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

Hu QIN, Xinxin SU, Teng REN, Zhixing LUO

PDF(1130 KB)
PDF(1130 KB)
Front. Eng ›› 2021, Vol. 8 ›› Issue (3) : 370-389. DOI: 10.1007/s42524-021-0157-1
REVIEW ARTICLE
REVIEW ARTICLE

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

Author information +
History +

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.

Graphical abstract

Keywords

electric vehicles / routing / recharging stations / exact algorithms / metaheuristics

Cite this article

Download citation ▾
Hu QIN, Xinxin SU, Teng REN, Zhixing LUO. A review on the electric vehicle routing problems: Variants and algorithms. Front. Eng, 2021, 8(3): 370‒389 https://doi.org/10.1007/s42524-021-0157-1

References

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

Acknowledgments

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.

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

RIGHTS & PERMISSIONS

2021 The Author(s) 2021. This article is published with open access at link.springer.com and journal.hep.com.cn
AI Summary AI Mindmap
PDF(1130 KB)

Accesses

Citations

Detail

Sections
Recommended

/