A Multi-thread GRASPxELS for the Heterogeneous Capacitated Vehicle Routing Problem

  • Christophe Duhamel
  • Christophe Gouinaud
  • Philippe Lacomme
  • Caroline Prodhon
Part of the Studies in Computational Intelligence book series (SCI, volume 434)


This chapter focuses on the definition of an efficient parallel metaheuristic which takes advantage of the multi-core design of recent processors. The approach is designed as a Greedy Randomized Adaptive Search Procedure (GRASP) hybridized with a multi-threaded version of an Evolutionary Local Search (ELS) metaheuristic scheme. Our approach is evaluated on an extension of the Vehicle Routing Problem where a heterogeneous fleet of vehicles is available to service a set of customers. The objective consists in designing a set of trips for a limited heterogeneous fleet of vehicles located at a depot node which minimizes the total transportation cost. Each type of vehicles is defined by a capacity and by the number of available vehicles. The efficiency of the parallel approach is evaluated on a new set of real-life instances built out of data from the French districts. A fair comparative study, using a same implementation, is done to evaluate the impact of the number of threads on the convergence rate. Thus, a better trade-off between solution quality and computational time can be reached. The numerical experiments show that the hybrid GRASPxparallel ELS outperforms the classical iterative version and provides numerous new best solutions.


Local Search Memetic Algorithm Greedy Randomize Adaptive Search Procedure Vehicle Route Problem Vehicle Route Problem With Time Window 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bortfeldt, A., Gehring, H., Mack, D.: A parallel tabu search algorithm for solving the container loading problem. Parallel Computing 29(5), 641–662 (2003)CrossRefGoogle Scholar
  2. 2.
    Le Bouthillier, A., Crainic, T.G.: A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Computers & Operations Research 32(7), 1685–1708 (2005)zbMATHCrossRefGoogle Scholar
  3. 3.
    Tantar, A.-A., Melab, N., Talbi, E.-G., Parent, B., Horvath, D.: A parallel hybrid genetic algorithm for protein structure prediction on the computational grid. Future Generation Computer Systems 23(3), 398–409 (2007)CrossRefGoogle Scholar
  4. 4.
    Brand, A.O.J.: A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem. Computers & Operations Research 38(1), 140–151 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Eksioglu, B., Vural, A.V., Reisman, A.: The vehicle routing problem: a taxonomic review. Computers and Industrial Engineering 57, 1472–1483 (2008)CrossRefGoogle Scholar
  6. 6.
    Golden, B.L., DeArmon, J.S., Baker, E.K.: Computational experiments with algorithms for a class of routing problems. Computers & Operations Research 10(1), 47–59 (1983)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Duhamel, C., Lacomme, P., Prins, C., Prodhon, C.: A memetic approach for the capacitated location routing problem. In: EU-MEeting 2008, Troyes, France (2008)Google Scholar
  8. 8.
    Duhamel, C., Lacomme, P., Prins, C., Prodhon, C.: A GRASPxELS approach for the capacitated location-routing problem. Computers & Operations Research 37(11), 1912–1923 (2010)zbMATHCrossRefGoogle Scholar
  9. 9.
    Duhamel, C., Lacomme, P., Prodhon, C.: Efficient frameworks for greedy split and new depth first search procedures for routing problems. Computers & Operations Research 38(4), 723–739 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research 31, 1985–2002 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Prins, C.: A GRASP x evolutionary local search hybrid for the vehicle routing problem. In: Pereira, F.B., Tavares, J. (eds.) Bio-Inspired Algorithms for the Vehicle Routing Problem. SCI, vol. 161, pp. 35–53. Springer (2009)Google Scholar
  12. 12.
    Prins, C.: Two memetic algorithms for heterogeneous fleet vehicle routing problems. Engineering Applications of Artificial Intelligence 22, 916–928 (2009)CrossRefGoogle Scholar
  13. 13.
