Abstract
In this paper, we address a bi-objective vehicle routing problem in which the total length of routes is minimized as well as the balance of routes, i.e. the difference between the maximal route length and the minimal route length. For this problem, we propose an implementation of the standard multi-objective evolutionary algorithm NSGA II. To improve its efficiency, two mechanisms have been added. First, a parallelization of NSGA II by means of an island model is proposed. Second, an elitist diversification mechanism is adapted to be used with NSGA II. Our method is tested on standard benchmarks for the vehicle routing problem. The contribution of the introduced mechanisms is evaluated by different performance metrics. All the experimentations indicate a strict improvement of the generated Pareto set.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lenstra, J.K., Rinnooy Kan, A.H.G.: Complexity of vehicle routing and scheduling problem. Networks 11, 221–227 (1981)
Toth, P., Vigo, D.: The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, vol. 9. SIAM, Philadelphia (2001)
Lee, T., Ueng, J.: A study of vehicle routing problems with load-balancing. International Journal of Physical Distribution and Logistics Management 29, 646–658 (1999)
Ribeiro, R., Lourenço, H.R.: A multi-objective model for a multi period distribution management problem. In: MIC 2001, pp. 97–102 (2001)
Corberan, A., Fernandez, E., Laguna, M., Marti, R.: Heuristic solutions to the problem of routing school buses with multiple objectives. Journal of the Operational Research Society 53, 427–435 (2002)
El-Sherbeny, N.: Resolution of a vehicle routing problem with multi-objective simulated annealing method. PhD thesis, Faculté Polytechnique de Mons (2001)
Christofides, N., Eilon, S.: An algorithm for the vehicle dispatching problem. Operational Research Quarterly 20, 309–318 (1969)
Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (eds.): Combinatorial Optimization. John Wiley, Chichester (1979)
Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Management Science 40, 1276–1290 (1994)
Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Computers and Operations Research (2004) (Article in Press)
Deb, K., Agrawal, S., Pratab, A., Meyunivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Transactions on Evolutionary Computing, 182–197 (2002)
Jozefowiez, N., Semet, F., Talbi, E.-G.: Parallel and hybrid models for multi-objective optimization: Application to the vehicle routing problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 271–280. Springer, Heidelberg (2002)
Jozefowiez, N.: Modélisation et résolution approchées de problèmes de tournées multi-objectif. PhD thesis, Laboratoire d’Informatique Fondamentale de Lille, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France (2004)
Potvin, J.Y., Bengio, S.: The vehicle routing problem with time windows part ii: genetic search. INFORMS Journal on Computing 8(8) (1996)
Knowles, J., Corne, D.: On metrics for comparing nondominated sets. In: Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 711–726. IEEE Service Center, Los Alamitos (2002)
Zitzler, E.: Evolutionary algorithm for multiobjective optimization: Methods and applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jozefowiez, N., Semet, F., Talbi, EG. (2006). Enhancements of NSGA II and Its Application to the Vehicle Routing Problem with Route Balancing. In: Talbi, EG., Liardet, P., Collet, P., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2005. Lecture Notes in Computer Science, vol 3871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11740698_12
Download citation
DOI: https://doi.org/10.1007/11740698_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33589-4
Online ISBN: 978-3-540-33590-0
eBook Packages: Computer ScienceComputer Science (R0)