Modeling and Analysis of Genetic Algorithms Based on the Viewpoint of Mixture Systems
Jun-ichi Imai*, Hiroyuki Shioya*, and Masahito Kurihara**
*Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, 050-8585, Japan
**Graduate School of Engineering, Hokkaido University, Kita 13, Nishi 8, Sapporo, 060-8628, Japan
Some mathematical models have been proposed for theoretical analyses of genetic algorithms (GAs). However, these works have limited their objects to a few kinds of GAs in order to formulate them accurately. In this paper, we regard a GA as an information source that generates input-output data. That is, we regard a population and its next population generated by the GA as input and output respectively. Then we model the GA by learning from these data. Since this method uses only the input-output relations of data and ignores interior structures, we can describe a variety of GAs in a common form, and analyze them from a new point of view. We use some mixture models for a representation of these input-output relations in this paper. By using a mixture model for modeling a GA, we can represent the GA system as a combination of some partial systems. In this paper, we treat two types of mixture models, and investigate how these models are effective for analyzing GAs through some numerical experiments.
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