  It is commonly assumed that the ability to track the frequencies of a set of
schemata in the evolving population of an infinite population genetic algorithm
(IPGA) under different fitness functions will advance efforts to obtain a
theory of adaptation for the simple GA. Unfortunately, for IPGAs with long
genomes and non-trivial fitness functions there do not currently exist
theoretical results that allow such a study. We develop a simple framework for
analyzing the dynamics of an infinite population evolutionary algorithm (IPEA).
This framework derives its simplicity from its abstract nature. In particular
we make no commitment to the data-structure of the genomes, the kind of
variation performed, or the number of parents involved in a variation
operation. We use this framework to derive abstract conditions under which the
dynamics of an IPEA can be coarse-grained. We then use this result to derive
concrete conditions under which it becomes computationally feasible to closely
approximate the frequencies of a family of schemata of relatively low order
over multiple generations, even when the bitstsrings in the evolving population
of the IPGA are long.
