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A chance constrained programming model and an improved large neighborhood search algorithm for the electric vehicle routing problem with stochastic travel times

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Abstract

The Electric Vehicle Routing Problem (EVRP) is an extension to the well-known Vehicle Routing Problem (VRP) where the fleet consists of electric vehicles, which may need to visit recharging stations while servicing the customers due to their battery capacities. This paper solves the Electric Vehicle Routing Problem with Stochastic Travel Times (EVRPSTT) by proposing a Chance Constrained Programming (CCP) Model, as well as a new scheme based on an Improved Large Neighborhood Search (ILS) algorithm and a Monte Carlo Sampling (MCS) procedure. The proposed approach is firstly tested in the deterministic environment using the EVRP benchmark data set, where the numerical results show that this approach is able to provide EVRP optimal solutions, within a very short computational time, for 39 out of 48 used benchmark instances with 20, 50, 75 and 100 customers. Thereafter, to show the efficiency of the proposed approach for solving the CCP model of the EVRPSTT, others tests are performed on the same set of instances, while taking into consideration a large number of scenarios.

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References

  1. Andelmin J, Bartolini E (2017) An exact algorithm for the green vehicle routing problem. Transp Sci 51(4):1288–1303

    Article  Google Scholar 

  2. Baptista S, Oliveira RC, Zúquete E (2002) A period vehicle routing case study. Eur J Oper Res 139(2):220–229

    Article  MATH  Google Scholar 

  3. Basso R, Balázs K, Ivan SD (2021) Electric vehicle routing problem with machine learning for energy prediction. Transp Res B-Meth 145:24–55

    Article  Google Scholar 

  4. Bent RW, Van Hentenryck P (2004) Scenario-based planning for partially dynamic vehicle routing with stochastic customers. Oper Res 52(6):977–987

    Article  MATH  Google Scholar 

  5. Bianchessi N, Righini G (2007) Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery. Comput Oper Res 34:578–594

    Article  MATH  Google Scholar 

  6. Charnes A, Cooper WW (1959) Chance-constrained programming. Manage Sci 6(1):73–79

    Article  MATH  Google Scholar 

  7. Chen X, Thomas BW, Hewitt M (2017) Multi-period technician scheduling with experience-based service times and stochastic customers. Comput Oper Res 82:1–14

    Article  MATH  Google Scholar 

  8. Christiansen C, Lysgaard J (2007) A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res Lett 35(6):773–781

    Article  MATH  Google Scholar 

  9. Dantzig G, Ramser J (1959) The truck dispatching problem. Manage Sci 6(1):80–91

    Article  MATH  Google Scholar 

  10. Erdelić T, Carić T (2019) A survey on the electric vehicle routing problem: Variants and solution approaches. J Adv Transp 1–48

  11. Erdogân S, Miller-Hooks E (2012) A green vehicle routing problem. Transp Res E Logist Transp Rev 48(1):100–114

    Article  Google Scholar 

  12. Flood M (1956) The traveling-salesman problem. Oper Res 4(1):61–75

    Article  MATH  Google Scholar 

  13. Florio AM, Absi N, Feillet D (2021) Routing electric vehicles on congested street networks. Transp Sci 55(1):238–256

    Article  Google Scholar 

  14. Fu Z, Eglese R, Li LYO (2005) A new tabu search heuristic for the open vehicle routing problem. J Oper Res Soc 56:267–274

    Article  MATH  Google Scholar 

  15. Gendreau M, Laporte G, Séguin R (1996) A tabu search algorithm for the vehicle routing problem with stochastic demands and customers. Oper Res 44(3):469–477

    Article  MATH  Google Scholar 

  16. Goeke D, Schneider M, Professorship DSEA (2014) Routing a mixed fleet of electric and conventional vehicles. Technical report, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies, BWL

  17. Kallehauge B, Larsen J, Madsen OBG, Solomon MM (2005) Vehicle routing problem with time windows. In: Column generation, GERAD 25th anniversaryseries, chap 3, New york, pp 67–98

  18. Kenyon A, Morton D (2003) Stochastic vehicle routing with random travel times. Transp Sci 37(1):69–82

    Article  Google Scholar 

  19. Keskin M, Çatay B, Laporte G (2021) A simulation-based heuristic for the electric vehicle routing problem with time windows and stochastic waiting times at recharging stations. Comput Oper Res 125

  20. Koç Ç, Karaoglan I (2016) The green vehicle routing problem: a heuristic based exact solution approach. Appl Soft Comput 39(1):154–164

    Article  Google Scholar 

  21. Lambert V, Laporte G, Louveaux F (1993) Designing collection routes through bank branches. Comput Oper Res 20(7):783–791

