On functions with a given fitness-distance relation

Recent work stresses the limitations of fitness distance correlation (FDC) as an indicator of landscape difficulty for genetic algorithms (GAs). Realizing that the fitness distance correlation (FDC) value cannot be reliably related to landscape difficulty, we investigate whether an interpretation of the whole correlation plot can yield reliable information about the behavior of the GA. Our approach is as follows. We present a generic method for constructing fitness functions which share the same fitness versus distance-to-optimum relation (FD relation). Special attention is given to FD relations which show no local optimum in the correlation plot, as is the case for the relation induced by Horn's longpath (J. Horn and D.E. Goldberg, 1995). We give an inventory of different types of GA behavior found within a class of fitness functions with a common correlation plot. We finally show that GA behavior can be very sensitive to small modifications of the fitness-distance relation.