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Annals of Operations Research

, Volume 273, Issue 1–2, pp 5–74 | Cite as

A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet

  • Puca Huachi Vaz PennaEmail author
  • Anand Subramanian
  • Luiz Satoru Ochi
  • Thibaut Vidal
  • Christian Prins
S.I.: OR in Transportation

Abstract

We consider a family of rich vehicle routing problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments.

Keywords

Rich vehicle routing Heterogeneous fleet Matheuristics Iterated local search Set partitioning 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments. This research was partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), under Grants: 446683/2014-0 (first author); 305223/2015-1, 428549/2016-0 (second author); 308498/2015-1 (fourth author); 400722/2013-5 (third and fifth authors).

References

  1. Amorim, P., Parragh, S., Sperandio, F., & Almada-Lobo, B. (2014). A rich vehicle routing problem dealing with perishable food: A case study. TOP, 22(2), 489–508.Google Scholar
  2. Baldacci, R., Battarra, M., & Vigo, D. (2008). The vehicle routing problem: Latest advances and new challenges. Chap. Routing a heterogeneous fleet of vehicles (pp. 11–35). Berlin: Springer.Google Scholar
  3. Baldacci, R., Battarra, M., & Vigo, D. (2009). Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs. Networks, 54(4), 178–189.Google Scholar
  4. Baldacci, R., Bartolini, E., Mingozzi, A., & Roberti, R. (2010a). An exact solution framework for a broad class of vehicle routing problems. Computational Management Science, 7(3), 229–268.Google Scholar
  5. Baldacci, R., Toth, P., & Vigo, D. (2010b). Exact algorithms for routing problems under vehicle capacity constraints. Annals of Operations Research, 175(1), 213–245.Google Scholar
  6. Belfiore, P., & Yoshizaki, H. T. Y. (2009). Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil. European Journal of Operational Research, 199, 750–758.Google Scholar
  7. Belmecheri, F., Prins, C., Yalaoui, F., & Amodeo, L. (2013). Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. Journal of Intelligent Manufacturing, 24(4), 775–789.Google Scholar
  8. Berghida, M., & Boukra, A. (2015). EBBO: An enhanced biogeography-based optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. The International Journal of Advanced Manufacturing Technology, 77(9–12), 1711–1725.Google Scholar
  9. Bettinelli, A., Ceselli, A., & Righini, G. (2011). A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows. Transportation Research Part C: Emerging Technologies, 19(5), 723–740.Google Scholar
  10. Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys (CSUR), 35(3), 268–308.Google Scholar
  11. Boudia, M., Prins, C., & Reghioui, M. (2007). An effective memetic algorithm with population management for the split delivery vehicle routing problem. In T. Bartz-Beielstein, M. Blesa Aguilera, C. Blum, B. Naujoks, A. Roli, G. Rudolph, & M. Sampels (Eds.), Hybrid metaheuristics. Lecture notes in computer science (Vol. 4771, pp. 16–30). Berlin: Springer.Google Scholar
  12. Brandão, J. (2009). A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. European Journal of Operational Research, 195, 716–728.Google Scholar
  13. Brandão, J. (2011). A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem. Computers & Operations Research, 38, 140–151.Google Scholar
  14. Bräysy, O., Dullaert, W., Hasle, G., Mester, D., & Gendreau, M. (2008). An effective multirestart deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. Transportation Science, 42(3), 371–386.Google Scholar
  15. Bräysy, O., Porkka, P. P., Dullaert, W., Repoussis, P. P., & Tarantilis, C. D. (2009). A well-scalable metaheuristic for the fleet size and mix vehicle routing problem with time windows. Expert Systems with Applications, 36, 8460–8475.Google Scholar
  16. Cáceres-Cruz, J., Arias, P., Guimarans, D., Riera, D., & Juan, A. A. (2014a). Rich vehicle routing problem: Survey. ACM Computing Surveys, 47(2), 1–28.Google Scholar