    Article  Google Scholar 

  22. Laporte G, Louveaux F, Mercure H (1992) The vehicle routing problem with stochastic travel times. Transp Sci 26(3):161–170

    Article  MATH  Google Scholar 

  23. Li F, Golden B, Wasil E (2007) The open vehicle routing problem: algorithms, largescale test problems and computational results. Comput Oper Res 34(10):2918–2930

    Article  MATH  Google Scholar 

  24. Li J, Pardalos PM, Sun H, Pei J, Zhang Y (2015) Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups. Expert Syst Appl 42(7):3551–3561

    Article  Google Scholar 

  25. Li X, Tian P, Leung S (2010) Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm. Int J Prod Econ 125(1):137–145

    Article  Google Scholar 

  26. Macrina G, di Puglia Pugliese L, Guerriero F, Laporte G (2019) The green mixed fleet vehicle routing problem with partial battery recharging and timewindows. Comput Oper Res 101:183–199

    Article  MATH  Google Scholar 

  27. Marinakis Y, Marinaki M, Migdalas A (2019) A multi-adaptive particle swarm optimization for the vehicle routing problem with time windows. Inf Sci 481:311–329

    Article  Google Scholar 

  28. Miranda DM, Conceição SV (2016) The vehicle routing problem with hard time windows and stochastic travel and service time. Expert Syst Appl 64(1):104–116

    Article  Google Scholar 

  29. Montane FA, Galvao RD (2006) A tabu search algorithm for the vehicle routing problem with simultaneous pickup and delivery service. Comput Oper Res 33(3):595–619

    Article  MATH  Google Scholar 

  30. Montoya A, Guéret C, Mendoza JE, Villegas JG (2017) The electric vehicle routing problem with nonlinear charging function. Transport Res B-Meth 103:87–110

    Article  Google Scholar 

  31. Peng B, Zhang Y, Gajpal Y, Chen X (2019) A memetic algorithm for the green vehicle routing problem. Sustainability 11(21):6055

    Article  Google Scholar 

  32. Penna PHV, Subramanian A, Ochi LS, Vidal T, Prins C (2019) A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet. Ann Oper Res 273(1):5–74

    Article  MATH  Google Scholar 

  33. Perboli G, Pezzella F, Tadei R (2008) EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem. Math Method Oper Res 68(2):361–382

    Article  MATH  Google Scholar 

  34. Pichka K, Ashjari B, Ziaeifar A, Nickbeen P (2014) Open vehicle routing problem optimization under realistic assumptions. Int J Res Ind Eng 3(2):46–55

    Google Scholar 

  35. Rodríguez-Martín I, Salazar-González JJ, Yaman H (2018) The periodic vehicle routing problem with driver consistency. Eur J Oper Res 273(2):575–584

    Article  MATH  Google Scholar 

  36. Salavati-Khoshghal MS, Gendreau M, Jabali O, Rei W (2019) An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy. Eur J Oper Res 273(1):175–189

    Article  MATH  Google Scholar 

  37. Schneider BM, Stenger A, Hof J (2015) An adaptive VNS algorithm for vehicle routing problems with intermediate stops. OR Spectrum 37(2):353–387

    Article  MATH  Google Scholar 

  38. Shaw P (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: CP-98 fourth international conference on principles and practice of constraint programming vol 1520, pp 417-431

  39. Taguchi G, Konishi S (1987) Tagushi methods, Orthogonal arrays and linear graphs, tools for quality

  40. Taillard ED, Badeau P, Gendreau M, Guertin F, Potvin JY (1997) A tabu search heuristic for the vehicle routing problem with soft time windows. Transp Sci 31(2):170–186

    Article  MATH  Google Scholar 

  41. Tarantilis C, Kiranoudis C, Vassiliadis V (2004) A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Eur J Oper Res 152(1):148–158

    Article  MATH  Google Scholar 

  42. Tas D (2021) Electric vehicle routing with flexible time windows: A column generation solution approach. Transp Lett 13(2):97–103

    Article  Google Scholar 

  43. Xiao Y, Zhao Q, Kaku I, Mladenovic N (2014) Variable neighbourhood simulated annealing algorithm for capacitated vehicle routing problems. Eng Optimiz 46(4):562–579

    Article  Google Scholar 

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Correspondence to Elhassania Messaoud.

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Messaoud, E. A chance constrained programming model and an improved large neighborhood search algorithm for the electric vehicle routing problem with stochastic travel times. Evol. Intel. 16, 153–168 (2023). https://doi.org/10.1007/s12065-021-00648-0

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  • DOI: https://doi.org/10.1007/s12065-021-00648-0

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