A comparison of predictive measures of problem difficulty in evolutionary algorithms

This paper studies a number of predictive measures of problem difficulty, among which epistasis variance and fitness distance correlation are the most widely known. Our approach is based on comparing the reference class of a measure to a number of known easy function classes. First, we generalize the reference classes of fitness distance correlation and epistasis variance, and construct a new predictive measure that is insensitive to nonlinear fitness scaling. We then investigate the relations between the reference classes of the measures and a number of intuitively easy classes. We also point out the need to further identify which functions are easy for a given class of evolutionary algorithms in order to design more efficient hardness indicators for them. We finally restrict attention to the genetic algorithm (GA), and consider both GA-easy and GA-hard fitness functions, and give experimental evidence that the values of the measures, based on random samples, can be completely unreliable and entirely uncorrelated to the convergence quality and convergence speed of GA instances using either proportional or ranking selection.