Skip to main content

Guiding ACO by Problem Relaxation: A Case Study on the Symmetric TSP

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 4771)

Abstract

In this paper the influence of structural information obtained from a problem relaxation on the performance of an ACO algorithm for the symmetric TSP is studied. More precisely, a very simple ACO algorithm is guided by including Minimal Spanning Tree information into the visibility. Empirical results on a large number of benchmark instances from TSPLIB are presented. The paper concludes with remarks on some more elaborate ideas for using problem relaxation within ACO.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-75514-2_4
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   69.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-75514-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   89.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blum, C., Dorigo, M.: The Hyper-Cube framework for ant colony optimization. IEEE Transactions on Systems, Man and Cybernetics B 34(2), 1161–1772 (2004)

    CrossRef  Google Scholar 

  2. Colorni, A., Dorigo, M., Maniezzo, V.: Distributed Optimization by Ant Colonies. In: Varela, F., Bourgine, P. (eds.) Proc. Europ. Conf. Artificial Life, Elsevier, Amsterdam (1991)

    Google Scholar 

  3. Croes, G.A.: A method for solving Traveling Salesman Problems. Operations Research 6, 791–801 (1958)

    MathSciNet  CrossRef  Google Scholar 

  4. Dorigo, M., Gambardella, L.M.: Ant Colony System: A cooperative learning approach to the Travelling Salesman Problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)

    CrossRef  Google Scholar 

  5. Dorigo, M., Stuetzle, T.: Ant Colony Optimization. MIT Press/Bradford Books, Cambridge, MA (2004)

    Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  7. Gendreau, M., Hertz, A., Laporte, G.: New insertion and postoptimization procedures for the travelling salesman problem. Operations Research 40, 1086–1094 (1992)

    MATH  MathSciNet  Google Scholar 

  8. Gutjahr, W.J.: A graph-based Ant System and its convergence. Future Generation Computing Systems 16, 873–888 (2000)

    CrossRef  Google Scholar 

  9. Gutjahr, W.J.: ACO algorithms with guaranteed convergence to the optimal solution. Information Processing Letters 82, 145–153 (2002)

    MATH  CrossRef  MathSciNet  Google Scholar 

  10. Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society 7, 48–50 (1956)

    CrossRef  MathSciNet  Google Scholar 

  11. Lawler, E.L., Lenstra, J.K., Kan, A.H.G.R., Schmoys, D.B. (eds.): The Traveling Salesman Problem. Wiley, Chichester (1985)

    MATH  Google Scholar 

  12. Le Louarn, F.-X., Gendreau, M., Potvin, J.-Y.: GENI Ants for the travelling salesman problem. Annals of Operations Research 131, 187–201 (2004)

    MATH  CrossRef  MathSciNet  Google Scholar 

  13. Maniezzo, V.: Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem. INFORMS Journal on Computing 11(4), 358–369 (1999)

    MATH  MathSciNet  Google Scholar 

  14. Stuetzle, T., Dorigo, M.: A short convergence proof for a class of ACO algorithms. IEEE Transactions on Evolutionary Computation 6(4), 358–365 (2002)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reimann, M. (2007). Guiding ACO by Problem Relaxation: A Case Study on the Symmetric TSP. In: , et al. Hybrid Metaheuristics. HM 2007. Lecture Notes in Computer Science, vol 4771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75514-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75514-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75513-5

  • Online ISBN: 978-3-540-75514-2

  • eBook Packages: Computer ScienceComputer Science (R0)