New Methods for Tunable, Random Landscapes

Abstract To understand the behaviour of search methods (including GAs), it is useful to understand the nature of the landscapes they search. What makes a landscape complex to 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 parameterised 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 (N, the size of the landscape, and K, the degree of epistasis). Previous work suggested an added parameter, which the authors called P, which affects the number of epistatic interactions. Although this provided generation of all possible search landscapes (with given epistasis K), previous work indicated that control over certain aspects of complexity was limited in the NKP generator. This paper 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. A generator based on these principles is presented, and it is examined, both analytically, and through actual GA runs on landscapes from this generator. In some cases, the GA’s performance is as analysis would suggest. However, for particular cases of K and P, the results run counter to analytical intuition. The paper presents the results of these examinations, discusses their implications, and suggests areas for further examination.