Solving the CVRP Problem Using a Hybrid PSO Approach

Part of the Studies in Computational Intelligence book series (SCI, volume 465)


The goal of the capacitated vehicle routing problem (CVRP) is to minimize the total distance of vehicle routes under the constraints of vehicles’ capacity. CVRP is classified as NP-hard problems and a number of meta-heuristic approaches have been proposed to solve the problem. This paper aims to develop a hybrid algorithm combining a discrete Particle Swarm Optimization (PSO) with Simulated Annealing (SA) to solve CVRPs. The two-stage approach of CVRP (cluster first and route second) has been adopted in the algorithm. To save computation time, a short solution representation has been adopted. The computational results demonstrate that our hybrid algorithm can effectively solve CVRPs within reasonable time.


Vehicle routing problem Particle swarm optimization Simulated annealing 


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  1. 1.
    Dantzig, G.B., Ramser, J.H.: The Truck Dispatching Problem. Manage. Sci. 6(1), 80–91 (1959)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Jozefowiez, N., Semet, F., Talbi, E.G.: Multi-objective Vehicle Routing Problems. Eur. J. Oper. Res. 189, 293–309 (2008)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Cordeau, J.F., Laporte, G., Savelsbergh, M.W.P., Vigo, D.: Chapter 6 Vehicle Routing. In: Barnhart, C., Laporte, G. (eds.) Handbook in Operations Research and Management Science, vol. 14, pp. 367–428. Elsevier (2007)Google Scholar
  4. 4.
    Baker, B.M., Ayechew, M.A.: A Genetic Algorithm for the Vehicle Routing Problem. Comput. Oper. Res. 30, 787–800 (2003)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Bell, J.E., McMullen, P.R.: Ant Colony Optimization Techniques for the Vehicle Routing Problem. Adv. Eng. Inform. 18, 41–48 (2004)CrossRefGoogle Scholar
  6. 6.
    Zhang, X., Tang, L.: A New Hybrid Ant Colony Optimization Algorithm for the Vehicle Routing Problem. Pattern Recognit. Lett. 30, 848–855 (2009)CrossRefGoogle Scholar
  7. 7.
    Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  8. 8.
    Chen, A.L., Yang, G.K., Wu, Z.M.: Hybrid Discrete Particle Swarm Optimization Algorithm for Capacitated Vehicle Routing Problem. Journal of Zhejiang University Science A 7(4), 607–614 (2006)MATHCrossRefGoogle Scholar
  9. 9.
    Ai, T.J., Kachitvichyanukul, V.: Particle Swarm Optimization and Two Solution Representations for Solvingthe Capacitated Vehicle Routing Problem. Comput. Ind. Eng. 56, 380–387 (2009)CrossRefGoogle Scholar
  10. 10.
    Marinakis, Y., Marinaki, M., Dounias, G.: A Hybrid Particle Swarm Optimization Algorithm for the Vehicle Routing Problem. Eng. Appl. Artif. Intell. 23(4), 463–472 (2010)CrossRefGoogle Scholar
  11. 11.
    Shi, Y., Eberhart, R.: A Modified Particle Swarm Optimizer. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 69–73 (1998)Google Scholar
  12. 12.
    Jarboui, B., Cheikh, M., Siarry, P., Rebai, A.: Combinatorial Particle Swarm Optimization (CPSO) for PartitionalClustering Problem. Appl. Math. Comput. 92, 337–345 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Patterson, D.A., Hennessy, J.L.: Computer Organization and Design: the Hardware/Software Interface. Morgan Kaufmann, Burlington (2011)MATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Information ManagementTatung UniversityTaipeiTaiwan

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