  17. Cáceres-Cruz, J., Grasas, A., Ramalhinho, H., & Juan, A. A. (2014b). A savings-based randomized heuristic for the heterogeneous fixed fleet vehicle routing problem with multi-trips. Journal of Applied Operational Research, 6(2), 69–81.Google Scholar
  18. Cáceres-Cruz, J., Riera, D., Buil, R., & Juan, A. A. (2013). Applying a savings algorithm for solving a rich vehicle routing problem in a real urban context. In 5th International conference on applied operational research. Lecture notes in management science (Vol. 5, pp. 84–92).Google Scholar
  19. Ceselli, A., Righini, G., & Salani, M. (2009). A column generation algorithm for a rich vehicle-routing problem. Transportation Science, 43(1), 56–69.Google Scholar
  20. Choi, E., & Tcha, D. W. (2007). A column generation approach to the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 34, 2080–2095.Google Scholar
  21. Clarke, G., & Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12, 568–581.Google Scholar
  22. Cordeau, J. F., & Laporte, G. (2001). A tabu search algorithm for the site dependent vehicle routing problem with time windows. INFOR, 39, 292–8.Google Scholar
  23. Cordeau, J. F., Laporte, G., & Mercier, A. (2001). A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society, 52, 928–936.Google Scholar
  24. Cordeau, J. F., Laporte, G., & Mercier, A. (2004). Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows. The Journal of the Operational Research Society, 55(5), 542–546.Google Scholar
  25. Cordeau, J. F., & Maischberger, M. (2012). A parallel iterated tabu search heuristic for vehicle routing problems. Computers & Operations Research, 39(9), 2033–2050.Google Scholar
  26. Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6, 80–91.Google Scholar
  27. de Armas, J., & Melián-Batista, B. (2015). Variable neighborhood search for a dynamic rich vehicle routing problem with time windows. Computers & Industrial Engineering, 85, 120–131.Google Scholar
  28. de Armas, J., Melián-Batista, B., Moreno-Pérez, J. A., & Brito, J. (2015). GVNS for a real-world rich vehicle routing problem with time windows. Engineering Applications of Artificial Intelligence, 42, 45–56.Google Scholar
  29. Dell’Amico, M., Monaci, M., Pagani, C., & Vigo, D. (2007). Heuristic approaches for the fleet size and mix vehicle routing problem with time windows. Transportation Science, 41(4), 516–526.Google Scholar
  30. Derigs, U., & Vogel, U. (2014). Experience with a framework for developing heuristics for solving rich vehicle routing problems. Journal of Heuristics, 20(1), 75–106.Google Scholar
  31. Dominguez, O., Juan, A. A., Barrios, B., Faulin, J., & Agustin, A. (2016). Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet. Annals of Operations Research, 236(2), 383–404.Google Scholar
  32. Dondo, R., & Cerdá, J. (2007). A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows. European Journal of Operational Research, 176(3), 1478–1507.Google Scholar
  33. Dongarra, J. J. (2010). Performance of various computers using standard linear equations software. Technical Report CS-89-85, Computer Science Department, University of TennesseeGoogle Scholar
  34. Dror, M., & Trudeau, P. (1990). Split delivery routing. Naval Research Logistics, 37(3), 383–402.Google Scholar
  35. Duhamel, C., Gouinaud, C., Lacomme, P., & Prodhon, C. (2013). A multi-thread GRASPxELS for the heterogeneous capacitated vehicle routing problem. In E. G. Talbi (Ed.), Hybrid metaheuristics. Studies in computational intelligence (Vol. 434, pp. 237–269). Berlin: Springer.Google Scholar
  36. Duhamel, C., Lacomme, P., & Prodhon, C. (2011). Efficient frameworks for greedy split and new depth first search split procedures for routing problems. Computers & Operations Research, 38(4), 723–739.Google Scholar
  37. Gendreau, M., Laporte, G., Musaraganyi, C., & Taillard, E. D. (1999). A tabu search heuristic for the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 26, 1153–1173.Google Scholar
