Abstract
The Vehicle Routing Problem with Time Windows is a complex combinatorial optimization problem which can be seen as a fusion of two well known sub-problems: the Travelling Salesman Problem and the Bin Packing Problem. Its main objective is to find the lowest-cost set of routes to deliver demand, using identical vehicles with limited capacity, to customers with fixed service time windows. In this paper, we consider the minimization of the number of routes and the total cost simultaneously. Although previous evolutionary studies have considered this problem, none of them has focused on the similarity of solutions in the population. We propose a method to measure route similarity and incorporate it into an evolutionary algorithm to solve the bi-objective VRPTW. We have applied this algorithm to a publicly available set of benchmark instances, resulting in solutions that are competitive or better than others previously published.
This is a preview of subscription content, log in via an institution to check access.
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
Berger, J., Barkaoui, M., Bräysi, O.: A Route-directed Hybrid Genetic Approach for the Vehicle Routing Problem with Time Windows. INFOR 41, 179–194 (2003)
Bräysy, O., Gendreau, M.: Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms. Transport. Sci. 39(1), 104–118 (2005)
Bräysy, O., Gendreau, M.: Vehicle Routing Problem with Time Windows, Part II: Metaheuristics. Transport. Sci. 39(1), 119–139 (2005)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE T. Evolut. Comput. 6(2), 182–197 (2002)
Desrochers, M., Desrosiers, J., Solomon, M.: A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows. Oper. Res. 40(2), 342–354 (1992)
Garcia-Najera, A., Bullinaria, J.A.: A Multi-Objective Density Restricted Genetic Algorithm for the Vehicle Routing Problem with Time Windows. In: 2008 UK Workshop on Computational Intelligence. Leicester, UK (2008)
Homberger, J., Gehring, H.: A Two-phase Hybrid Metaheuristic for the Vehicle Routing Problem with Time Windows. Eur. J. Oper. Res. 162, 220–238 (2005)
Jozefowicz, N., Semet, F., Talbi, E.: Multi-objective Vehicle Routing Problems. Eur. J. Oper. Res. 189, 293–309 (2008)
Le Bouthillier, A., Crainic, T.G.: A Cooperative Parallel Metaheuristic for Vehicle Routing with Time Windows. Comput. Oper. Res. 32, 1685–1708 (2005)
Martí, R., Laguna, M., Campos, V.: Scatter Search vs. Genetic Algorithms: An Experimental Evaluation with Permutation Problems. In: Rego, C., Alidaee, B. (eds.) Metaheuristic Optimization Via Adaptive Memory and Evolution: Tabu Search and Scatter Search, pp. 263–282. Kluwer Academic, Dordrecht (2005)
McGill, R., Tukey, J.W., Larsen, W.A.: Variations of Box Plots. Am. Stat. 32(1), 12–16 (1978)
Ombuki, B., Ross, B.J., Hanshar, F.: Multi-Objective Genetic Algorithms for Vehicle Routing Problem with Time Windows. Appl. Intell. 24(1), 17–30 (2006)
Potvin, J.Y., Bengio, S.: The Vehicle Routing Problem with Time Windows — Part II: Genetic Search. INFORMS J. Comp. 8, 165–172 (1996)
Ronald, S.: More distance functions for order-based encodings. In: 1998 IEEE International Conference on Evolutionary Computation, pp. 558–563. IEEE Press, Piscataway (1998)
Sörensen, K.: Distance Measures Based on the Edit Distance for Permutation-type Representations. J. Heuristics 13(1), 35–47 (2007)
Solomon, M.M.: Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints. Oper. Res. 35(2), 254–265 (1987)
Tan, K.C., Chew, Y.H., Lee, L.H.: A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows. Comput. Optim. Appl. 34(1), 115–151 (2006)
Tavares, J., Machado, P., Pereira, F.B., Costa, E.: On the Influence of GVR in Vehicle Routing. In: 2003 ACM Symposium on Applied Computing, pp. 753–758. ACM Press, New York (2003)
Toth, P., Vigo, D.: The Vehicle Routing Problem. SIAM, Philadelphia (2001)
Zhu, K.Q.: A Diversity-Controlling Adaptive Genetic Algorithm for the Vehicle Routing Problem with Time Windows. In: 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 176–183. IEEE Computer Society Press, Washington (2003)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Giannakoglou, K., Tsahalis, D., Periaux, J., Papailiou, K., Fogarty, T. (eds.) Evolutionary Methods for Design, Optimisation and Control, pp. 19–26. CIMNE (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Garcia-Najera, A., Bullinaria, J.A. (2009). Bi-objective Optimization for the Vehicle Routing Problem with Time Windows: Using Route Similarity to Enhance Performance. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, JK., Sevaux, M. (eds) Evolutionary Multi-Criterion Optimization. EMO 2009. Lecture Notes in Computer Science, vol 5467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01020-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-01020-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01019-4
Online ISBN: 978-3-642-01020-0
eBook Packages: Computer ScienceComputer Science (R0)