Advertisement

Solving Traveling Salesman Problems by Artificial Immune Response

  • Maoguo Gong
  • Licheng Jiao
  • Lining Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4247)

Abstract

This paper introduces a computational model simulating the dynamic process of human immune response for solving Traveling Salesman Problems (TSPs). The new model is a quaternion (G, I, R, Al), where G denotes exterior stimulus or antigen, I denotes the set of valid antibodies, R denotes the set of reaction rules describing the interactions between antibodies, and Al denotes the dynamic algorithm describing how the reaction rules are applied to antibody population. The set of immunodominance rules, the set of clonal selection rules, and a dynamic algorithm TSP-PAISA are designed. The immunodominance rules construct an immunodominance set based on the prior knowledge of the problem. The antibodies can gain the immunodominance from the set. The clonal selection rules strengthen these superior antibodies. The experiments indicate that TSP-PAISA is efficient in solving TSPs and outperforms a known TSP algorithm, the evolved integrated self-organizing map.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jin, H.D., Leung, K.S., Wong, M.L., Xu, Z.B.: An Efficient Self-Organizing Map Designed by Genetic Algorithms for the Traveling Salesman Problem. IEEE Transactions on Systems, Man, and Cybernetics-Part B 33(6), 877–888 (2003)CrossRefGoogle Scholar
  2. 2.
    Durbin, R., Willshaw, D.: An analogue approach to the traveling salesman problem. Nature 326, 689–691 (1987)CrossRefGoogle Scholar
  3. 3.
    Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Garrett, S.M.: How Do We Evaluate Artificial Immune Systems. Evolutionary Computation 13(2), 145–178 (2005)CrossRefGoogle Scholar
  5. 5.
    Gong, M.G., Jiao, L.C., Liu, F., Du, H.F.: The Quaternion Model of Artificial Immune Response. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 207–219. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Gong, M.G., Du, H.F., Jiao, L.C.: Optimal approximation of linear systems by artificial immune response. Science in China: Series F Information Sciences 49(1), 63–79 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yewdell, J.W., Bennink, J.R.: Immunodominance in major histocompatibility complex class I-restricted T lymphocyte responses. Annual Review of Immunology 17, 51–88 (1999)CrossRefGoogle Scholar
  8. 8.
    Burnet, F.M.: The Clonal Selection Theory of Acquired Immunity. Cambridge University Press, Cambridge (1959)Google Scholar
  9. 9.
    Burnet, F.M.: Clonal selection and after. Theoretical Immunology, pp. 63–85. Marcel Dekker, New York (1978)Google Scholar
  10. 10.
    Garrett, S.M.: Parameter-free, Adaptive Clonal Selection. In: The Proceedings of IEEE Congress on Evolutionary Computing (CEC 2004), Portland Oregon, June 2004, pp. 1052–1058 (2004)Google Scholar
  11. 11.
    de Castro, L.N., Von Zuben, F.J.: Learning and Optimization Using the Clonal Selection Principle. IEEE Transactions on Evolutionary Computation 6(3), 239–251 (2002)CrossRefGoogle Scholar
  12. 12.
    Reinelt, G.: TSPLIB—A traveling salesman problem library. ORSA Journal of Computing 3(4), 376–384 (1991)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maoguo Gong
    • 1
  • Licheng Jiao
    • 1
  • Lining Zhang
    • 1
  1. 1.Institute of Intelligent Information ProcessingXidian UniversityXi’anChina

Personalised recommendations