Tailoring Mutation to Landscape Properties

We present numerical results on Kau man's NK landscape family indicating that the optimal distance at which to search for tter variants depends on both the current tness and the sampling that can be a orded at each distance. The optimal search distance from average tness con gurations is large to escape local correlation limits and decreases as tness increases. An analytic derivation of the optimal search distance as a function the landscape correlation , the current tness f , and the number of samples n is determined by introducing a new landscape family { -landscapes. The utility of -landscapes is demonstrated by determining a few of their simple properties.