Representation, Search and Genetic Algorithms

L. Darrell Whitley, Soraya B. Rana

Abstract: Wolpert and Macready's No Free Lunch theorem proves that no search algorithm is better than any other over all possible discrete functions. The meaning of the No Free Lunch theorem has, however, been the subject of intense debate. We prove that for local neighborhood search on problems of bounded complexity, where complexity is measured In terms of number of basins of attraction in the search space a Gray coded representation is better than Binary in the sense that on average it induces fewer minima in a Hamming distance 1 search neighborhood.