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Hybrid Chromosome Genetic Algorithm for Generalized Traveling Salesman Problems

  • Han Huang
  • Xiaowei Yang
  • Zhifeng Hao
  • Chunguo Wu
  • Yanchun Liang
  • Xi Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3612)

Abstract

Generalized Traveling Salesman Problem (GTSP) is one of the challenging combinatorial optimization problems in a lot of applications. In general, GTSP is more complex than Traveling Salesman Problem (TSP). In this paper, a novel hybrid chromosome genetic algorithm (HCGA), in which the hybrid binary and integer codes are adopted, is proposed as an improvement of generalized chromosome genetic algorithm (GCGA). In order to examine the effectiveness of HCGA, 16 benchmark problems are simulated. The experimental results show that HCGA can perform better than GCGA does in solving GTSP.

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References

  1. 1.
    Henry-Labordere, A.L.: The record balancing problem: A dynamic programming solution of a generalized traveling salesman problem. RAIRO B 2, 43–49 (1969)Google Scholar
  2. 2.
    Saksena, J.P.: Mathematical model of scheduling clients through welfare agencies. CORS Journal 8, 185–200 (1970)MathSciNetGoogle Scholar
  3. 3.
    Srivastava, S.S.S., Kumar, R.C.G., Sen, P.: Generalized traveling salesman problem through n sets of nodes. CORS Journal 7, 97–101 (1969)MathSciNetGoogle Scholar
  4. 4.
    Easwaran, M., Pitt, J., Poslad, S.: The agent service brokering problem as a generalized travelling salesman problem. In: Proceedings of the Third Annual Conference on Autononlous Agents, Seattle WA, USA, pp. 414–415 (1999)Google Scholar
  5. 5.
    Laporte, G., Asef-Vaziri, A., Sriskandarajah, C.: Some applications of the generalized traveling salesman problem. J. Oper. Res. Soc. 47, 1461–1467 (1996)zbMATHGoogle Scholar
  6. 6.
    Wu, C.G., Liang, Y.C., Lee, H.P., Lu, C.: Generalized chromosome genetic algorithm for generalized traveling salesman problems and its applications for machining. Physical Review E 70, 016701 (2004)CrossRefGoogle Scholar
  7. 7.
    Fischetti, M., Salazar, J.J., Toth, P.: Branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Operations Research 45(3), 378–394 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Laporte, G., Nobert, Y.: Generalized traveling salesman through n sets of nodes: an integer programming approach. INFOR 21, 61–75 (1983)zbMATHGoogle Scholar
  9. 9.
    Laporte, G., Mercure, H., Nobert, Y.: Generalized traveling salesman problem through n sets of nodes: the asymmetrical cases. Discrete Appl. Math. 18, 185–197 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fischetti, M., Salazar, J.J., Toth, P.: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem, Working paper, University of Bologna (1993)Google Scholar
  11. 11.
    Fischetti, M., Salazar, J.J., Toth, P.: The symmetric generalized traveling salesman polytope. Networks 26, 113–123 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Renaud, J., Boctor, F.F.: An efficient composite heuristic for the symmetric generalized traveling salesman problem. European Journal of Operational Research 108, 571–584 (1998)zbMATHCrossRefGoogle Scholar
  13. 13.
    Noon, C.E., Bean, J.C.: An efficient transformation of the generalized traveling salesman problem. INFOR 31, 39–44 (1993)zbMATHGoogle Scholar
  14. 14.
    Lien, Y., Ma, E., Wah, B.W.S.: Transformation of the generalized traveling salesman problem into the standard traveling salesman problem. Information Science 74, 177–189 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Dimitrijevic, V., Saric, Z.: An efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphs. Information Science 102, 105–110 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Reinelt, G.: TSPLIB. A traveling salesman problem library. ORSA Journal on Computing 3(4), 376–384 (1991)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Han Huang
    • 1
  • Xiaowei Yang
    • 2
  • Zhifeng Hao
    • 2
  • Chunguo Wu
    • 3
  • Yanchun Liang
    • 3
  • Xi Zhao
    • 2
  1. 1.College of Computer Science and EngineeringSouth China University of TechnologyGuangzhouP.R. China
  2. 2.College of Mathematical ScienceSouth China University of TechnologyGuangzhouP.R. China
  3. 3.College of Computer Science and TechnologyJilin UniversityChangchunP.R. China

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