The Gambler’s Ruin Problem and Population Sizing

Abstract

This chapter presented a solution to a long-standing problem in genetic algorithms: how to determine an adequate population size to reach a solution of a particular quality. The model is based on a random walk where the position of a particle on a bounded one-dimensional space represents the number of copies of the correct BBs in the population. The probability that the particle will be absorbed by the boundaries is well known, and it was used to derive an equation that relates the population size with the required solution quality and several domain-dependent parameters.

The accuracy of the model was verified with experiments using test problems that ranged from the very simple to the moderately hard. The results confirmed that the model is accurate, and that its predictions scale well with the difficulty of the domain. In addition, the basic model was extended to consider explicit noise in the fitness evaluation and different selection schemes.

A correctly-sized population is the first step toward competent and efficient genetic algorithms. The next chapter describes how to make single-population GAs faster by using multiple processors to evaluate the fitness of the population in parallel. Subsequent chapters extend the gambler’s ruin model to parallel GAs with multiple populations.