzi A, Roberti R, Wolfler Calvo R. An exact algorithm for the two-echelon capacitated vehicle routing problem. Operations Research. 2013;61(2):298–314. doi: 10.1287/opre.1120.1153. [DOI] [Google Scholar]
  10. Beasley J E. Route first-Cluster second methods for vehicle routing. Omega. 1983;11(4):403–408. doi: 10.1016/0305-0483(83)90033-6. [DOI] [Google Scholar]
  11. Bongiovanni C, Kaspi M, Geroliminis N. The electric autonomous dial-a-ride problem. Transportation Research Part B: Methodological. 2019;122:436–456. doi: 10.1016/j.trb.2019.03.004. [DOI] [Google Scholar]
  12. Braekers K, Ramaekers K, van Nieuwenhuyse I. The vehicle routing problem: State-of-the-art classification and review. Computers & Industrial Engineering. 2016;99:300–313. doi: 10.1016/j.cie.2015.12.007. [DOI] [Google Scholar]
  13. Bräysy O, Gendreau M. Vehicle routing problem with time windows, part I: Route construction and local search algorithms. Transportation Science. 2005;39(1):104–118. doi: 10.1287/trsc.1030.0056. [DOI] [Google Scholar]
  14. Bräysy O, Gendreau M. Vehicle routing problem with time windows, part II: Metaheuristics. Transportation Science. 2005;39(1):119–139. doi: 10.1287/trsc.1030.0057. [DOI] [Google Scholar]
  15. Breunig U, Baldacci R, Hartl R F, Vidal T. The electric two-echelon vehicle routing problem. Computers & Operations Research. 2019;103:198–210. doi: 10.1016/j.cor.2018.11.005. [DOI] [Google Scholar]
  16. Campbell A M, Wilson J H. Forty years of periodic vehicle routing. Networks. 2014;63(1):2–15. doi: 10.1002/net.21527. [DOI] [Google Scholar]
  17. Clarke G, Wright J W. Scheduling of vehicles from a central depot to a number of delivery points. Operations Research. 1964;12(4):568–581. doi: 10.1287/opre.12.4.568. [DOI] [Google Scholar]
  18. Corberán A, Prins C. Recent results on Arc Routing Problems: An annotated bibliography. Networks. 2010;56(1):50–69. [Google Scholar]
  19. Cordeau J F, Laporte G. The dial-a-ride problem: Models and algorithms. Annals of Operations Research. 2007;153(1):29–46. doi: 10.1007/s10479-007-0170-8. [DOI] [Google Scholar]
  20. Cortés-Murcia D L, Prodhon C, Murat Afsar H. The electric vehicle routing problem with time windows, partial recharges and satellite customers. Transportation Research Part E: Logistics and Transportation Review. 2019;130:184–206. doi: 10.1016/j.tre.2019.08.015. [DOI] [Google Scholar]
  21. Crevier B, Cordeau J F, Laporte G. The multi-depot vehicle routing problem with inter-depot routes. European Journal of Operational Research. 2007;176(2):756–773. doi: 10.1016/j.ejor.2005.08.015. [DOI] [Google Scholar]
  22. da Silva R F, Urrutia S. A general VNS heuristic for the traveling salesman problem with time windows. Discrete Optimization. 2010;7(4):203–211. doi: 10.1016/j.disopt.2010.04.002. [DOI] [Google Scholar]
  23. Dantzig G B, Ramser J H. The truck dispatching problem. Management Science. 1959;6(1):80–91. doi: 10.1287/mnsc.6.1.80. [DOI] [Google Scholar]
  24. Dascioglu B G, Tuzkaya G. A literature review for hybrid vehicle routing problem. In: Calisir F, Cevikcan E, Camgoz Akdag H, editors. Industrial Engineering in the Big Data Era. Cham: Springer; 2019. pp. 249–257. [Google Scholar]
  25. Desaulniers G. Branch-and-price-and-cut for the split-delivery vehicle routing problem with time windows. Operations Research. 2010;58(1):179–192. doi: 10.1287/opre.1090.0713. [DOI] [Google Scholar]
  26. Desaulniers G, Errico F, Irnich S, Schneider M. Exact algorithms for electric vehicle-routing problems with time windows. Operations Research. 2016;64(6):1388–1405. doi: 10.1287/opre.2016.1535. [DOI] [Google Scholar]
  27. Doppstadt C, Koberstein A, Vigo D. The hybrid electric vehicle-traveling salesman problem. European Journal of Operational Research. 2016;253(3):825–842. doi: 10.1016/j.ejor.2016.03.006. [DOI] [Google Scholar]
  28. Dror M (2000). Arc Routing: Theory, Solutions and Applications. Springer
