On Classifications of Fitness Functions

Abstract

It is well-known that evolutionary algorithms succeed to optimize some functions efficiently and fail for others. Therefore, one would like to classify fitness functions as more or less hard to optimize for evolutionary algorithms. The aim of this paper is to clarify limitations and possibilities for classifications of fitness functions from theoretical point of view. We distinguish two different types of classifications, descriptive and analytical ones. We shortly discuss three widely known approaches, namely the NK model, epistasis variance, and fitness distance correlation. Furthermore, we consider nother recent measure, bit-wise epistasis introduced by Fonlupt, Robilliard,and Preux (1998). We discuss shortcomings and counter-examples for all four measures and use this to motivate discussion of possibilities and limitations of classifications of fitness functions in broader context and find out its shortcomings.