On geometric and statistical properties of the attractors of a generic evolutionary algorithm

In this work, evolutionary algorithms are modeled as random dynamical systems. The combined action of selection and variation is expressed as a stochastic operator acting on the space of populations. The long term behavior of selection and variation is studied separately. Then the combined effect is analyzed by characterizing the attractor and stationary measure of the dynamics. As a main result it is proved that the stationary measure is supported on populations made up of optimizers. Also, some experiments are carried out in order to visualize the evolvable populations, the attractor sets and the stationary measure. Some geometric properties of such sets are discussed.