Applying the ANT System to the Vehicle Routing Problem

  • Bernd Bullnheimer
  • Richard F. Hartl
  • Christine Strauss


In this paper we use a recently proposed metaheuristic, the Ant System, to solve the Vehicle Routing Problem in its basic form, i.e., with capacity and distance restrictions, one central depot and identical vehicles. A “hybrid” Ant System algorithm is first presented and then improved using problem-specific information (savings, capacity utilization). Experiments on various aspects of the algorithm and computational results for fourteen benchmark problems are reported and compared to those of other metaheuristic approaches such as Tabu Search, Simulated Annealing and Neural Networks.


Tabu Search Capacity Utilization Vehicle Route Problem Quadratic Assignment Problem Vehicle Route 
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]
    B. Bullnheimer, R.F. Hartl, and C. Strauss. A new rank based version of the ant system: a computational study. Working Paper No.1, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna, 1997.Google Scholar
  2. [2]
    B. Bullnheimer, G. Kotsis, and C. Strauss. Parallelization Strategies for the Ant System. Paper presented at Conference on High Performance Software for Nonlinear Optimization: Status and Perspectives (HPSNO’97), Ischia (Italy), 4–6 June 1997.Google Scholar
  3. [3]
    E.K. Burke, D.G. Elliman, and R.F. Weare. A Hybrid Genetic Algorithm for Highly Constrained Timetabling Problems. In Proc. 6-th Int. Conf. Genetic Algorithms (ICGA’ 95), pages 605–610, Morgan Kaufmann, 1995.Google Scholar
  4. [4]
    N. Christofides, A. Mingozzi, and P. Toth. The Vehicle Routing Problem. In N. Christofides, A. Mingozzi, P. Toth, and C. Sandi, editors, Combinatorial Optimization, pages 315–338, Wiley, 1979.Google Scholar
  5. [5]
    G. Clarke, and J.W. Wright. Scheduling of Vehicles from a Central Depot to a Number of Delivery Points. Oper. Res. 12 (1964), pages 568–581.CrossRefGoogle Scholar
  6. [6]
    A. Colorni, M. Dorigo, and V. Maniezzo. Distributed Optimization by Ant Colonies. In F. Varela, and P. Bourgine, editors, Proc. Europ. Conf. Artificial Life (ECAL’91), pages 134–142, Elsevier Publishing, 1991.Google Scholar
  7. [7]
    A. Colorni, M. Dorigo, V. Maniezzo, and M. Trubian. Ant system for Job-Shop Scheduling. JORBEL — Belgian Journal of Operations Research, Statistics and Computer Science 34 (1994) 1, pages 39–53.Google Scholar
  8. [8]
    D. Costa, and A. Hertz. Ants can colour graphs. J. Oper. Res. Soc. 48 (1997), pages 295–305.Google Scholar
  9. [9]
    G.A. Croes. A Method for solving Traveling-Salesman Problems. Oper. Res. 6 (1958), pages 791–812.CrossRefGoogle Scholar
  10. [10]
    M. Dorigo. Optimization, Learning and Natural Algorithms. Doctoral Dissertation, Politecnico di Milano, Italy (in Italian), 1992.Google Scholar
  11. [11]
    M. Dorigo, and L.M. Gambardella. Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Trans. Evol. Comput. 1 (1997) 1, pages 53–66.CrossRefGoogle Scholar
  12. [12]
    M. Dorigo, V. Maniezzo, and A. Colorili. Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans. Sys., Man, Cybernetics 26 (1996) 1, pages 29–41.CrossRefGoogle Scholar
  13. [13]
    M. Gendreau, A. Hertz, and G. Laporte. A Tabu Search Heuristic for the Vehicle Routing Problem. Management Sci. 40 (1994), pages 1276–1290.CrossRefGoogle Scholar
  14. [14]
    H. Ghaziri. Supervision in the Self-Organizing Feature Map: Application to the Vehicle Routing Problem. In I. Osman, and J. Kelly, editors, Meta-Heuristics: Theory & Applications, pages 651–660, Kluwer Academic Publishers, 1996.Google Scholar
  15. [15]
    B.E. Gillett, and L.R. Miller. A Heuristic Algorithm for the Vehicle Dispatch Problem. Oper. Res. 22 (1974) pages 340–347.CrossRefGoogle Scholar
  16. [16]
    D. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 1989.Google Scholar
  17. [17]
    H. Kopfer, G. Pankratz, and E. Erkens. Entwicklung eines hybriden Genetischen Algorithmus zur Tourenplanug. Oper. Res. Spekt. 16 (1994), pages 21–31.CrossRefGoogle Scholar
  18. [18]
    V. Maniezzo, A. Colorni, and M. Dorigo. The Ant System applied to the Quadratic Assignment Problem. Technical Report IRIDIA/94-28, Université Libre de Bruxelles, Belgium, 1994.Google Scholar
  19. [19]
    I. Osman. Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann. Oper. Res. 41 (1993), pages 421–451.CrossRefGoogle Scholar
  20. [20]
    E. Pesch. Learning in Automated Manufacturing. Physica, 1994.Google Scholar
  21. [21]
    C. Rego, and C. Roucairol. A Parallel Tabu Search Algorithm Using Ejection Chains for the Vehicle Routing Problem. In I. Osman, and J. Kelly, editors, Meta-Heuristics: Theory & Applications, pages 661–675, Kluwer Academic Publishers, 1996.Google Scholar
  22. [22]
    Y. Rochat, and E. Taillard. Probabilistic Diversification and Intensification in Local Search for Vehicle Routing. J. Heuristics 1 (1995), pages 147–167.CrossRefGoogle Scholar
  23. [23]
    T. Stuetzle, and H. Hoos. The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem. Proc. ICEC’97 — 1997 IEEE 4-th Int. Conf. Evolutionary Computation, IEEE Press, pages 308–313.Google Scholar
  24. [24]
    E. Taillard. Parallel Iterative Search Methods for Vehicle Routing Problems. Networks 23 (1993), pages 661–673.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Bernd Bullnheimer
    • 1
  • Richard F. Hartl
    • 1
  • Christine Strauss
    • 1
  1. 1.Department of Management ScienceUniversity of ViennaViennaAustria

Personalised recommendations