The Dynamics of a Genetic Algorithm for a Simple Learning Problem

TL;DR

This paper models the dynamics of genetic algorithms for a simple learning task using statistical mechanics, providing insights into optimal batch sizes and population effects to improve efficiency.

Contribution

It introduces a formalism for analyzing GA dynamics with statistical mechanics, deriving analytical solutions and optimal parameters for training efficiency.

Findings

Analytical expressions for GA dynamics under certain conditions.

Optimal population size can eliminate noise effects from finite batch sizes.

Guidelines for choosing batch size to minimize training patterns used.

Abstract

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.