Schemata, Distributions and Graphical Models in Evolutionary Optimization

  • Authors:
  • Heinz Mü/hlenbein;Thilo Mahnig;Alberto Ochoa Rodriguez

  • Affiliations:
  • Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—/Forschungszentrum Informationstechnik 53754 St. Augustin. muehlenbein@gmd.de;Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—/Forschungszentrum Informationstechnik 53754 St. Augustin;Real World Computing Partnership Theoretical Foundation GMD Laboratory, GMD—/Forschungszentrum Informationstechnik 53754 St. Augustin&semi/ Centre of Artificial Intelligence, ICIMAF, Cuba. ...

  • Venue:
  • Journal of Heuristics
  • Year:
  • 1999

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Abstract

In this paper the optimization of additively decomposeddiscrete functions is investigated. For these functions geneticalgorithms have exhibited a poor performance. First the schema theoryof genetic algorithms is reformulated in probability theory terms. Aschema defines the structure of a marginal distribution. Then theconceptual algorithm BEDA is introduced. BEDA uses a Boltzmanndistribution 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. Thefactorization problem is closely connected to the theory ofconditional independence graphs. For the test functions considered,the performance of FDA—in number of generations tillconvergence—is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.