  38. Goel, A. (2010). A column generation heuristic for the general vehicle routing problem. In C. Blum & R. Battiti (Eds.), Learning and intelligent optimization. Lecture notes in computer science (Vol. 6073, pp. 1–9). Berlin: Springer.Google Scholar
  39. Goel, A., & Gruhn, V. (2008). A general vehicle routing problem. European Journal of Operational Research, 191(3), 650–660.Google Scholar
  40. Golden, B. L., Assad, A. A., Levy, L., & Gheysens, F. G. (1984). The fleet size and mix vehicle routing problem. Computers & Operations Research, 11, 49–66.Google Scholar
  41. Hansen, P., Mladenović, N., & Pérez, J. M. (2010). Variable neighbourhood search: Methods and applications. Annals of Operations Research, 175, 367–407.Google Scholar
  42. Hoff, A., Andersson, H., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Fleet composition and routing. Computers & Operations Research, 37, 2041–2061.Google Scholar
  43. Imran, A., Salhi, S., & Wassan, N. A. (2009). A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem. European Journal of Operational Research, 197, 509–518.Google Scholar
  44. Irnich, S., Schneider, M., & Vigo, D. (2014) Vehicle routing: Problems, methods, and applications, chap Four variants of the vehicle routing problem (pp. 241–271). MOS-SIAM series on optimization.Google Scholar
  45. Koç, Ç., Bektaş, T., Jabali, O., & Laporte, G. (2015). A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Computers & Operations Research, 64, 11–27.Google Scholar
  46. Koç, Ç., Bektaş, T., Jabali, O., & Laporte, G. (2016). Thirty years of heterogeneous vehicle routing. European Journal of Operational Research, 249(1), 1–21.Google Scholar
  47. Lahyani, R., Khemakhem, M., & Semet, F. (2015). Rich vehicle routing problems: From a taxonomy to a definition. European Journal of Operational Research, 241(1), 1–14.Google Scholar
  48. Lee, Y., Kim, J., Kang, K., & Kim, K. (2008). A heuristic for vehicle fleet mix problem using tabu search and set partitioning. Journal of the Operational Research Society, 59, 833–841.Google Scholar
  49. Li, F., Golden, B., & Wasil, E. (2007). A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem. Computers & Operations Research, 34, 2734–2742.Google Scholar
  50. Li, X., Leung, S. C., & Tian, P. (2012). A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39, 365–374.Google Scholar
  51. Li, X., Tian, P., & Aneja, Y. (2010). An adaptive memory programming metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 46(6), 1111–1127.Google Scholar
  52. Lima, C. M. R. R., Goldbarg, M. C., & Goldbarg, E. F. G. (2004). A memetic algorithm for the heterogeneous fleet vehicle routing problem. Electronic Notes in Discrete Mathematics, 18, 171–176.Google Scholar
  53. Liu, F. H., & Shen, S. Y. (1999). The fleet size and mix vehicle routing problem with time windows. The Journal of the Operational Research Society, 50(7), 721–732.Google Scholar
  54. Liu, S., Huang, W., & Ma, H. (2009). An effective genetic algorithm for the fleet size and mix vehicle routing problems. Transportation Research Part E, 45, 434–445.Google Scholar
  55. Lourenço, H. R., Martin, O. C., & Stützle, T. (2010). Iterated local search: Framework and applications. In M. Gendreau & J. Y. Potvin (Eds.), Handbook of metaheuristics. International series in operations research & management science (Vol. 146, pp. 363–397). New York: Springer.Google Scholar
  56. Mancini, S. (2016). A real-life multi depot multi period vehicle routing problem with a heterogeneous fleet: Formulation and adaptive large neighborhood search based matheuristic. Transportation Research Part C: Emerging Technologies, 70, 100–112.Google Scholar
  57. Mar-Ortiz, J., González-Velarde, J., & Adenso-Díaz, B. (2013). Designing routes for weee collection: The vehicle routing problem with split loads and date windows. Journal of Heuristics, 19(2), 103–127.Google Scholar
  58. McGinnis, L. F. (1983). Implementation and testing of a primal–dual algorithm for the assignment problem. Operations Research, 31(2), 277–291.Google Scholar
