New Methods for Tunable, Random Landscapes

Abstract

To understand the behavior of search methods (including genetic algorithms (GAs)), it is useful to understand the nature of the landscapes they search. Since there are an infinite number of landscapes, with an infinite number of characteristics, this is a difficult question. Therefore, it is interesting to consider parameterized landscape generators if the parameters they employ have direct and identifiable effects on landscape complexity. A prototypical examination of this sort is the generator provided by NK landscapes. However, previous work by the authors and others has shown that NK models are limited in the landscapes they generate, and in the complexity control provided by their two parameters. Previous work suggested an added parameter, which the authors called P, that affects the number of epistatic interactions. Although this provided generation of all possible search landscapes, previous work indicated that control over certain aspects of complexity was limited in the NKP generator. This chapter builds on previous work, suggesting that two additional parameters are helpful in controlling complexity: the relative scale of higher order and lower order epistatic effects, and the correlation of higher order and lower order effects. This chapter presents a generator based on these principles, and examines it, both analytically, and through actual GA runs on landscapes from this generator. The chapter also presents the results of these examinations, discusses their implications, and suggests areas for further examination.