Skip to main content
SpringerLink
Log in

Inver-over operator for the TSP

  • Conference paper
  • First Online:
Book cover Parallel Problem Solving from Nature — PPSN V (PPSN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1498))

Included in the following conference series:

Abstract

In this paper we investigate the usefulness of a new operator, inver-over, for an evolutionary algorithm for the TSP. Inver-over is based on simple inversion, however, knowledge taken from other individuals in the population influences its action. Thus, on one hand, the proposed operator is unary, since the inversion is applied to a segment of a single individual, however, the selection of a segment to be inverted is population driven, thus the operator displays some characterictics of recombination.

This operator outperforms all other ‘genetic’ operators, whether unary or binary, which have been proposed in the past for the TSP in connection with evolutionary systems and the resulting evolutionary algorithm is very fast. For test cases, where the number of cities is around 100, the algorithm reaches the optimum in every execution in a couple of seconds. For larger instances (e.g., 10,000 cities) the results stay within 3% from the estimated optimum.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Applegate, D. Bixby, R.E., Chvatal, V., and Cook, W., Finding cuts in the TSP: a preliminary report. Report 95-05, DIMACS, Rutgers University, NJ.

    Google Scholar 

  2. Braun, H., On solving traveling salesman problems by genetic algorithms. In Proc. PPSN'90, pp.129–133.

    Google Scholar 

  3. Davis, L., (Editor), Genetic Algorithms and Simulated Annealing, Morgan Kaufmann Publishers, San Mateo, CA, 1987.

    MATH  Google Scholar 

  4. Davis, L., Handbook of Genetic Algorithms, Van Nostrand Reinhold, NY, 1991.

    Google Scholar 

  5. Eshelman, L., The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic recombination. In Proc. FOGA'90, pp.265–283.

    Google Scholar 

  6. Fogel, D.B., An evolutionay approach to the traveling salesman problem. Biol. Cybern., Vol.60, pp.139–144, 1988.

    Article  MathSciNet  Google Scholar 

  7. Gorges-Schleuter, M., ASPARAGOS: An asynchronous parallel genetic optimization strategy. In Proc. ICGA'91, pp.422–427.

    Google Scholar 

  8. Grefenstette, J.J., Incorporating Problem Specific Knowledge into Genetic Algorithms. In [3], pp.42–60.

    Google Scholar 

  9. Herdy, M., Application of the Evolution Strategy to Discrete Optimization Problems. In Proc. PPSN'90, pp.188–192.

    Google Scholar 

  10. Johnson, D.S., The Traveling Salesman Problem: A Case Study. In Local Search in Combinatorial Optimization, E. Aarts and J.K. Lenstra (Editors), John Wiley, 1996, pp.215–310.

    Google Scholar 

  11. Johnson, D.S., McGeoch, L.A., and Rothberg, E.E., Asymptotic experimental analysis for the Held-Karp traveling salesman bound. Proc. Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, and SIAM, Philadelphia, PA, pp. 341–350.

    Google Scholar 

  12. Karp, R.M., Probabilistic Analysis of Partitioning Algorithm for the Traveling Salesman Problem in the Plane. Mathematics of Operations Research, Vol.2, No.3, 1977, pp.209–224.

    Article  MATH  MathSciNet  Google Scholar 

  13. Lidd, M.L., Traveling Salesman Problem Domain Application of a Fundamentally New Approach to Utilizing Genetic Algorithms. Tech. Rep., MITRE Corp., 1991.

    Google Scholar 

  14. Lin, S. and Kerninghan, B.W., An Effective Heuristic Algorithm for the Traveling Salesman Problem. Operations Research, pp.498–516, 1972.

    Google Scholar 

  15. Maekawa, K., Mori, N.,Tamaki, H., Kita, H. and Nishikawa, Y., A genetic solution for the traveling salesman problem by means of a thermodynamical selection rule. Proc. IEEE ICEC '96.

    Google Scholar 

  16. Matias, K. and D. Whitley, Genetic operators, the fitness landscape and the traveling salesman problem. In Proc. PPSN'92, pp.219–228.

    Google Scholar 

  17. Merz, P. and B. Freisleben, Genetic local search for the TSP: New results. Proc. IEEE ICEC '97.

    Google Scholar 

  18. Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 3rd edition, 1996.

    Google Scholar 

  19. Mühlenbein, H., Evolution in time and space — The parallel genetic algorithm. In Proc. FOGA'90, pp.316–337.

    Google Scholar 

  20. Nagata, Y. and Kobayashi, S., Edge assembly crossover: A high-power genetic algorithm for the traveling salesman problem. Proc. ICGA '97.

    Google Scholar 

  21. Number, H.-T. and Beyer, H.-G., The dynamics of Evolution Strategies in the optimization of traveling salesman problem, Proc. of EP'97.

    Google Scholar 

  22. Reinelt, G., TSPLIB — A Traveling Salesman Problem Library. ORSA Journal on Computing, Vol.3, No.4, pp.376–384, 1991.

    MATH  Google Scholar 

  23. Starkweather, T., McDaniel, S., Mathias, K., Whitley, C., and Whitley, D., A Comparison of Genetic Sequencing Operators. In Proc. ICGA'91, pp.69–76.

    Google Scholar 

  24. Tao, G. and Michalewicz, Z., Evolutionary Algorithms for the TSP. In preparation.

    Google Scholar 

  25. Ulder, N.L.J., Aarts, E.H.L., Bandelt, H.-J., van Laarhoven, P.J.M., Pesch, E., Genetic Local Search Algorithms for the Traveling Salesman Problem. In Proc. PPSN'90, pp.109–116.

    Google Scholar 

  26. Valenzuela, Ch.L. and Willians, L.P., Improving Simple Heuristic Algorithms for the Travelling Salesman Problem using a Genetic Algorithm. In Proc. ICGA'97, pp.458–464.

    Google Scholar 

  27. Whitley, D., Starkweather, T., and Fuquay, D'A., Scheduling Problems and Traveling Salesman: The Genetic Edge Recombination Operator. In Proc. ICGA'89, pp. 133–140.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Labortory of Software Engineering, Wuhan University, 430072, Wuhan, Hubei, P.R. China

    Guo Tao

  2. Department of Computer Science, University of North Carolina, 28223, Charlotte, NC, USA

    Zbigniew Michalewicz

Authors
  1. Guo Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zbigniew Michalewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Agoston E. Eiben Thomas Bäck Marc Schoenauer Hans-Paul Schwefel

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tao, G., Michalewicz, Z. (1998). Inver-over operator for the TSP. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN V. PPSN 1998. Lecture Notes in Computer Science, vol 1498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056922

Download citation

  • DOI: https://doi.org/10.1007/BFb0056922

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65078-2

  • Online ISBN: 978-3-540-49672-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation