We present numerical results on Kauffman's NK landscape family indicating that the optimal distance at which to search for fitter variants depends on both the current fitness and the sampling that can be afforded at each distance. The optimal search distance from average fitness configurations is large to escape local correlation limits and decreases as fitness increases. An analytic derivation of the optimal search distance as a function the landscape correlation p, the current fitness f_#mu#, and the number of samples n is determined by introducing a new landscape family - p-landscapes, The utility of p-landscapes is demonstrated by determining a few of their simple properties.
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