Journal of Heuristics

, Volume 5, Issue 2, pp 215–247

Schemata, Distributions and Graphical Models in Evolutionary Optimization

Authors

  • Heinz Mühlenbein
    • Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—Forschungszentrum Informationstechnik
  • Thilo Mahnig
    • Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—Forschungszentrum Informationstechnik
  • Alberto Ochoa Rodriguez
    • Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—Forschungszentrum Informationstechnik
Article

DOI: 10.1023/A:1009689913453

Cite this article as:
Mühlenbein, H., Mahnig, T. & Rodriguez, A.O. Journal of Heuristics (1999) 5: 215. doi:10.1023/A:1009689913453

Abstract

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema defines the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA—in number of generations till convergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.

graphical modelsconditional independence graphsadditively decomposed functionsestimation of distributionspopulation based searchgenetic algorithm

Copyright information

© Kluwer Academic Publishers 1999