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A Hybrid Bat Algorithm with Path Relinking for the Capacitated Vehicle Routing Problem

  • Yongquan ZhouEmail author
  • Qifang Luo
  • Jian Xie
  • Hongqing Zheng
Chapter
Part of the Modeling and Optimization in Science and Technologies book series (MOST, volume 7)

Abstract

The capacitated vehicle routing problem (CVRP) is an NP-hard problem with both engineering and theoretical interests. In this paper, a hybrid bat algorithm with path relinking (HBA-PR) is proposed to solve CVRP. The HBA-PR is constructed based on the framework of the continuous bat algorithm, the greedy randomized adaptive search procedure (GRASP) and path relinking are effectively integrated into the bat algorithm. Moreover, in order to further improve the performance, the random subsequences and single-point local search are operated with certain loudness (a probability). In order to verify the effectiveness of our approach and its efficiency and compare with other existing methodologies, several classical CVRP instances from three classes of CVRP benchmarks are selected to test. Experimental results and comparisons show the HBA-PR is effective for solving CVRPs.

Keywords

Bat algorithm Capacitated vehicle routing problem Path relinking GRASP Metaheuristic algorithm 

Notes

Acknowledgments

This work is supported by the National Science Foundation of China under Grants No.s 61165015 and 61463007. The Key Project of Guangxi Science Foundation under Grant No. 2012GXNSFDA053028, Key Project of Guangxi High School Science Foundation under Grant No. 20121ZD008.

References

  1. 1.
    Dantzig, G., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6, 80–91 (1959)Google Scholar
  2. 2.
    Haimovich, M., Rinnooy Kan, A.H.G., Stougie, L.: Analysis of heuristics for vehicle routing problems. In: Golden, B.L., Assad, A.A. (eds.) Vehicle Routing: Methods and Studies. Elsevier, Amsterdam, North-Holland (1988)Google Scholar
  3. 3.
    Toth, P., Tramontani, A.: An integer linear programming local search for capacitated vehicle routing problems. In: The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 275–295. Springer, New York (2008)Google Scholar
  4. 4.
    Nazif, H., Lee, L.S.: Optimised crossover genetic algorithm for capacitated vehicle routing problem. Appl. Math. Model. 36(5), 2110–2117 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ai, T.J., Kachitvichyanukul, V.: Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Comput. Ind. Eng. 56(1), 380–387 (2009)CrossRefGoogle Scholar
  6. 6.
    Szeto, W.Y., Wu, Y.Z., Ho, S.C.: An artificial bee colony algorithm for the capacitated vehicle routing problem. Eur. J. Oper. Res. 215(1), 126–135 (2011)CrossRefGoogle Scholar
  7. 7.
    Chen, P., Huang, H.K., Dong, X.Y.: Iterated variable neighborhood descent algorithm for the capacitated vehicle routing problem. Expert Syst. Appl. 37(2), 1620–1627 (2010)CrossRefGoogle Scholar
  8. 8.
    Yurtkuran, A., Emel, E.: A new Hybrid Electromagnetism-like Algorithm for capacitated vehicle routing problems. Expert Syst. Appl. 37(4), 3427–3433 (2010)CrossRefGoogle Scholar
  9. 9.
    Juan, A.A., Faulin, J., Ruiz, R., Barrios, B., Caballé, S.: The SR-GCWS hybrid algorithm for solving the capacitated vehicle routing problem. Appl. Soft Comput. 10(1), 215–224 (2010)CrossRefGoogle Scholar
  10. 10.
    Zheng, H.Q., Zhou, Y.Q., Luo, Q.F.: A hybrid cuckoo search algorithm-GRASP for vehicle routing problem. J. Convergence Inf. Technol. 8(3) (2013)Google Scholar
  11. 11.
    Yang, X.S.: A new metaheuristic bat-Inspired algorithm. Nature Inspired Cooperative Strategies for Optimization (NICSO). SCI 284, B65–B74 (2010)Google Scholar
  12. 12.
    Gandomi, A.H., Yang, X.S., Alavi, A.H., Talatahari, S.: Bat algorithm for constrained optimization tasks. Neural Comput. Appl. 1–17 (2012)Google Scholar
  13. 13.
    Yang, X.S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29, 464–483 (2012)CrossRefGoogle Scholar
  14. 14.
    Mishra, S., Shaw, K., Mishra, D.: A new meta-heuristic bat inspired classification approach for microarray data. Procedia Technol. 4, 802–806 (2012)CrossRefGoogle Scholar
  15. 15.
    Xie, J., Zhou, Y.Q., Chen, H.: A novel bat algorithm based on differential operator and Lévy-flights trajectory. Comput. Intell. Neurosci. http://dx.doi.org/10.1155/2013/453812 (2013)
  16. 16.
    Wang, G., Guo, L., Duan, H., Liu, L., Wang, H.: A bat algorithm with mutation for UCAV path planning. Sci. World J. http://dx.doi.org/10.1100/2012/418946 (2012)
  17. 17.
    Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Global Optim. 6(2), 109–133 (1995)Google Scholar
  18. 18.
    Resendel, M.G.C, Ribeiro, C.C.: GRASP with path-relinking: recent advances and applications. In: Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Springer, New York (2005)Google Scholar
  19. 19.
    Festa, P., Resende, M.: An annotated bibliography of GRASP, part I: algorithms. Int. Trans. Oper. Res. 16, 1–24 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Festa, P., Resende, M.: An annotated bibliography of GRASP, Part II: Applications. Int. Trans. Oper. Res. 16, 131–172 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Mestria, M., et al.: GRASP with path relinking for the symmetric euclidean clustered traveling salesman problem. Comput. Oper. Res. http://dx.doi.org/10.1016/j.cor.2012
  22. 22.
    Resende, M.G.C., Ribeiro, C.C., Glover, F., Mart, R.: Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau, M., Potvin, J.Y. (eds) Handbook of Metaheuristics, pp. 87–107. Springer, Boston (2010)Google Scholar
  23. 23.
    Glover, F.: Tabu search and adaptive memory programming–advances, applications and challenges. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer, Dordrecht (1996)Google Scholar
  24. 24.
    Laguna, M., Martı́, R.: GRASP and path relinking for 2-layer straight line crossing minimization. J. Comput. 11(1), 44–52 (1999)Google Scholar
  25. 25.
    Bekdaş, G., Nigdeli, S.M., Yang, X.-S.: Metaheuristic optimization for the design of reinforced concrete beams under flexure moments. In: 5th European Conference of Civil Engineering (ECCIE’14), 22–24 Nov 2014, Florence, ItalyGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yongquan Zhou
    • 1
    • 2
    Email author
  • Qifang Luo
    • 1
  • Jian Xie
    • 1
  • Hongqing Zheng
    • 1
  1. 1.College of Information Science and EngineeringGuangxi University for NationalitiesNanningChina
  2. 2.Guangxi High School Key Laboratory of Complex System and Computational IntelligenceNanningChina

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