Journal of Heuristics

, Volume 19, Issue 3, pp 497–524 | Cite as

A path relinking algorithm for a multi-depot periodic vehicle routing problem

  • Alireza Rahimi-Vahed
  • Teodor Gabriel Crainic
  • Michel Gendreau
  • Walter Rei


In this paper, we consider a multi-depot periodic vehicle routing problem which is characterized by the presence of a homogeneous fleet of vehicles, multiple depots, multiple periods, and two types of constraints that are often found in reality, i.e., vehicle capacity and route duration constraints. The objective is to minimize total travel costs. To tackle the problem, we propose an efficient path relinking algorithm whose exploration and exploitation strategies enable the algorithm to address the problem in two different settings: (1) As a stand-alone algorithm, and (2) As a part of a co-operative search algorithm called integrative co-operative search. The performance of the proposed path relinking algorithm is evaluated, in each of the above ways, based on standard benchmark instances. The computational results show that the developed PRA performs well, in both solution quality and computational efficiency.


Multi-depot periodic vehicle routing problem Path relinking Integrative co-operative search 


  1. Cordeau, J.F., Gendreau, M., Laporte, G.: A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30, 105–119 (1997)MATHCrossRefGoogle Scholar
  2. Coy, S.P., Golden, B.L., Runger, G.C., Wasil, E.A.: Using experimental design to find effective parameter settings for heuristics. J. Heuristics 7(1), 77–97 (2000)CrossRefGoogle Scholar
  3. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6, 80 (1959)MathSciNetMATHCrossRefGoogle Scholar
  4. Gendreau, M., Hertz, A., Laporte, G.: New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40, 1086–1094 (1992)MathSciNetMATHCrossRefGoogle Scholar
  5. Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Manag. Sci. 40, 1276–1290 (1994)MATHCrossRefGoogle Scholar
  6. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131(1–4), 109–133 (2004)MathSciNetMATHCrossRefGoogle Scholar
  7. Glover, F., Laguna, M.: Fundamentals of scatter search and path relinking. Control Cybern. 29(3), 653–684 (2000)MathSciNetMATHGoogle Scholar
  8. Hadjiconstantinou, E., Baldacci, R.: A multi-depot period vehicle routing problem arising in the utilities sector. J. Oper. Res. Soc. 49, 1239–1248 (1998)MATHGoogle Scholar
  9. Kang, K.H., Lee, Y.H., Lee, B.K.: An exact algorithm for multi depot and multi period vehicle scheduling problem. In: Computational Science and Its Applications-ICCSA, Lecture Notes in Computer Science, pp. 350–359. ICCSA, Springer-Verlag, Berlin, Heidelberg (2005)Google Scholar
  10. Kytöjoki, J., Nuortio, T., Bräysy, O., Gendreau, M.: An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comp. Oper. Res. 34(9), 2743–2757 (2007)MATHCrossRefGoogle Scholar
  11. Lahrichi, N., Crainic, T.G., Gendreau, M., Rei, W., Crisan, G.C., Vidal, T.: An integrative cooperative search framework for multi-decision-attribute combinatorial optimization. Technical Report, CIRRELT, p. 42 (2012)Google Scholar
  12. Parthanadee, P., Logendran, R.: Periodic product distribution from multi-depots under limited supplies. IIE Trans. 38(11), 1009–1026 (2006)CrossRefGoogle Scholar
  13. Smith, S.K., Eiben, A.E.: Parameter Tuning of Evolutionary Algorithms: Generalist and Specialist. Applications of Evolutionary Computation, LNCS vol. 6024, pp. 542–551. Springer, Heidelberg (2010)Google Scholar
  14. Toth, P., Vigo, D.: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia (2002)MATHCrossRefGoogle Scholar
  15. Vidal, T., Crainic, T.G., Gendreau, M., Lahrichi, N., Rei, W.: A hybrid genetic algorithm for multi-depots and periodic vehicle routing problems. Oper. Res. 60(3), 611–624 (2012)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alireza Rahimi-Vahed
    • 1
  • Teodor Gabriel Crainic
    • 2
  • Michel Gendreau
    • 3
  • Walter Rei
    • 2
  1. 1.Département Informatique et recherche opérationnelle and Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation (CIRRELT)Université de MontréalMontrealCanada
  2. 2.Département Management et technologie, ESG and Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation (CIRRELT)Université du Québec à MontréalMontrealCanada
  3. 3.Département de mathématiques et génie Industriel and Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation (CIRRELT)École PolytechniqueMontrealCanada

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