zbMATH — the first resource for mathematics

Modelling genetic algorithm dynamics. (English) Zbl 1001.68184
Kallel, Leila (ed.) et al., Theoretical aspects of evolutionary computing. 2nd EvoNet Summer School, Middelheim campus, Univ. of Antwerp, Belgium, September 1999. Berlin: Springer. Natural Computing Series. 59-85 (2001).
Summary: This tutorial is an introduction to the mathematical modeling of the dynamics of Genetic Algorithms (GAs). The distinguishing feature of this approach is that we consider macroscopic properties of the system. After some brief introductory remarks, we look at a generational GA, with tournament selection, tackling the ones-counting problem. Initially we ignore recombination. We start with a two-parameter model of the evolution. This is sufficient to explain the qualitative features of the dynamics, although it does not give a good quantitative agreement with simulations. We show how the agreement can be improved by using more parameters to describe the population and by introducing finite population corrections. Finally, we come back to recombination and show how this can be modeled.
For the entire collection see [Zbl 0962.00007].

68W05 Nonnumerical algorithms
68T05 Learning and adaptive systems in artificial intelligence