  59. Nagata, Y., Bräysy, O., & Dullaert, W. (2010). A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Computers & Operations Research, 37(4), 724–737.Google Scholar
  60. Ochi, L., Vianna, D., Drummond, L. M. A., & Victor, A. (1998a). An evolutionary hybrid metaheuristic for solving the vehicle routing problem with heterogeneous fleet. Lecture Notes in Computer Science, 1391, 187–195.Google Scholar
  61. Ochi, L., Vianna, D., Drummond, L. M. A., & Victor, A. (1998b). A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet. Future Generation Computer Systems, 14, 285–292.Google Scholar
  62. Ozfirat, P. M., & Ozkarahan, I. (2010). A constraint programming heuristic for a heterogeneous vehicle routing problem with split deliveries. Applied Artificial Intelligence, 24(4), 277–294.Google Scholar
  63. Paraskevopoulos, D., Repoussis, P., Tarantilis, C., Ioannou, G., & Prastacos, G. (2008). A reactive variable neighborhood tabu search for the heterogeneous fleet vehicle routing problem with time windows. Journal of Heuristics, 14, 425–455.Google Scholar
  64. Pellegrini, P., Favaretto, D., & Moretti, E. (2007). Multiple ant colony optimization for a rich vehicle routing problem: A case study. In B. Apolloni, R. Howlett, & L. Jain (Eds.), Knowledge-based intelligent information and engineering systems. Lecture notes in computer science (Vol. 4693, pp. 627–634). Berlin: Springer.Google Scholar
  65. Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2013). An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 19(2), 201–232.Google Scholar
  66. Pessoa, A., Uchoa, E., & de Aragão, M. P. (2009). A robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem. Networks, 54(4), 167–177.Google Scholar
  67. Pisinger, D., & Røpke, S. (2007). A general heuristic for vehicle routing problems. Computers & Operations Research, 34(8), 2403–2435.Google Scholar
  68. Prins, C. (2002). Efficient heuristics for the heterogeneous fleet multitrip VRP with application to a large-scale real case. Journal of Mathematical Modelling and Algorithms, 1, 135–150.Google Scholar
  69. Prins, C. (2009). Two memetic algorithms for heterogeneous fleet vehicle routing problems. Engineering Applications of Artificial Intelligence, 22(6), 916–928.Google Scholar
  70. Prins, C., Lacomme, P., & Prodhon, C. (2014). Order-first split-second methods for vehicle routing problems: A review. Transportation Research Part C, 40, 179–200.Google Scholar
  71. Repoussis, P., & Tarantilis, C. (2010). Solving the fleet size and mix vehicle routing problem with time windows via adaptive memory programming. Transportation Research Part C: Emerging Technologies, 18(5), 695–712.Google Scholar
  72. Reyes, L. C., Barbosa, J. G., Vargas, D. R., Huacuja, H. F., Valdez, N. R., Ortiz, J. H., Cruz, B. A., & Orta, J. D. (2007) A distributed metaheuristic for solving a real-world scheduling–routing–loading problem. In I. Stojmenovic, R. Thulasiram, L. Yang, W. Jia, M. Guo, R. de Mello (Eds.), Parallel and distributed processing and applications. Lecture notes in computer science (Vol. 4742, pp. 68 – 77).Google Scholar
  73. Rieck, J., & Zimmermann, J. (2010). A new mixed integer linear model for a rich vehicle routing problem with docking constraints. Annals of Operations Research, 181(1), 337–358.Google Scholar
  74. Rochat, Y., & Taillard, R. D. (1995). Probabilistic diversification and intensification in local search for vehicle routing. Journal of Heuristics, 1, 147–167.Google Scholar
  75. Røpke, S., & Pisinger, D. (2006). A unified heuristic for a large class of vehicle routing problems with backhauls. European Journal of Operational Research, 171(3), 750–775.Google Scholar
  76. Salhi, S., Imran, A., & Wassan, N. A. (2014). The multi-depot vehicle routing problem with heterogeneous vehicle fleet: Formulation and a variable neighborhood search implementation. Computers & Operations Research, 52, 315–325.Google Scholar
