A methodology for the statistical characterization of genetic algorithms

Abstract

The inherent complexity of the Genetic Algorithms (GAs) has led to various theoretical an experimental approaches whose ultimate goal is to better understand the dynamics of such algorithms. Through such understanding, it is hoped, we will be able to improve their efficiency. Experiments, typically, explore the GA’s behavior by testing them versus a set of functions with characteristics deemed adequate. In this paper we present a methodology which aims at achieving a solid relative evaluation of alternative GAs by resorting to statistical arguments. With it we may categorize any iterative optimization algorithm by statistically finding the basic parameters of the probability distribution of the GA’s optimum values without resorting to a priori functions. We analyze the behavior of 6 algorithms (5 variations of a GA and a hill climber) which we characterize and compare. We make some remarks regarding the relation between statistical studies such as ours and the well known “No Free Lunch Theorem”.