    Ribeiro, C.C., Rosseti, I.: Efficient parallel cooperative implementations of GRASP heuristics. Parallel Computing 33(1), 21–35 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Tarantilis, C.D., Kiranoudis, C.T., Vassiliadis, V.S.: A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem. European Journal of Operational Research 152, 148–158 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Fiechter, C.N.: A parallel tabu search algorithm for large traveling salesman problems. Discrete Applied Mathematics 51(3), 243–267 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Lourenço, H., Martin, O., Stttzle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 321–353. Kluwer, Dordrecht (2003)Google Scholar
  17. 17.
    Bertsekas, D.P., Tsitsiklis, J.N., Wu, C.: Rollout algorithms for combinatorial optimization problems. Journal of Heuristics 3, 245–262 (1997)zbMATHCrossRefGoogle Scholar
  18. 18.
    Talbi, E.-G., Cahon, S., Melab, N.: Designing cellular networks using a parallel hybrid metaheuristic on the computational grid. Computer Communications 30(4), 698–713 (2007)CrossRefGoogle Scholar
  19. 19.
    Taillard, E.D.: A heuristic column generation method for the heterogeneous fleet VRP. RAIRO Operations Research 31(1), 1–14 (1999)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Guerriero, F., Mancini, M.: A cooperative parallel rollout algorithm for the sequential ordering problem. Parallel Computing 29(5), 663–677 (2003)CrossRefGoogle Scholar
  21. 21.
    Li, F., Golden, B.L., Wasil, E.A.: A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problems. Computers & Operations Research 34, 2734–2742 (2007)zbMATHCrossRefGoogle Scholar
  22. 22.
    López, F.G., Torres, M.G., Batista, B.M., Pérez, J.A.M., Moreno-Vega, J.M.: Solving feature subset selection problem by a parallel scatter search. European Journal of Operational Research 169(2), 477–489 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12, 568–581 (1964)CrossRefGoogle Scholar
  24. 24.
    Berger, J., Barkaoui, M.: A parallel hybrid genetic algorithm for the vehicle routing problem with time windows. Computers & Operations Research 31, 2037–2053 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Dongarra, J.: Performance of various computers using standard linear equations software. Report CS-89-85. University of Tennessee (2009)Google Scholar
  26. 26.
    Cordeau, J.-F., Gendreau, M., Hertz, A., Laporte, G., Sormany, J.S.: New heuristics for the vehicle routing problem. In: Langevin, A., Riopel, D. (eds.) Logistics Systems - Design and Optimization, pp. 279–298. Springer (2005)Google Scholar
  27. 27.
    Beasley, J.E.: Route-first cluster-second methods for vehicle routing. Omega 11, 403–408 (1983)CrossRefGoogle Scholar
  28. 28.
    Cadenas, J.M., Garrido, M.C., Muñoz, E.: Using machine learning in a cooperative hybrid parallel strategy of metaheuristics. Information Sciences 179(19), 3255–3267 (2009)CrossRefGoogle Scholar
  29. 29.
    Current, J.R., Marsh, M.: Multiobjective transportation network design and routing problems: Taxonomy and annotation. European Journal of Operational Research 65, 4–19 (1993)zbMATHCrossRefGoogle Scholar
  30. 30.
    Sörensen, K.: Distance measures based on the edit distance for permutation-type representations. In: Barry, A. (ed.) Proceedings of the Workshop on Analysis and Design of Representations and Operators (ADoRo), GECCO Conference, pp. 15–21 (2003)Google Scholar
  31. 31.
    Sörensen, K., Sevaux, M.: MA|PM: memetic algorithms with population management. Computers & Operations Research 33(5), 1214–1225 (2006)zbMATHCrossRefGoogle Scholar
  32. 32.
    Drummond, L.M.A., Ochi, L.S., Vianna, D.S.: An asynchronous parallel metaheuristic for the period vehicle routing problem. Future Generation Computer Systems 17(4), 379–386 (2001)zbMATHCrossRefGoogle Scholar
  33. 33.
    Ochi, L.S., Vianna, D.S., Drummond, L.M.A., Victor, A.O.: A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet. Future Generation Computer System 14, 285–292 (1998)CrossRefGoogle Scholar
  34. 34.