  29. Eksioglu B, Vural A V, Reisman A. The vehicle routing problem: A taxonomic review. Computers & Industrial Engineering. 2009;57(4):1472–1483. doi: 10.1016/j.cie.2009.05.009. [DOI] [Google Scholar]
  30. Environmental Protection Agency (2018). Inventory of US greenhouse gas emissions and sinks: 1990–2016. Available at: http://epa.gov/sites/production/files/2018-01/documents/2018_complete_report.pdf
  31. Erdelić T, Carić T. Journal of Advanced Transportation. 2019. A survey on the electric vehicle routing problem: Variants and solution approaches; p. 5075671. [Google Scholar]
  32. Erdoğan S, Miller-Hooks E. A green vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review. 2012;48(1):100–114. doi: 10.1016/j.tre.2011.08.001. [DOI] [Google Scholar]
  33. Escobar J W, Linfati R, Baldoquin M G, Toth P. A granular variable tabu neighborhood search for the capacitated location-routing problem. Transportation Research Part B: Methodological. 2014;67:344–356. doi: 10.1016/j.trb.2014.05.014. [DOI] [Google Scholar]
  34. Ester M, Kriegel H P, Sander J, Xu X (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining. AAAI Press, 96: 226–231
  35. Eusuff M, Lansey K, Pasha F. Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization. Engineering Optimization. 2006;38(2):129–154. doi: 10.1080/03052150500384759. [DOI] [Google Scholar]
  36. Felipe A, Ortuño M T, Righini G, Tirado G. A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges. Transportation Research Part E: Logistics and Transportation Review. 2014;71:111–128. doi: 10.1016/j.tre.2014.09.003. [DOI] [Google Scholar]
  37. Froger A, Mendoza J E, Jabali O, Laporte G. Improved formulations and algorithmic components for the electric vehicle routing problem with nonlinear charging functions. Computers & Operations Research. 2019;104:256–294. doi: 10.1016/j.cor.2018.12.013. [DOI] [Google Scholar]
  38. Goeke D. Granular tabu search for the pickup and delivery problem with time windows and electric vehicles. European Journal of Operational Research. 2019;278(3):821–836. doi: 10.1016/j.ejor.2019.05.010. [DOI] [Google Scholar]
  39. Goeke D, Schneider M. Routing a mixed fleet of electric and conventional vehicles. European Journal of Operational Research. 2015;245(1):81–99. doi: 10.1016/j.ejor.2015.01.049. [DOI] [Google Scholar]
  40. Golden B L, Raghavan S, Wasil E A. The Vehicle Routing Problem: Latest Advances and New Challenges. Boston, MA: Springer; 2008. [Google Scholar]
  41. Granada-Echeverri M, Cubides L C, Bustamante J O. The electric vehicle routing problem with backhauls. International Journal of Industrial Engineering Computations. 2020;11(1):131–152. doi: 10.5267/j.ijiec.2019.6.001. [DOI] [Google Scholar]
  42. Gutin G, Punnen A P (2007). The Traveling Salesman Problem and Its Variations. Springer
  43. Hiermann G, Hartl R F, Puchinger J, Vidal T. Routing a mix of conventional, plug-in hybrid, and electric vehicles. European Journal of Operational Research. 2019;272(1):235–248. doi: 10.1016/j.ejor.2018.06.025. [DOI] [Google Scholar]
  44. Hiermann G, Puchinger J, Ropke S, Hartl R F. The electric fleet size and mix vehicle routing problem with time windows and recharging stations. European Journal of Operational Research. 2016;252(3):995–1018. doi: 10.1016/j.ejor.2016.01.038. [DOI] [Google Scholar]
  45. Ho S C, Szeto W Y, Kuo Y H, Leung J M Y, Petering M, Tou T W H. A survey of dial-a-ride problems: Literature review and recent developments. Transportation Research Part B: Methodological. 2018;111:395–421. doi: 10.1016/j.trb.2018.02.001. [DOI] [Google Scholar]
  46. Hof J, Schneider M, Goeke D. Solving the battery swap station location-routing problem with capacitated electric vehicles using an AVNS algorithm for vehicle-routing problems with intermediate stops. Transportation Research Part B: Methodological. 2017;97:102–112. doi: 10.1016/j.trb.2016.11.009. [DOI] [Google Scholar]
