The state space of the Markov chain modelling an evolutionary algorithm

is quite large especially if the population space and the search space are

large. I shell introduce an appropriate notion of "coarse graining" for

such Markov chains. Indeed, from the mathematical point of view, this can

be called a quotient of a Markov chain by an equivalence relation over the

state space. The newly obtained Markov chain has a significantly smaller

state space and it's stationary distribution is "coherent" with the

initial large chain. Although the transition probabilities of the

coarse-grained Markov chain are defined in terms of the stationary

distribution of the original big chain, in some cases it is possible to

deduce interesting information about the stationary distribution of the

original chain in terms of the quatient chain. I will demonstrate how

this method works. I shell also present some simple results and open

questions.