Abstract
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.
Original language  English 

Title of host publication  Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004 
Pages  12401247 
Number of pages  8 
Volume  2 
Publication status  Published  13 Sep 2004 
Externally published  Yes 
Event  IEEE Congress on Evolutionary Computation 2004  Portland, United States of America Duration: 19 Jun 2004 → 23 Jun 2004 https://ieeexplore.ieee.org/xpl/conhome/9256/proceeding (Proceedings) 
Conference
Conference  IEEE Congress on Evolutionary Computation 2004 

Abbreviated title  IEEE CEC 2004 
Country  United States of America 
City  Portland 
Period  19/06/04 → 23/06/04 
Internet address 
