Schemata, Distributions and Graphical Models in Evolutionary Optimization

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.

[1]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

[2]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[3]  Kalyanmoy Deb,et al.  RapidAccurate Optimization of Difficult Problems Using Fast Messy Genetic Algorithms , 1993, ICGA.

[4]  Michael I. Jordan Graphical Models , 1998 .

[5]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  Brendan J. Frey,et al.  Graphical Models for Machine Learning and Digital Communication , 1998 .

[8]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[9]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[10]  Bruce Tidor,et al.  An Analysis of Selection Procedures with Particular Attention Paid to Proportional and Boltzmann Selection , 1993, International Conference on Genetic Algorithms.

[11]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[12]  L. Darrell Whitley,et al.  Test driving three 1995 genetic algorithms: New test functions and geometric matching , 1995, J. Heuristics.

[13]  John H. Holland,et al.  Distributed genetic algorithms for function optimization , 1989 .

[14]  S. Baluja,et al.  Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space , 1997 .

[15]  Heinz Mühlenbein,et al.  The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA) , 1993, Evolutionary Computation.

[16]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[17]  Gang Wang,et al.  Revisiting the GEMGA: scalable evolutionary optimization through linkage learning , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[18]  David E. Goldberg,et al.  SEARCH, Blackbox Optimization, And Sample Complexity , 1996, FOGA.