Misleading functions designed from alternation

The paper proposes the design of difficult functions for a GA (genetic algorithm) where the deceptive attractor is at mid-distance from the global optimum. First, piecewise-linear trap functions of alternation are investigated. We consider alternation based distance to enable the ability of fitness distance correlation coefficient to predict GA behavior on such functions. Then, we generalize to any function by way of the derivative transformation applied on bit strings. These preliminary results support the following conjecture: derivative transforms are difficult problems, where competition occurs between complementary strings, and lead to misleading problems where crossover is an effective operator and competitors are at mid-distance from each other.