Abstract
In this paper we propose a hybrid approach for solving the capacitated vehicle routing problem (CVRP). We combine an Ant Colony System (ACS) with a Savings algorithm and, then, we improve solutions by a local search heuristic. The CVRP is a class of well-known NP-hard combinatorial optimization problem, which can be formally defined as a complete graph G=(V,E) where V={0, ... ,n} is a set of vertices and E is a set of arcs [4]. The vertex {0} represents the depot and the other vertices represent customers. The cost of travel between vertices i and j is denoted d ij and represents the distance or the travel time. We assume that costs are symmetric(i.e. d ij = d ji ), and an unlimited fleet of identical vehicles, each of capacity Q>0, is available. Each customer i has a demand q i , with 0<q i ≤ Q. Each customer must be served by a single vehicle and no vehicle can serve a set of customers whose demand exceeds its capacity. The task is to find a set of vehicle routes of minimum cost, where each vehicle used leaves from and returns to the depot. In the following, we explain our algorithm then, we give results and conclusions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bullnheimer, B., Hartl, R.F., Strauss, C.: An improved ant system algorithm for the vehicle routing problem. Annals of Operations Research 89, 319–328 (1999)
Doerner, K., Gronalt, M., Hartl, R.F., Reiman, M., Strauss, C., Stummer, M.: SavingsAnts for the Vehicle Routing Problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 11–20. Springer, Heidelberg (2002)
Dorigo, M., Gambardella, L.: Ant Colony System: A Cooperative Learning Approach to the Travelling Salesman Problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)
Letchford, A.N., Eglese, R.W., Lysgaard, J.: Multistars, Partial Multistars and the Capacitated Vehicle Routing Problem (2001), Technical Report available at http://www.lancs.ac.uk/staff/letchfoa/pubs.htm
Paessens, H.: The savings algorithm for the vehicle routing problem. Eur. J. Oper. Res. 34, 336–344 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouhafs, L., Hajjam, A., Koukam, A. (2004). A Hybrid Ant Colony System Approach for the Capacitated Vehicle Routing Problem. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds) Ant Colony Optimization and Swarm Intelligence. ANTS 2004. Lecture Notes in Computer Science, vol 3172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28646-2_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-28646-2_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22672-7
Online ISBN: 978-3-540-28646-2
eBook Packages: Springer Book Archive