Journal of Combinatorial Optimization

, Volume 10, Issue 4, pp 327–343 | Cite as

Ant Colony System for a Dynamic Vehicle Routing Problem

  • R. Montemanni
  • L. M. Gambardella
  • A. E. Rizzoli
  • A. V. Donati


An aboundant literature on vehicle routing problems is available. However, most of the work deals with static problems, where all data are known in advance, i.e. before the optimization has started.

The technological advances of the last few years give rise to a new class of problems, namely the dynamic vehicle routing problems, where new orders are received as time progresses and must be dynamically incorporated into an evolving schedule.

In this paper a dynamic vehicle routing problem is examined and a solving strategy, based on the Ant Colony System paradigm, is proposed.

Some new public domain benchmark problems are defined, and the algorithm we propose is tested on them.

Finally, the method we present is applied to a realistic case study, set up in the city of Lugano (Switzerland).


dynamic vehicle routing ant colony optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. E. Bonabeau, M. Dorigo, and G. Theraulaz, “Inspiration for optimization from social insect behaviour,” Nature, vol. 406, pp. 39–42, 2000.CrossRefGoogle Scholar
  2. N. Christofides and J. Beasley, “The period routing problem,” Networks, vol. 14, pp. 237–256, 1984.zbMATHGoogle Scholar
  3. A. Colorni, M. Dorigo, and V. Maniezzo, “Distributed optimization by ant colonies,” in Elsevier Publishing (eds.), European Conference on Artificial Life 1991 (ECAL91), 1991, pp. 134–142.Google Scholar
  4. M. Dorigo, G. Di Caro, and L.M. Gambardella, “Ant algorithms for discrete optimization,” Artificial Life, vol. 5, pp. 137–172, 1999.CrossRefGoogle Scholar
  5. M. Dorigo, V. Maniezzo, and A. Colorni, “The ant system: optimization by a colony of cooperating agents,” IEEE Transactions on Systems, Man and Cybernetics—Part B: Cybernetics, vol. 26, no. 1, 29–41, 1996.Google Scholar
  6. M. Fisher, R. Jakumar, and L. van Wassenhove, “A generalized assignment heuristic for vehicle routing,” Networks, vol. 11, pp. 109–124, 1981.MathSciNetGoogle Scholar
  7. L.M. Gambardella and M. Dorigo, “Solving symmetric and asymmetric TSPs by ant colonies,” in IEEE Conference on Evolutionary Computation (ICEC96), 1996, pp. 622–627.Google Scholar
  8. L.M. Gambardella, É. Taillard, and G. Agazzi, “MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows,” in D. Corne et al. (eds.), New Ideas in Optimization, pp. 63–76, 1999.Google Scholar
  9. M. Gendreau, F. Guertin, J.-Y. Potvin, and É. Taillard, “Parallel tabu search for real-time vehicle routing and dispatching,” Transportation Science, vol. 33, no. 4, pp. 381–390, 1999.Google Scholar
  10. M. Gendreau, G. Laporte, and R. Séguin, “Stochastic vehicle routing,” European Journal of Operational Research, vol. 88, pp. 3–12, 1996a.CrossRefzbMATHGoogle Scholar
  11. M. Gendreau, G. Laporte, and R. Séguin, “A tabu search heuristic for the vehicle routing problem with stochastic demands and customers,” Operations Research, vol. 44, pp. 469–477, 1996b.zbMATHGoogle Scholar
  12. M. Gendreau and J.-Y. Potvin, “Dynamic vehicle routing and dispatching,” in T.G. Crainic and G. Laporte (eds.), Fleet Management and Logistic, pp. 115–226, 1998.Google Scholar
  13. M. Guntsch and M. Middendorf, “Pheromone modification strategies for ant algorithms applied to dynamic TSP,” in E.J.W. Boers et al. (eds.), Application of evolutionary computing: Proceedings of EcoWorkshops 2001, volume Lecture Notes in Computer Science 2037, 2001, pp. 213–222.Google Scholar
  14. M. Guntsch and M. Middendorf, “Applying population based ACO to dynamic optimization problems,” in M. Dorigo et al. (eds.), ANTS 2002, volume Lecture Notes in Computer Science 2463, 2002, pp. 111–122.Google Scholar
  15. L.M. Hvattum, A. Lokketangen, and G. Laporte, “A heuristic solution method to a stochastic vehicle routing problem,” in Proceedings of TRISTAN V—The Fifth Triennial Symposium on Transportation Analysis, 2004.Google Scholar
  16. S. Ichoua, M. Gendreau, and J.-Y. Potvin, “Diversion issues in real-time vehicle dispatching,” Transportation Science, vol. 34, no. 4, pp. 426–438, November 2000.Google Scholar
  17. P. Kilby, P. Prosser, and P. Shaw, “Dynamic VRPs: A study of scenarios,” Technical Report APES-06-1998, University of Strathclyde, U.K., 1998.Google Scholar
  18. G. Kontoravdis and J.F. Brand, “A GRASP for the vehicle routing problem with time windows,” ORSA Journal on Computing, vol. 7, no. 1, pp. 10–23, 1995.Google Scholar
  19. H. Psaraftis, “Dynamic vehicle routing problems,” in B.L. Golden and A.A. Assad (eds.), Vehicle Routing: methods and Studies, 1988, pp. 223–248.Google Scholar
  20. H. Psaraftis, “Dynamic vehicle routing: status and prospects,” Annals of Operations Research, vol. 61, pp. 143–164, 1995.CrossRefzbMATHGoogle Scholar
  21. M.G.C. Resende and C.C. Ribeiro, “Greedy Randomized Adaptive search procedures,” in F. Glover and G. Kochenberger (eds.), Handbook of Metaheuristics, 2003, pp. 219–249.Google Scholar
  22. M.W.P. Savelsbergh and M. Sol, “DRIVE: Dynamic routing of independent VEhicles,” Operations Research, vol. 46, pp. 474–490, 1998.CrossRefzbMATHGoogle Scholar
  23. M. Sol, Column generation techniques for pickup and delivery problems. PhD thesis, Technische Universiteit Eindhoven, The Netherlands, 1994.Google Scholar
  24. É. Taillard, “Parallel iterative search methods for vehicle-routing problems,” Networks, vol. 23, no. 8, pp. 661–673, 1994.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • R. Montemanni
    • 1
  • L. M. Gambardella
    • 1
  • A. E. Rizzoli
    • 1
  • A. V. Donati
    • 1
  1. 1.Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA)Manno-LuganoSwitzerland

Personalised recommendations