Modelling GA Dynamics: 1st

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Description/Abstract

This paper is an introduction to the mathematical modelling of the dynamics of genetic algorithms. 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 modelled.