Rigorous Runtime Analysis of Inversely Fitness Proportional Mutation Rates

  • Christine Zarges
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

Artificial Immune Systems (AIS) are an emerging new field of research in Computational Intelligence that are applied to many areas of application, e.g., optimization, anomaly detection and classification. For optimization tasks, the use of hypermutation operators constitutes a common concept in AIS. By now, only little theoretical work has been done in this field. In this paper, we present a detailed theoretical runtime analysis that gives an insight into the dynamics of fitness based hypermutation processes. Two specific mutation rates are considered using a simple immune inspired algorithm. Our main focus lies thereby on the influence of parameters embedded in popular immune inspired hypermutation operators from the literature. Our theoretical findings are accompanied by some empirical results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dasgupta, D. (ed.): Artificial Immune Systems and Their Applications. Springer, Heidelberg (1998)Google Scholar
  2. 2.
    de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Heidelberg (2002)Google Scholar
  3. 3.
    Timmis, J., Andrews, P.S., Owens, N., Clark, E.: An interdisciplinary perspective on artificial immune systems. Evolutionary Intelligence 1, 5–26 (2008)CrossRefGoogle Scholar
  4. 4.
    Burnet, F.M.: The Clonal Selection Theory of Acquired Immunity. Cambridge University Press, Cambridge (1959)CrossRefGoogle Scholar
  5. 5.
    de Castro, L.N., Zuben, F.J.V.: Learning and Optimization Using the Clonal Selection Principle. IEEE Trans. on Evol. Comp. 6(3), 239–251 (2002)CrossRefGoogle Scholar
  6. 6.
    Cutello, V., Nicosia, G., Pavone, M.: Exploring the Capability of Immune Algorithms: A Characterization of Hypermutation Operators. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 263–276. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Kelsey, J., Timmis, J.: Immune Inspired Somatic Contiguous Hypermutation for Function Optimisation. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 207–218. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Cortés, N.C., Coello, C.A.C.: Multiobjective Optimization Using Ideas from the Clonal Selection Principle. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 158–170. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Timmis, J.: Artificial Immune Systems – Today and Tomorrow. Natural Computing 6(1), 1–18 (2007)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Hart, E., Timmis, J.: Application Areas of AIS: The Past, the Present and the Future. Applied Soft Computing 8(1), 191–201 (2008)CrossRefGoogle Scholar
  11. 11.
    Timmis, J., Hone, A., Stibor, T., Clark, E.: Theoretical Advances in Artificial Immune Systems. Theoretical Computer Science (in press, 2008)Google Scholar
  12. 12.
    Villalobos-Arias, M., Coello Coello, C.A., Hernández-Lerma, O.: Convergence analysis of a multiobjective artificial immune system algorithm. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 226–235. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Clark, E., Hone, A., Timmis, J.: A Markov Chain Model of the B-Cell Algorithm. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 318–330. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Cutello, V., Nicosia, G., Romeo, M., Oliveto, P.S.: On the Convergence of Immune Algorithms. In: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), pp. 409–415. IEEE Press, Los Alamitos (2007)CrossRefGoogle Scholar
  15. 15.
    Jansen, T., Wegener, I.: On the Choice of the Mutation Probability for the (1+1) EA. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 89–98. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Jansen, T., Sudholt, D.: Design and analysis of an asymmetric mutation operator. In: Proceedings of the 2005 IEEE Congress on Evolutionary Computation (CEC 2005). IEEE Press, Los Alamitos (2005)Google Scholar
  17. 17.
    Doerr, B., Hebbinghaus, N., Neumann, F.: Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators. Evol. Comput. 15(4), 401–410 (2007)CrossRefGoogle Scholar
  18. 18.
    Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley & Sons, Chichester (1995)Google Scholar
  19. 19.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1-2), 51–81 (2002)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Hagerup, T., Rüb, C.: A guided tour of Chernoff bounds. Information Processing Letters 33, 305–308 (1990)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    de Castro, L.N., Timmis, J.: An Artificial Immune Network for Multimodal Function Optimization. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation (CEC 2002), pp. 674–699. IEEE Press, Los Alamitos (2002)Google Scholar
  22. 22.
    Cutello, V., Narzisi, G., Nicosia, G., Pavone, M.: Clonal selection Algorithms: A Comparative Case Study Using Effective Mutation Potentials. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 13–28. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christine Zarges
    • 1
  1. 1.Fakultät für Informatik, TU DortmundDortmundGermany

Personalised recommendations