Advertisement

The Convergence Behavior of the PBIL Algorithm: A Preliminary Approach

  • C. González
  • J. A. Lozano
  • P. Larrañaga

Abstract

In this paper the simplest version of Population Based Incremental Learning (PBIL) is used to minimize the One Max function in two dimensions. After carrying out several experiments to reveal the limit behavior of the algorithm in this function we obtain that the convergence results depend on the initial vector p (0), and on the a parameter value. This experienced behavior is guaranteed for mathematical proof. The probability that the algorithm converges to any point of the search space goes to 1 when p (0) and a go to suitable values. Thus, even though the experimental results seem more stable when the α value is near to zero, we can not ensure that PBIL converges to the optimum.

Keywords

Search Space Bayesian Network Probability Vector Joint Probability Distribution Basque Country 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Mühlenbein and G. Paaβ, “From Recombination of Genes to the Estimation of Distributions I. Binary Parameters”, Lecture Notes in Computer Science 1411: Parallel Problem Solving from Nature, PPSN IV, pp. 178–187, 1996.Google Scholar
  2. [2]
    P. Larrañaga and J.A. Lozano, Estimation of Distribution Algorithms. A new tool for Evolutionary Computation, Kluwer Academic Publishers, in press.Google Scholar
  3. [3]
    G. Syswerda, “Simulated Crossover in Genetic Algorithms”, Foundations of Genetic Algorithms, II, pp. 239–255, 1993.Google Scholar
  4. [4]
    S. Baluja, “Population Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning”, Carnegie Mellon Report, CMU-CS-94-163, 1994.Google Scholar
  5. [5]
    V. Kvasnicka, M. Pelikan, and J. Pospichal, “Hill Climbing with Learning (an Abstraction of Genetic Algorithms),” Neural Networks World, vol. 6, pp. 773–796, 1996.Google Scholar
  6. [6]
    H. Mühlenbein, “The equation for Response to Selection and its Use for Prediction”, Evolutionary Computation vol. 5, pp. 303–346, 1998.CrossRefGoogle Scholar
  7. [7]
    J.S. De Bonet, C.L. Isbell and P. Viola, “MIMIC: Finding Optima by Estimating Prob ability Densities”, Advances in Neural Information Processing Systems, vol. 9, 1997.Google Scholar
  8. [8]
    S. Baluja and S. Davies, “Fast Probabilistic Modeling for Combinatorial Optimization”, AAAI-98, 1998.Google Scholar
  9. [9]
    H. Mühlenbein, T. Mahnig and A. Ochoa, “Schemata, Distributions and Graphical Models in Evolutionary Optimization”, Journal of Heuristics, vol. 5, pp. 215–247, 1999.CrossRefMATHGoogle Scholar
  10. [10]
    R. Etxeberria and P. Larrañaga, “Global optimization using Bayesian networks”, II Symposium on Artificial Intelligence, CIMAF99, Special Session on Distributions and Evolutionary Optimization, pp. 332–339, 1999.Google Scholar
  11. [11]
    M. Pelikan, D.E. Goldberg and E. CantúPaz, “BOA: Bayesian Optimization Algorithm”, GECCO’99:Proceedings of the Genetic and Evolutionary Computation Conference, pp. 525–532, 1999.Google Scholar
  12. [12]
    H. Mühlenbein and T. Mahnig, “The Factorized Distribution Algorithm for Additively Decomposed Functions”, Proceedings of the 1999 Congress on Evolutionary Optimization, pp. 752–759, 1999.Google Scholar
  13. [13]
    M. Höhfeld and G. Rudolph, “Towards a theory of population-based incremental learning”, 4th IEEE Conference on Evolutionary Computation, Piscat-away, NJ: IEEE, Press, vol. 1, pp. 1–5, 1997.Google Scholar
  14. [14]
    A. Berny, “Selection and Reinforcement Learning for Combinatorial Optimization” Parallel Problem Solving from Nature, PPSN-VI, pp. 601–610, 2000.Google Scholar
  15. [15]
    C. González, J.A. Lozano and P. Larrañarraga, “Analyzing the PBIL algorithm by means of discrete dynamical systems”, Complex Systems, accepted.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • C. González
  • J. A. Lozano
  • P. Larrañaga
    • 1
  1. 1.Department of Computer Science and Artificial IntelligenceUniversity of the Basque CountrySpain

Personalised recommendations