Analysis of Population Evolution in Classifier Systems Using Symbolic Representations

  • Pier Luca Lanzi
  • Stefano Rocca
  • Kumara Sastry
  • Stefania Solari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4998)

Abstract

This paper presents an approach to analyze population evolution in classifier systems using a symbolic representation. Given a sequence of populations, representing the evolution of a solution, the method simplifies the classifiers in the populations by reducing them to their “canonical form”. Then, it extracts all the subexpressions that appear in all the classifier conditions and, for each subexpression, it computes the number of occurrences in each population. Finally, it computes the trend of all the subexpressions considered. The expressions which show an increasing trend through the course of evolution are viewed as building blocks that the system has used to construct the solution.

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References

  1. 1.
    Booker, L.B.: Representing Attribute-Based Concepts in a Classifier System. In: Gregory, J.E. (ed.) Proceedings of the First Workshop on Foundations of Genetic Algorithms (FOGA 1991), pp. 115–127. Morgan Kaufmann, San Mateo (1991)Google Scholar
  2. 2.
    Dignum, S., Poli, R.: Generalisation of the limiting distribution of program sizes in tree-based genetic programming and analysis of its effects on bloat. In: GECCO 2007: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pp. 1588–1595. ACM Press, New York (2007)Google Scholar
  3. 3.
    Koza, J.R.: Hierarchical automatic function definition in genetic programming. In: Whitley, L.D. (ed.) Foundations of Genetic Algorithms 2, Vail, Colorado, USA, 24–29, 1992, pp. 297–318. Morgan Kaufmann, San Francisco (1992)Google Scholar
  4. 4.
    Lanzi, P.L.: Extending the Representation of Classifier Conditions Part I: From Binary to Messy Coding. In: Banzhaf, W., et al. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), Orlando (FL), July 1999, pp. 337–344. Morgan Kaufmann, San Francisco (1999)Google Scholar
  5. 5.
    Lanzi, P.L.: Mining interesting knowledge from data with the XCS classifier system. In: Spector, L., Goodman, E.D., Wu, A., Langdon, W.B., Voigt, H.-M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M.H., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), 7-11 July 2001, pp. 958–965. Morgan Kaufmann, San Francisco (2001)Google Scholar
  6. 6.
    Lanzi, P.L., Perrucci, A.: Extending the Representation of Classifier Conditions Part II: From Messy Coding to S-Expressions. In: Banzhaf, W., et al. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), Orlando (FL), July 1999, pp. 345–352. Morgan Kaufmann, San Francisco (1999)Google Scholar
  7. 7.
    Luke, S., Panait, L.: A comparison of bloat control methods for genetic programming. Evolutionary Computation 14, 309–344 (2006)CrossRefGoogle Scholar
  8. 8.
    Poli, R.: A simple but theoretically-motivated method to control bloat in genetic programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 204–217. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Wolfram Research. Mathematica 5, http://www.wolfram.com
  10. 10.
    Rocca, S., Solari, S.: Building blocks analysis and exploitation in genetic programming. Master’s thesis (April 2006) Master thesis supervisor: Prof. Pier Luca Lanzi. Electronic version available from, http://www.dei.polimi.it/people/lanzi
  11. 11.
    Schaffer, J.D. (ed.): Proceedings of the 3rd International Conference on Genetic Algorithms (ICGA 1989), George Mason University, June 1989. Morgan Kaufmann, San Francisco (1989)Google Scholar
  12. 12.
    Schuurmans, D., Schaeffer, J.: Representational Difficulties with Classifier Systems. In: Schaffer (ed.) [11], pp. 328–333, http://www.cs.ualberta.ca/~jonathan/Papers/Papers/classifier.ps
  13. 13.
    Sen, S.: A Tale of two representations. In: Proc. 7th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, pp. 245–254 (1994)Google Scholar
  14. 14.
    Shu, L., Schaeffer, J.: VCS: Variable Classifier System. In: Schaffer (ed.) [11], pp. 334–339, http://www.cs.ualberta.ca/~jonathan/Papers/Papers/vcs.ps
  15. 15.
    Wilson, S.W.: Get real! XCS with continuous-valued inputs. In: Booker, L., Forrest, S., Mitchell, M., Riolo, R.L. (eds.) Festschrift in Honor of John H. Holland, pp. 111–121. Center for the Study of Complex Systems (1999), http://prediction-dynamics.com/
  16. 16.
    Wilson, S.W.: Mining Oblique Data with XCS. In: Lanzi, P.L., Stolzmann, W., Wilson, S.W. (eds.) IWLCS 2000. LNCS (LNAI), vol. 1996. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Wilson, S.W.: Mining oblique data with XCS. In: Lanzi, P.L., Stolzmann, W., Wilson, S.W. (eds.) IWLCS 2000. LNCS (LNAI), vol. 1996, pp. 158–176. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pier Luca Lanzi
    • 1
    • 2
  • Stefano Rocca
    • 1
  • Kumara Sastry
    • 2
  • Stefania Solari
    • 1
  1. 1.Artificial Intelligence and Robotics Laboratory (AIRLab)Politecnico di MilanoMilanoItaly
  2. 2.Illinois Genetic Algorithm LaboratoryUniversity of Illinois at Urbana-ChampaignUrbana, IllinoisUSA

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