The paper investigates the optimization of additively decomposable functions (ADF) by a new evolutionary algorithm called Factorized Distribution Algorithm (FDA). FDA is based on a factorization of the distribution to generate search points. First separable ADFs are considered. These are mapped to generalized linear functions with metavariables defined for multiple alleles. The mapping transforms FDA into an Univariate Marginal Frequency Algorithm (UMDA). For UMDA the exact equation for the response to selection is.computed under the assumption of proportionate selection. For truncation selection an approximate equation for the time to convergence is used, derived from an analysis of the OneMax function. FDA is also numerically investigated for non separable functions. The time to convergence is very similar to separable ADFs. FDA outpe1iorms the genetic algorithm with recombination of strings by far.
[1]
Heinz Mühlenbein,et al.
The Equation for Response to Selection and Its Use for Prediction
,
1997,
Evolutionary Computation.
[2]
Heinz Mühlenbein,et al.
The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA)
,
1993,
Evolutionary Computation.
[3]
David E. Goldberg,et al.
Genetic Algorithms in Search Optimization and Machine Learning
,
1988
.
[4]
R. Punnett,et al.
The Genetical Theory of Natural Selection
,
1930,
Nature.
[5]
L. Baum,et al.
An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology
,
1967
.