Complex Systems

Application of Eigen's Evolution Model to Infinite Population Genetic Algorithms with Selection and Mutation Download PDF

Hiroshi Furutani
Department of Information Science,
Kyoto University of Education,
Fukakusa-Fujinomori-cho 1,
Fushimi-ku, Kyoto, 612 Japan


Eigen's model for the molecular evolution of self-replicating macromolecules is used to develop a method for predicting the distribution of alleles in the framework of infinite population genetic algorithms (GAs) with selection and mutation. A set of ordinary differential equations which take into account selection and mutation is derived and applied to GAs. By calculating the spectrum of a matrix appearing in the equations, the method makes it possible to obtain the distribution of alleles. It is shown that eigenvectors of the matrix which includes only mutation are Walsh monomials. Some approximate expressions for the asymptotic behavior of GAs with small mutation rates are also presented.