Skip to main content
SpringerLink
Log in

Effective Neighborhood Structures for the Generalized Traveling Salesman Problem

  • Conference paper
Evolutionary Computation in Combinatorial Optimization (EvoCOP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4972))

Abstract

We consider the generalized traveling salesman problem in which a graph with nodes partitioned into clusters is given. The goal is to identify a minimum cost round trip visiting exactly one node from each cluster. For solving difficult instances of this problem heuristically, we present a new Variable Neighborhood Search (VNS) approach that utilizes two complementary, large neighborhood structures. One of them is the already known generalized 2-opt neighborhood for which we propose a new incremental evaluation technique to speed up the search significantly. The second structure is based on node exchanges and the application of the chained Lin-Kernighan heuristic. A comparison with other recently published metaheuristics on TSPlib instances with geographical clustering indicates that our VNS, though requiring more time than two genetic algorithms, is able to find substantially better solutions.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Behzad, A., Modarres, M.: A new efficient transformation of the generalized traveling salesman problem into traveling salesman problem. In: Proceedings of the 15th International Conference of Systems Engineering, pp. 6–8 (2002)

    Google Scholar 

  2. Dimitrijevic, V., Saric, Z.: An efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphs. Information Science 102(1-4), 105–110 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Feremans, C.: Generalized Spanning Trees and Extensions. PhD thesis, Universite Libre de Bruxelles (2001)

    Google Scholar 

  4. Fischetti, M., Salazar, J.J., Toth, P.: The symmetric generalized traveling salesman polytope. Networks 26, 113–123 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fischetti, M., Salazar, J.J., Toth, P.: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Operations Research 45, 378–394 (1997)

    MATH  MathSciNet  Google Scholar 

  6. Hansen, P., Mladenovic, N.: An introduction to variable neighborhood search. In: Voss, S., et al. (eds.) Meta-heuristics, Advances and trends in local search paradigms for optimization, pp. 433–458. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  7. Henry-Labordere.: The record balancing problem: A dynamic programming solution of a generalized traveling salesman problem. RAIRO Operations Research B2, 43–49 (1969)

    Google Scholar 

  8. Huang, H., Yang, X., Hao, Z., Wu, C., Liang, Y., Zhao, X.: Hybrid chromosome genetic algorithm for generalized traveling salesman problems. Advances in Natural Computation 3612, 137–140 (2005)

    Article  Google Scholar 

  9. Laporte, G., Asef-Vaziri, A., Sriskandarajah, C.: Some applications of the generalized travelling salesman problem. Journal of the Operational Research Society 47(12), 1461–1467 (1996)

    Article  MATH  Google Scholar 

  10. Laporte, G., Mercure, H., Nobert, Y.: Generalized traveling salesman problem through n sets of nodes: The asymmetric case. Discrete Applied Mathematics 18, 185–197 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  11. Laporte, G., Nobert, Y.: Generalized traveling salesman problem through n sets of nodes: An integer programming approach. INFOR 21(1), 61–75 (1983)

    MATH  Google Scholar 

  12. Laporte, G., Semet, F.: Computational evaluation of a transformation procedure for the symmetric generalized traveling salesman problem. INFOR 37(2), 114–120 (1999)

    Google Scholar 

  13. Lien, Y.N., Ma, E., Wah, B.W.S.: Transformation of the generalized traveling salesman problem into the standard traveling salesman problem. Information Sciences 74(1–2), 177–189 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lin, S.: Computer solutions of the traveling salesman problem. Bell Systems Computer Journal 44, 2245–2269 (1965)

    MATH  Google Scholar 

  15. Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for the traveling salesman problem. Complex Systems 5, 299–326 (1991)

    MATH  MathSciNet  Google Scholar 

  16. Noon, C., Bean, J.C.: An efficient transformation of the generalized traveling salesman problem. INFOR 31(1), 39–44 (1993)

    MATH  Google Scholar 

  17. Noon, C.E.: The Generalized Traveling Salesman Problem. PhD thesis, University of Michigan (1988)

    Google Scholar 

  18. 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)

    Article  MATH  Google Scholar 

  19. Renaud, J., Boctor, F.F., Laporte, G.: A fast composite heuristic for the symmetric traveling salesman problem. INFORMS Journal on Computing 8(2), 134–143 (1996)

    Article  MATH  Google Scholar 

  20. Saskena, J.P.: Mathematical model of scheduling clients through welfare agencies. Journal of the Canadian Operational Research Society 8, 185–200 (1970)

    Google Scholar 

  21. Snyder, L.V., Daskin, M.S.: A random-key genetic algorithm for the generalized traveling salesman problem. Technical Report 04T-018, Dept. of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA (2004)

    Google Scholar 

  22. Srivastava, Kumar, S.S.S., Garg, R.C., Sen, P.: Generalized traveling salesman problem through n sets of nodes. CORS Journal 7, 97–101 (1969)

    MathSciNet  Google Scholar 

  23. Wu, C., Liang, Y., Lee, H.P., Lu, C.: Generalized chromosome genetic algorithm for generalized traveling salesman problems and its applications for machining. Physical Review E 70(1) (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Graphics and Algorithms, Vienna University of Technology, Favoritenstraße 9–11/1861, 1040, Vienna, Austria

    Bin Hu & Günther R. Raidl

Authors
  1. Bin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Günther R. Raidl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jano van Hemert Carlos Cotta

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hu, B., Raidl, G.R. (2008). Effective Neighborhood Structures for the Generalized Traveling Salesman Problem. In: van Hemert, J., Cotta, C. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2008. Lecture Notes in Computer Science, vol 4972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78604-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78604-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78603-0

  • Online ISBN: 978-3-540-78604-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation