Skip to main content

A New Approach for Solving the Generalized Traveling Salesman Problem

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6373))

Abstract

The generalized traveling problem (GTSP) is an extension of the classical traveling salesman problem. The GTSP is known to be an NP-hard problem and has many interesting applications. In this paper we present a local-global approach for the generalized traveling salesman problem. Based on this approach we describe a novel hybrid metaheuristic algorithm for solving the problem using genetic algorithms. Computational results are reported for Euclidean TSPlib instances and compared with the existing ones. The obtained results point out that our hybrid algorithm is an appropriate method to explore the search space of this complex problem and leads to good solutions in a reasonable amount of time.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bäck, T., Hoffmeister, F., Schwefel, H.: A survey of evolution strategies. In: Proc. of the 4th International Conference on Genetic Algorithms, San Diego, CA (July 1991)

    Google Scholar 

  2. Bontoux, B., Artigues, C., Feillet, D.: A Memetic Algorithm with a Large Neighborhood Crossover Operator for the Generalized Traveling Salesman Problem. Computers & Operations Research (2009) (in press)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gutin, G., Karapetyan, D.: A memetic algorithm for the generalized traveling salesman problem. Natural Computing 9, 47–60 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Hu, B., Raidl, G.: Effective neighborhood structures for the generalized traveling salesman problem. In: van Hemert, J., Cotta, C. (eds.) EvoCOP 2008. LNCS, vol. 4972, pp. 36–47. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Laporte, G., Nobert, Y.: Generalized Traveling Salesman through n sets of nodes: an integer programming approach. INFOR 21, 61–75 (1983)

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Matei, O.: Evolutionary Computation: Principles and Practices, Risoprint (2008)

    Google Scholar 

  11. Noon, C.E., Bean, J.C.: A Lagrangian based approach for the asymmetric generalized traveling salesman problem. Operations Research 39, 623–632 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pintea, C., Pop, P.C., Chira, C.: Reinforcing Ant Colony System for the Generalized Traveling Salesman Problem. In: Proc. of International Conference Bio-Inspired Computing-Theory and Applications (BIC-TA), Wuhan, China. Evolutionary Computing Section, pp. 245–252 (2006)

    Google Scholar 

  13. Pop, P.C.: The generalized minimum spanning tree problem. Twente University Press, The Netherlands (2002)

    MATH  Google Scholar 

  14. Pop, P.C., Kern, W., Still, G.J.: A new relaxation method for the generalized minimum spanning tree problem. European Journal of Operational Research 170, 900–908 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pop, P.C.: A survey of different integer programming formulations of the generalized minimum spanning tree problem. Carpathian J. of Math. 25(1), 104–118 (2009)

    MathSciNet  MATH  Google Scholar 

  16. Pop, P.C., Matei, O., Pop Sitar, C., Chira, C.: A Genetic Algorithm for Solving the Generalized Vehicle Routing Problem. In: Corchado, E., Graña Romay, M., Manhaes Savio, A. (eds.) HAIS 2010, Part II. LNCS, vol. 6077, pp. 119–126. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Renaud, J., Boctor, F.F.: An efficient composite heuristic for the Symmetric Generalized Traveling Salesman Problem. European Journal of Operational Research 108(3), 571–584 (1998)

    Article  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  19. Schwefel, H.P.: Collective phenomena in evolutionary systems. In: Proc. of 31st Annual Meetting of the International Society for General System Research, pp. 1025–1033 (1987)

    Google Scholar 

  20. Snyder, L.V., Daskin, M.S.: A random-key genetic algorithm for the generalized traveling salesman problem. European Journal of Operations Research 174, 38–53 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  22. Yanga, J., Shi, X., Marchese, M., Liang, Y.: An ant colony optimization method for generalized TSP problem. Progress in Natural Science 18(11), 1417–1422 (2008)

    Article  MathSciNet  Google Scholar 

  23. http://www.iwr.uni-heidelberg.de/groups/comopt/software/ TSPLIB95/vrp/

  24. http://verify.stanford.edu/uli/java_cpp.html

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pop, P.C., Matei, O., Sabo, C. (2010). A New Approach for Solving the Generalized Traveling Salesman Problem. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds) Hybrid Metaheuristics. HM 2010. Lecture Notes in Computer Science, vol 6373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16054-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16054-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16053-0

  • Online ISBN: 978-3-642-16054-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics