Skip to main content
Log in

Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem

  • Published:
Journal of Zhejiang University-SCIENCE A Aims and scope Submit manuscript

Abstract

Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid approximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimization (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baker, B.M., Ayechew, M.A., 2003. A genetic algorithm for the vehicle routing problem. Computers & Operations Research, 30(5):787–800. [doi: 10.1016/S0305-0548(02)00051-5]

    Article  MathSciNet  MATH  Google Scholar 

  • Bell, J.E., McMullen, P.R., 2004. Ant colony optimization techniques for the vehicle routing problem. Advanced Engineering Informatics, 18(1):41–48. [doi: 10.1016/j.aei.2004.07.001]

    Article  Google Scholar 

  • Bodin, L., Golden, B.L., Assad, A., Ball, M.O., 1983. The state of the art in the routing and scheduling of vehicles and crews. Computers & Operations Research, 10:69–221.

    MathSciNet  Google Scholar 

  • Christofides, N., Mignozzi, A., Toth, P., 1981. Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations. Mathematical Programming, 20(1):255–282. [doi: 10.1007/BF01589353]

    Article  MathSciNet  MATH  Google Scholar 

  • Cordeau, J.F., Laporte, G., Mercier, A., 2001. A unified tabu search heuristic for vehicle routing problems with time windows. Journal of the Operational Research Society, 52(8):928–936. [doi: 10.1057/palgrave/jors/2601163]

    Article  MATH  Google Scholar 

  • Dantzig, G.B., Ramser, R.H., 1959. The truck dispatching problem. Management Science, 6:80–91.

    Article  MathSciNet  MATH  Google Scholar 

  • Eberhart, R., Kennedy, J., 1995. A New Optimizer Using Particle Swarm Theory. Proceeding of the Sixth International Symposium on Micro Machine and Human Science, p.39–43.

  • Gendreau, M., Hertz, A., Laporte G., 1994. A tabu search heuristic for the vehicle routing problem. Management Science, 40:1276–1290.

    Article  MATH  Google Scholar 

  • Hasan, M., Osman, I.H., 1995. Local search algoirthm for the maximal planar layout problem. International Transactions in Operational Research, 2(1):89–106. [doi: 10.1016/0969-6016(95)00029-7]

    Article  MATH  Google Scholar 

  • Kennedy, J., Eberhart, R., 1995. Particle Swarm Optimization. Proceeding of the 1995 IEEE International Conference on Neural Network, p.1942–1948.

  • Laporte, G., 1992. The vehicle routing problem: an overview of exact and approximate algorithms. European Journal of Operational Research, 59(3):345–358. [doi: 10.1016/0377-2217(92)90192-C]

    Article  MATH  Google Scholar 

  • Osman, I.H., 1993. Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of Operations Research, 41(4):421–451. [doi: 10.1007/BF02023004]

    Article  MathSciNet  MATH  Google Scholar 

  • Osman, I.H., Potts, C.N., 1989. Simulated annealing for permutation flow shop scheduling. Omega, 17(6):551–557. [doi: 10.1016/0305-0483(89)90059-5]

    Article  Google Scholar 

  • Salman, A., Ahmad, I., Madani, S.A., 2002. Particle swarm optimization for task assignment problem. Microprocessors and Microsystems, 26(8):363–371. [doi: 10.1016/S0141-9331(02)00053-4]

    Article  Google Scholar 

  • Shi, Y., Eberhart, R., 1999. Empirical Study of Particle Swarm Optimization. Proceedings of Congress on Evolutionary Computation, p.1945–1950.

  • Shigenori, N., Takamu, G.J., Toshiki, Y., Yoshikazu, F., 2003. A hybrid particle swarm optimization for distribution state estimation. IEEE Trans. on Power Systems, 18(1):60–68. [doi: 10.1109/TPWRS.2002.807051]

    Article  Google Scholar 

  • Toth, P., Vigo, D., 1998. Exact Solution of the Vehicle Routing Problem. In: Crainic, T.G., Laporte, G. (Eds.), Fleet Management and Logistics. Kluwer Academic Publishers, Norwell, MA, p.1–31.

    Chapter  Google Scholar 

  • Toth, P., Vigo, D., 2002. The Vehicle Routing Problem. SIAM Monographs on Discrete Mathematics and Applications, Vol. 9. SIAM, Philadelphia, PA.

    Google Scholar 

  • van Laarhoven, P.J.M., Aarts, E.H.L., Lenstra, J.K., 1992. Job shop scheduling by simulated annealing. Operations Research, 40:113–125.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, Z.Z., Cheng, J.X., Fang, H.G., Qian, F.L., 2004. A hybrid optimization algorithm solving vehicle routing problems. Operations Research and Management Science, 13:48–52 (in Chinese).

    Google Scholar 

  • Xia, W.J., Wu, Z.M., 2005. An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Computers & Industrial Engineering, 48(2):409–425. [doi: 10.1016/j.cie.2005.01.018]

    Article  MathSciNet  Google Scholar 

  • Yang, S.Y., Wang, M., Jiao, L.C., 2004. A Quantum Particle Swarm Optimization. Proceedings of the 2004 IEEE Congress on Evolutionary Computation, 1:320–324.

    Article  Google Scholar 

  • Zhao, Y.W., Wu, B., Jiang, L., Dong, H.Z., Wang, W.L., 2004. Study of the optimizing of physical distribution routing problem based on genetic algorithm. Computer Integrated Manufacturing Systems, 10(3):303–306 (in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project (No. 60174009) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Al., Yang, Gk. & Wu, Zm. Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J. Zhejiang Univ. - Sci. A 7, 607–614 (2006). https://doi.org/10.1631/jzus.2006.A0607

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.2006.A0607

Key words

CLC number

Navigation