  77. Salhi, S., & Sari, M. (1997). A multi-level composite heuristic for the multi-depot vehicle fleet mix problem. European Journal of Operational Research, 103(1), 95–112.Google Scholar
  78. Salhi, S., Wassan, N., & Hajarat, M. (2013). The fleet size and mix vehicle routing problem with backhauls: Formulation and set partitioning-based heuristics. Transportation Research Part E: Logistics and Transportation Review, 56, 22–35.Google Scholar
  79. Silva, M. M., Subramanian, A., & Ochi, L. S. (2015). An iterated local search heuristic for the split delivery vehicle routing problem. Computers & Operations Research, 53, 234–249.Google Scholar
  80. Subramanian, A., Penna, P. H. V., Uchoa, E., & Ochi, L. S. (2012). A hybrid algorithm for the heterogenous fleet vehicle routing problem. European Journal of Operational Research, 221, 285–295.Google Scholar
  81. Subramanian, A., Uchoa, E., & Ochi, L. S. (2013). A hybrid algorithm for a class of vehicle routing problems. Computers & Operations Research, 40(10), 2519–2531.Google Scholar
  82. Taillard, E. D. (1999). A heuristic column generation method for heterogeneous fleet. RAIRO (Recherche opérationnelle), 33, 1–14.Google Scholar
  83. Tarantilis, C. D., Kiranoudis, C. T., & Vassiliadis, V. S. (2003). A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Journal of the Operational Research Society, 54, 65–71.Google Scholar
  84. Tarantilis, C. D., Kiranoudis, C. T., & Vassiliadis, V. S. (2004). A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. European Journal of Operational Research, 152, 148–158.Google Scholar
  85. Tavakkoli-Moghaddam, R., Safaei, N., Kah, M., & Rabbani, M. (2007). A new capacitated vehicle routing problem with split service for minimizing fleet cost by simulated annealing. Journal of the Franklin Institute, 344(5), 406–425. (Modeling, simulation and applied optimization Part II).Google Scholar
  86. Tütüncü, G. Y. (2010). An interactive gramps algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls. European Journal of Operational Research, 201, 593–600.Google Scholar
  87. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013a). Heuristics for multi-attribute vehicle routing problems: A survey and synthesis. European Journal of Operational Research, 231(1), 1–21.Google Scholar
  88. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013b). A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows. Computers & Operations Research, 40(1), 475–489.Google Scholar
  89. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2014). A unified solution framework for multi-attribute vehicle routing problems. European Journal of Operational Research, 234(3), 658–673.Google Scholar
  90. Vidal, T., Crainic, T., Gendreau, M., & Prins, C. (2015). Time-window relaxations in vehicle routing heuristics. Journal of Heuristics, 21(3), 329–358.Google Scholar
  91. Wassan, N. A., & Osman, I. H. (2002). Tabu search variants for the mix fleet vehicle routing problem. Journal of the Operational Research Society, 53, 768–782.Google Scholar
  92. Yao, B., Yu, B., Hu, P., Gao, J., & Zhang, M. (2016). An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Annals of Operations Research, 242(2), 303–320.Google Scholar
  93. Yousefikhoshbakht, M., Didehvar, F., & Rahmati, F. (2014). Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm. International Journal of Production Research, 52(9), 2565–2575.Google Scholar

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Authors and Affiliations

  1. 1.Departamento de ComputaçãoUniversidade Federal de Ouro PretoOuro PrêtoBrazil
  2. 2.Departamento de Sistemas de Computação, Centro de InformáticaUniversidade Federal da ParaíbaJoão PessoaBrazil
  3. 3.Instituto de ComputaçãoUniversidade Federal FluminenseNiteróiBrazil
  4. 4.Pontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  5. 5.ICD-LOSI, UMR CNRS 6281Université de Technologie de TroyesTroyes CedexFrance

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