  A formalism for describing the dynamics of Genetic Algorithms (GAs) using
methods from statistical mechanics is applied to the problem of generalization
in a perceptron with binary weights. The dynamics are solved for the case where
a new batch of training patterns is presented to each population member each
generation, which considerably simplifies the calculation. The theory is shown
to agree closely to simulations of a real GA averaged over many runs,
accurately predicting the mean best solution found. For weak selection and
large problem size the difference equations describing the dynamics can be
expressed analytically and we find that the effects of noise due to the finite
size of each training batch can be removed by increasing the population size
appropriately. If this population resizing is used, one can deduce the most
computationally efficient size of training batch each generation. For
independent patterns this choice also gives the minimum total number of
training patterns used. Although using independent patterns is a very
inefficient use of training patterns in general, this work may also prove
useful for determining the optimum batch size in the case where patterns are
recycled.
