Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
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.
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.
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.
D. Costa, and A. Hertz. Ants can colour graphs. J. Oper. Res. Soc. 48 (1997), pages 295–305.
G.A. Croes. A Method for solving Traveling-Salesman Problems. Oper. Res. 6 (1958), pages 791–812.
M. Dorigo. Optimization, Learning and Natural Algorithms. Doctoral Dissertation, Politecnico di Milano, Italy (in Italian), 1992.
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.
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.
M. Gendreau, A. Hertz, and G. Laporte. A Tabu Search Heuristic for the Vehicle Routing Problem. Management Sci. 40 (1994), pages 1276–1290.
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.
B.E. Gillett, and L.R. Miller. A Heuristic Algorithm for the Vehicle Dispatch Problem. Oper. Res. 22 (1974) pages 340–347.
D. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 1989.
H. Kopfer, G. Pankratz, and E. Erkens. Entwicklung eines hybriden Genetischen Algorithmus zur Tourenplanug. Oper. Res. Spekt. 16 (1994), pages 21–31.
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.
I. Osman. Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann. Oper. Res. 41 (1993), pages 421–451.
E. Pesch. Learning in Automated Manufacturing. Physica, 1994.
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.
Y. Rochat, and E. Taillard. Probabilistic Diversification and Intensification in Local Search for Vehicle Routing. J. Heuristics 1 (1995), pages 147–167.
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.
E. Taillard. Parallel Iterative Search Methods for Vehicle Routing Problems. Networks 23 (1993), pages 661–673.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bullnheimer, B., Hartl, R.F., Strauss, C. (1999). Applying the ANT System to the Vehicle Routing Problem. In: Voß, S., Martello, S., Osman, I.H., Roucairol, C. (eds) Meta-Heuristics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5775-3_20
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5775-3_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7646-0
Online ISBN: 978-1-4615-5775-3
eBook Packages: Springer Book Archive