  47. International Energy Agency (2018). Global EV outlook 2018. Available at: http://iea.org/reports/global-ev-outlook-2018
  48. Jepsen M, Spoorendonk S, Ropke S. A branch-and-cut algorithm for the symmetric two-echelon capacitated vehicle routing problem. Transportation Science. 2013;47(1):23–37. doi: 10.1287/trsc.1110.0399. [DOI] [Google Scholar]
  49. Jie W, Yang J, Zhang M, Huang Y. The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology. European Journal of Operational Research. 2019;272(3):879–904. doi: 10.1016/j.ejor.2018.07.002. [DOI] [Google Scholar]
  50. Kancharla S R, Ramadurai G. An adaptive large neighborhood search approach for electric vehicle routing with load-dependent energy consumption. Transportation in Developing Economies. 2018;4(2):10. doi: 10.1007/s40890-018-0063-3. [DOI] [Google Scholar]
  51. Kempton W, Letendre S E. Electric vehicles as a new power source for electric utilities. Transportation Research Part D: Transport and Environment. 1997;2(3):157–175. doi: 10.1016/S1361-9209(97)00001-1. [DOI] [Google Scholar]
  52. Keskin M, Çatay B. Partial recharge strategies for the electric vehicle routing problem with time windows. Transportation Research Part C: Emerging Technologies. 2016;65:111–127. doi: 10.1016/j.trc.2016.01.013. [DOI] [Google Scholar]
  53. Keskin M, Çatay B. A matheuristic method for the electric vehicle routing problem with time windows and fast chargers. Computers & Operations Research. 2018;100:172–188. doi: 10.1016/j.cor.2018.06.019. [DOI] [Google Scholar]
  54. Koç Ç, Jabali O, Mendoza J E, Laporte G. The electric vehicle routing problem with shared charging stations. International Transactions in Operational Research. 2019;26(4):1211–1243. doi: 10.1111/itor.12620. [DOI] [Google Scholar]
  55. Koç Ç, Karaoglan I. The green vehicle routing problem: A heuristic based exact solution approach. Applied Soft Computing. 2016;39:154–164. doi: 10.1016/j.asoc.2015.10.064. [DOI] [Google Scholar]
  56. Küçükoğlu I, Dewil R, Cattrysse D. Hybrid simulated annealing and tabu search method for the electric travelling salesman problem with time windows and mixed charging rates. Expert Systems with Applications. 2019;134:279–303. doi: 10.1016/j.eswa.2019.05.037. [DOI] [Google Scholar]
  57. Leggieri V, Haouari M. A practical solution approach for the green vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review. 2017;104:97–112. doi: 10.1016/j.tre.2017.06.003. [DOI] [Google Scholar]
  58. Li C, Ding T, Liu X, Huang C. An electric vehicle routing optimization model with hybrid plug-in and wireless charging systems. IEEE Access. 2018;6:27569–27578. doi: 10.1109/ACCESS.2018.2832187. [DOI] [Google Scholar]
  59. Li Y, Soleimani H, Zohal M. An improved ant colony optimization algorithm for the multi-depot green vehicle routing problem with multiple objectives. Journal of Cleaner Production. 2019;227:1161–1172. doi: 10.1016/j.jclepro.2019.03.185. [DOI] [Google Scholar]
  60. Lin J, Zhou W, Wolfson O. Electric vehicle routing problem. Transportation Research Procedia. 2016;12:508–521. doi: 10.1016/j.trpro.2016.02.007. [DOI] [Google Scholar]
  61. Liu M, Luo Z, Lim A. A branch-and-cut algorithm fora realistic dial-a-ride problem. Transportation Research Part B: Methodological. 2015;81(Part1):267–288. doi: 10.1016/j.trb.2015.05.009. [DOI] [Google Scholar]
  62. Liu T, Luo Z, Qin H, Lim A. A branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints. European Journal of Operational Research. 2018;266(2):487–497. doi: 10.1016/j.ejor.2017.10.017. [DOI] [Google Scholar]
  63. Luo Z, Liu M, Lim A. A two-phase branch-and-price-and-cut for a dial-a-ride problem in patient transportation. Transportation Science. 2019;53(1):113–130. doi: 10.1287/trsc.2017.0772. [DOI] [Google Scholar]