    Desrochers, M.: An algorithm for the shortest path problem with resource constraints. Technical report G-88-27. GERAD (1988)Google Scholar
  35. 35.
    Toulouse, M., Crainic, T.G., Thulasiraman, K.: Global optimization properties of parallel cooperative search algorithms: A simulation study. Parallel Computing 26(1), 91–112 (2000)zbMATHCrossRefGoogle Scholar
  36. 36.
    Caricato, P., Ghiani, G., Grieco, A., Guerriero, E.: Parallel tabu search for a pickup and delivery problem under track contention. Parallel Computing 29, 631–639 (2003)CrossRefGoogle Scholar
  37. 37.
    Lacomme, P., Prins, C., Ramdane-Chérif, W.: A Genetic Algorithm for the Capacitated Arc Routing Problem and Its Extensions. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) EvoIASP 2001, EvoWorkshops 2001, EvoFlight 2001, EvoSTIM 2001, EvoCOP 2001, and EvoLearn 2001. LNCS, vol. 2037, pp. 473–483. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  38. 38.
    Lacomme, P., Prins, C., Ramdane-Cherif, W.: Competitive memetic algorithms for arc routing problems. Annals of Operations Research 131, 159–185 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Toth, P., Vigo, D.: An overview of vehicle routing problems. In: The Vehicle Routing Problem, pp. 1–26. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia (2002)CrossRefGoogle Scholar
  40. 40.
    Baldacci, R., Battarra, M., Vigo, D.: Routing a heterogeneous fleet of vehicles. In: Wasil, E., Raghavan, S., Golden, B.L. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, vol. 43, pp. 3–27. Springer, Berlin (2008)CrossRefGoogle Scholar
  41. 41.
    Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. Journal of the Association for Computing Machinery 21, 168–173 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Ronald, S.: Distance functions for order-based encodings. In: Fogel, D. (ed.) Proceedings of the IEEE Conference on Evolutionary Computation, pp. 641–646 (1997)Google Scholar
  43. 43.
    Ronald, S.: More distance functions for order-based encodings. In: Proceedings of the IEEE Conference on Evolutionary Computation, pp. 558–563 (1998)Google Scholar
  44. 44.
    Porto, S.C.S., Kitajima, J.P.F.W., Ribeiro, C.C.: Efficient parallel cooperative implementations of GRASP heuristics performance evaluation of a parallel tabu search task scheduling algorithm. Parallel Computing 26(1), 73–90 (2000)zbMATHCrossRefGoogle Scholar
  45. 45.
    James, T., Rego, C., Glover, F.: A cooperative parallel tabu search algorithm for the quadratic assignment problem european. Journal of Operational Research 195(3), 810–826 (2009)zbMATHCrossRefGoogle Scholar
  46. 46.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6, 109–133 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Crainic, T.G., Toulouse, M., Gendreau, M.: Parallel asynchronous tabu search for multicommodity location-allocation with balancing requirements. Annals of Operations Research 63, 277–299 (1996)zbMATHCrossRefGoogle Scholar
  48. 48.
    Cormen, T.H., Leiserson, C.L., Rivest, M.L.: Introduction to algorithms. MIT Press (1990)Google Scholar
  49. 49.
    Bajart, V., Charles, C.: Systèmes d’information géographique. 3rd Year Project Report. ISIMA (2009),
  50. 50.
    Campos, V., Laguna, M., Martí, R.: Context-independent scatter and tabu search for permutation problems. INFORMS Journal on Computing 17, 111–122 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  51. 51.
    Bozejko, W.: Solving the flow shop problem by parallel programming. Journal of Parallel and Distributed Computing 69(5), 470–481 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christophe Duhamel
    • 1
  • Christophe Gouinaud
    • 2
  • Philippe Lacomme
    • 1
  • Caroline Prodhon
    • 2
  1. 1.Laboratoire d’Informatique (LIMOS, UMR CNRS 6158)Aubière CedexFrance
  2. 2.Institut Charles Delaunay (LOSI) and STMR (UMR CNRS 6279)Université de Technologie de TroyesTroyes CedexFrance

Personalised recommendations