Relative Building-Block Fitness and the Building Block Hypothesis

The building-block hypothesis states that the GA works well when short, low-order, highly-fit schemas recombine to form even more highly fit higher-order schemas. The ability to produce fitter and fitter partial solutions by combining building blocks is believed to be a primary source of the GA’s search power, but the GA research community currently lacks precise and quantitative descriptions of how schema processing actually takes place during the typical evolution of a GA search. Another open problem is to characterize in detail the types of fitness landscapes for which crossover will be an effective operator. In this paper we first describe a class of fitness landscapes (the “Royal Road” functions) that we have designed to investigate these questions. We then present some unexpected experimental results concerning the GA’s performance on simple instances of these landscapes, in which we vary the strength of reinforcement from “stepping stones”—fit intermediate-order schemas obtained by recombining fit low-order schemas. Finally, we compare the performance of the GA on these functions with that of three commonly used hill-climbing schemes, Current address: Santa Fe Institute, 1660 Old Pecos Trail, Suite A, Santa Fe, NM 87501 and find that one of them, “random-mutation hill-climbing”, significantly outperforms the GA on these functions.