  64. Luo Z, Qin H, Che C H, Lim A. On service consistency in multi-period vehicle routing. European Journal of Operational Research. 2015;243(3):731–744. doi: 10.1016/j.ejor.2014.12.019. [DOI] [Google Scholar]
  65. Luo Z, Qin H, Zhu W, Lim A. Branch and price and cut for the split-delivery vehicle routing problem with time windows and linear weight-related cost. Transportation Science. 2017;51(2):668–687. doi: 10.1287/trsc.2015.0666. [DOI] [Google Scholar]
  66. Macrina G, Di Puglia Pugliese L, Guerriero F, Laporte G. The green mixed fleet vehicle routing problem with partial battery recharging and time windows. Computers & Operations Research. 2019;101:183–199. doi: 10.1016/j.cor.2018.07.012. [DOI] [Google Scholar]
  67. Macrina G, Laporte G, Guerriero F, Di Puglia Pugliese L. An energy-efficient green-vehicle routing problem with mixed vehicle fleet, partial battery recharging and time windows. European Journal of Operational Research. 2019;276(3):971–982. doi: 10.1016/j.ejor.2019.01.067. [DOI] [Google Scholar]
  68. Mancini S. The hybrid vehicle routing problem. Transportation Research Part C: Emerging Technologies. 2017;78:1–12. doi: 10.1016/j.trc.2017.02.004. [DOI] [Google Scholar]
  69. Masmoudi M A, Hosny M, Demir E, Genikomsakis K N, Cheikhrouhou N. The dial-a-ride problem with electric vehicles and battery swapping stations. Transportation Research Part E: Logistics and Transportation Review. 2018;118:392–420. doi: 10.1016/j.tre.2018.08.005. [DOI] [Google Scholar]
  70. Mladenovic N, Hansen P. Variable neighborhood search. Computers & Operations Research. 1997;24(11):1097–1100. doi: 10.1016/S0305-0548(97)00031-2. [DOI] [Google Scholar]
  71. Mladenović N, Todosijević R, Urošević D. An efficient GVNS for solving traveling salesman problem with time windows. Electronic Notes in Discrete Mathematics. 2012;39:83–90. doi: 10.1016/j.endm.2012.10.012. [DOI] [Google Scholar]
  72. Molenbruch Y, Braekers K, Caris A. Typology and literature review for dial-a-ride problems. Annals of Operations Research. 2017;259(1–2):295–325. doi: 10.1007/s10479-017-2525-0. [DOI] [Google Scholar]
  73. Montoya A, Guéret C, Mendoza J E, Villegas J G. A multi-space sampling heuristic for the green vehicle routing problem. Transportation Research Part C: Emerging Technologies. 2016;70:113–128. doi: 10.1016/j.trc.2015.09.009. [DOI] [Google Scholar]
  74. Montoya A, Guéret C, Mendoza J E, Villegas J G. The electric vehicle routing problem with nonlinear charging function. Transportation Research Part B: Methodological. 2017;103:87–110. doi: 10.1016/j.trb.2017.02.004. [DOI] [Google Scholar]
  75. Murakami K. A new model and approach to electric and diesel-powered vehicle routing. Transportation Research Part E: Logistics and Transportation Review. 2017;107:23–37. doi: 10.1016/j.tre.2017.09.004. [DOI] [Google Scholar]
  76. Murakami K. Formulation and algorithms for route planning problem of plug-in hybrid electric vehicles. Operational Research. 2018;18(2):497–519. doi: 10.1007/s12351-016-0274-5. [DOI] [Google Scholar]
  77. Nagy G, Salhi S. Location-routing: Issues, models and methods. European Journal of Operational Research. 2007;177(2):649–672. doi: 10.1016/j.ejor.2006.04.004. [DOI] [Google Scholar]
  78. Nagy G, Wassan N A, Speranza M G, Archetti C. The vehicle routing problem with divisible deliveries and pickups. Transportation Science. 2015;49(2):271–294. doi: 10.1287/trsc.2013.0501. [DOI] [Google Scholar]
  79. Nejad M M, Mashayekhy L, Grosu D, Chinnam R B. Optimal routing for plug-in hybrid electric vehicles. Transportation Science. 2017;51(4):1304–1325. doi: 10.1287/trsc.2016.0706. [DOI] [Google Scholar]
  80. Pelletier S, Jabali O, Laporte G. The electric vehicle routing problem with energy consumption uncertainty. Transportation Research Part B: Methodological. 2019;126:225–255. doi: 10.1016/j.trb.2019.06.006. [DOI] [Google Scholar]
