GA-hard functions built by combination of Trap functions

We propose to construct hard functions for genetic algorithms by combining two types of misleading functions. We consider on one hand the traditional Trap functions defined over the unitation, and on the other hand new Trap functions based on the alternation. We recall the performance of GA on these functions as well as the results on the predictive value of the coefficients of correlation between distance to the optimum and fitness. We show that the combination of such functions can generate misleading problems for a genetic algorithm. Moreover, some of these combinations constitute counterexamples for the predictive value of the coefficient of correlation.