Test Function Generators as Embedded Landscapes

NK-landscapes and kSAT problems have been proposed as potential test problem domains for Genetic Algorithms. We demonstrate that GAs have diiculty solving both kSAT and NK-landscape problems. The construction of random kSAT and NK-landscape problems are very similar, but the diierences between kSAT and NK-landscape generation result in vastly diierent tness landscapes. In this paper we introduce a parameterized model for the construction of test function generators. This model, called embedded landscapes, can be used to isolate the features of combinatorial optimization problems for more control during experimentation. We also show that common forms of embedded landscapes allow for a polynomial time Walsh analysis. This means we also can compose exact schema averages in polynomial time for schema up to order-K, where K is a constant. Yet, in the general case, this information does not allow one to infer the global optimum of a function unless the complexity classes P and NP are equal.