  81. Perboli G, Tadei R, Vigo D. The two-echelon capacitated vehicle routing problem: Models and math-based heuristics. Transportation Science. 2011;45(3):364–380. doi: 10.1287/trsc.1110.0368. [DOI] [Google Scholar]
  82. Prins C, Lacomme P, Prodhon C. Order-first split-second methods for vehicle routing problems: A review. Transportation Research Part C: Emerging Technologies. 2014;40:179–200. doi: 10.1016/j.trc.2014.01.011. [DOI] [Google Scholar]
  83. Prodhon C, Prins C. A survey of recent research on location-routing problems. European Journal of Operational Research. 2014;238(1):1–17. doi: 10.1016/j.ejor.2014.01.005. [DOI] [Google Scholar]
  84. Roberti R, Wen M. The electric traveling salesman problem with time windows. Transportation Research Part E: Logistics and Transportation Review. 2016;89:32–52. doi: 10.1016/j.tre.2016.01.010. [DOI] [Google Scholar]
  85. Ropke S, Pisinger D. An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science. 2006;40(4):455–472. doi: 10.1287/trsc.1050.0135. [DOI] [Google Scholar]
  86. Sassi O, Oulamara A. Electric vehicle scheduling and optimal charging problem: Complexity, exact and heuristic approaches. International Journal of Production Research. 2017;55(2):519–535. doi: 10.1080/00207543.2016.1192695. [DOI] [Google Scholar]
  87. Savelsbergh M W P, Sol M. The general pickup and delivery problem. Transportation Science. 1995;29(1):17–29. doi: 10.1287/trsc.29.1.17. [DOI] [Google Scholar]
  88. Schiffer M, Walther G. The electric location routing problem with time windows and partial recharging. European Journal of Operational Research. 2017;260(3):995–1013. doi: 10.1016/j.ejor.2017.01.011. [DOI] [Google Scholar]
  89. Schneider F, Thonemann U W, Klabjan D. Optimization of battery charging and purchasing at electric vehicle battery swap stations. Transportation Science. 2018;52(5):1211–1234. doi: 10.1287/trsc.2017.0781. [DOI] [Google Scholar]
  90. Schneider M, Stenger A, Goeke D. The electric vehicle-routing problem with time windows and recharging stations. Transportation Science. 2014;48(4):500–520. doi: 10.1287/trsc.2013.0490. [DOI] [Google Scholar]
  91. Schneider M, Stenger A, Hof J. An adaptive VNS algorithm for vehicle routing problems with intermediate stops. OR-Spektrum. 2015;37(2):353–387. doi: 10.1007/s00291-014-0376-5. [DOI] [Google Scholar]
  92. Schneider M, Drexl M. A survey of the standard location-routing problem. Annals of Operations Research. 2017;259(1–2):389–414. doi: 10.1007/s10479-017-2509-0. [DOI] [Google Scholar]
  93. Shao S, Guan W, Bi J. Electric vehicle-routing problem with charging demands and energy consumption. IET Intelligent Transport Systems. 2018;12(3):202–212. doi: 10.1049/iet-its.2017.0008. [DOI] [Google Scholar]
  94. Shi J, Gao Y, Yu N (2018). Routing electric vehicle fleet for ride-sharing. In: 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2). Beijing, 1–6
  95. Solomon M M. Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research. 1987;35(2):254–265. doi: 10.1287/opre.35.2.254. [DOI] [Google Scholar]
  96. Sweda T M, Dolinskaya I S, Klabjan D. Adaptive routing and recharging policies for electric vehicles. Transportation Science. 2017;51(4):1326–1348. doi: 10.1287/trsc.2016.0724. [DOI] [Google Scholar]
  97. Sweda T M, Dolinskaya I S, Klabjan D. Optimal recharging policies for electric vehicles. Transportation Science. 2017;51(2):457–479. doi: 10.1287/trsc.2015.0638. [DOI] [Google Scholar]
  98. Toth P, Vigo D. The Vehicle Routing Problem. Philadelphia: Society for Industrial and Applied Mathematics; 2002. [Google Scholar]
  99. Toth P, Vigo D. The granular tabu search and its application to the vehicle-routing problem. INFORMS Journal on Computing. 2003;15(4):333–346. doi: 10.1287/ijoc.15.4.333.24890. [DOI] [Google Scholar]
  100. Verma A. Electric vehicle routing problem with time windows, recharging stations and battery swapping stations. EURO Journal on Transportation and Logistics. 2018;7(4):415–451. doi: 10.1007/s13676-018-0136-9. [DOI] [Google Scholar]
