Towards a genetic theory of easy and hard functions

Abstract

According to the literature that deals with the difficulty of functions with respect to genetic algorithms (GA), the so-called GA-hard functions are usually hard for other methods. In this paper, we firstly show that a gradient easy function can be fully deceptive, and thus hard for a GA to optimize while being unimodal. More generally, we show that the global search method introduced by (Das and Whitley 1991) to optimize GA-easy functions can be simply adapted to solve GA-hard functions. The resulting algorithm, called GSC1, generates a set of binary strings and outputs the string that wins the first order schemas competitions as well as its binary complement. According to the theory of deceptiveness in GAs, this method solves GA-easy and GA-hard problems efficiently, as shown effectively in the reported experiments. This method is however only well suited for these functions, and does not deal with partially deceptive functions. It is then shown how it could be combined with a GA.