Fitness landscapes and evolutionary algorithms

Abstract

Evolutionary algorithms (EAs) have been increasingly, and successfully, applied to combinatorial optimization problems. However, EAs are relatively complicated algorithms (compared to local search, for example) and it is not always clear to what extent their behaviour can be explained by the particular set of strategies and parameters used. One of the most commonly-used metaphors to describe the process of simple methods such as local search is that of a `fitness landscape', but even in this case, describing what we mean by such a term is not as easy as might be assumed. In this paper, we first present some intuitive ideas and mathematical definitions of what is meant by a landscape and its properties, and review some of the theoretical and experimental work that has been carried out over the past 6 years. We then consider how the concepts associated with a landscape can be extended to search by means of evolutionary algorithms, and connect this with previous work on epistasis variance measurement. The example of the landscapes of the Onemax function will be conside- red in some detail, and finally, some conclusions will be drawn on how knowledge of typical landscape properties can be used to improve the effciency and effectiveness of heuristic search techniques.