Experiments with tuneable fitness landscapes

Abstract

Kauffman's N K'-landscapes have become a popular tool for investigating properties of heuristic search algorithms. In this paper we carry out some experiments with a mole general, but still tuneable, class of landscapes which we call l, Ө landscapes. These landscapes are characterized by a parameter Ө which allows interactions at all orders, rather than merely at orders up to a fixed level as is the case with NK-landscapes. This is accomplished by fixing the magnitude and sign of the effects in an experimental design (ED) decomposition of a function. In some cases the cpistasis variance is a simple Function of Ө, and can be specified in advance. I'urther, by choosing some measure of the Hamming landscape associated with these functions, such as the number of local optima or the size of the global optimum's basin, it is possible to tune the landscape by mapping the effects onto a search problem. Some experiments arc reported with a GA on these landscapes, with results that are rather surprising, in that the quality of the solution obtained appears to be poorly predicted by the properties of the associated Hamming landscape.