  101. Wang Y, Assogba K, Fan J, Xu M, Liu Y, Wang H. Multi-depot green vehicle routing problem with shared transportation resource: Integration of time-dependent speed and piecewise penalty cost. Journal of Cleaner Production. 2019;232:12–29. doi: 10.1016/j.jclepro.2019.05.344. [DOI] [Google Scholar]
  102. Wen M, Linde E, Ropke S, Mirchandani P, Larsen A. An adaptive large neighborhood search heuristic for the electric vehicle scheduling problem. Computers & Operations Research. 2016;76:73–83. doi: 10.1016/j.cor.2016.06.013. [DOI] [Google Scholar]
  103. Yang J, Sun H. Battery swap station location-routing problem with capacitated electric vehicles. Computers & Operations Research. 2015;55:217–232. doi: 10.1016/j.cor.2014.07.003. [DOI] [Google Scholar]
  104. Yavuz M. An iterated beam search algorithm for the green vehicle routing problem. Networks. 2017;69(3):317–328. doi: 10.1002/net.21737. [DOI] [Google Scholar]
  105. Yavuz M, Çapar I. Alternative-fuel vehicle adoption in service fleets: Impact evaluation through optimization modeling. Transportation Science. 2017;51(2):480–493. doi: 10.1287/trsc.2016.0697. [DOI] [Google Scholar]
  106. Yu M, Jin X, Zhang Z, Qin H, Lai Q. The split-delivery mixed capacitated arc-routing problem: Applications and a forest-based tabu search approach. Transportation Research Part E: Logistics and Transportation Review. 2019;132:141–162. doi: 10.1016/j.tre.2019.09.017. [DOI] [Google Scholar]
  107. Yu V F, Redi AANP, Hidayat Y A, Wibowo O J. A simulated annealing heuristic for the hybrid vehicle routing problem. Applied Soft Computing. 2017;53:119–132. doi: 10.1016/j.asoc.2016.12.027. [DOI] [Google Scholar]
  108. Yu Y, Wang S, Wang J, Huang M. A branch-and-price algorithm for the heterogeneous fleet green vehicle routing problem with time windows. Transportation Research Part B: Methodological. 2019;122:511–527. doi: 10.1016/j.trb.2019.03.009. [DOI] [Google Scholar]
  109. Zhang S, Chen M, Zhang W. A novel location-routing problem in electric vehicle transportation with stochastic demands. Journal of Cleaner Production. 2019;221:567–581. doi: 10.1016/j.jclepro.2019.02.167. [DOI] [Google Scholar]
  110. Zhang S, Gajpal Y, Appadoo S S. A meta-heuristic for capacitated green vehicle routing problem. Annals of Operations Research. 2018;269(1):753–771. doi: 10.1007/s10479-017-2567-3. [DOI] [Google Scholar]
  111. Zhang S, Gajpal Y, Appadoo S S, Abdulkader M M S. Electric vehicle routing problem with recharging stations for minimizing energy consumption. International Journal of Production Economics. 2018;203:404–413. doi: 10.1016/j.ijpe.2018.07.016. [DOI] [Google Scholar]
  112. Zhang Z, Che O, Cheang B, Lim A, Qin H. A memetic algorithm for the multiperiod vehicle routing problem with profit. European Journal of Operational Research. 2013;229(3):573–584. doi: 10.1016/j.ejor.2012.11.059. [DOI] [Google Scholar]
  113. Zhang Z, Qin H, Zhu W, Lim A. The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach. European Journal of Operational Research. 2012;220(2):295–304. doi: 10.1016/j.ejor.2012.01.035. [DOI] [Google Scholar]
  114. Zhao M, Lu Y. A heuristic approach for a real-world electric vehicle routing problem. Algorithms. 2019;12(2):45. doi: 10.3390/a12020045. [DOI] [Google Scholar]
  115. Zhen L, Xu Z, Ma C, Xiao L. Hybrid electric vehicle routing problem with mode selection. International Journal of Production Research. 2020;58(2):562–576. doi: 10.1080/00207543.2019.1598593. [DOI] [Google Scholar]
  116. Zuo X, Xiao Y, You M, Kaku I, Xu Y. A new formulation of the electric vehicle routing problem with time windows considering concave nonlinear charging function. Journal of Cleaner Production. 2019;236:117687. doi: 10.1016/j.jclepro.2019.117687. [DOI] [Google Scholar]

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