The pace of progress in the fields of Evolutionary Computation and Machine Learning is currently limited -- in the former field, by the improbability of making advantageous extensions to evolutionary algorithms when their capacity for adaptation is p
oorly understood, and in the latter by the difficulty of finding effective semi-principled reductions of hard real-world problems to relatively simple optimization problems. In this paper we explain why a theory which can accurately explain the simple genetic algorithms remarkable capacity for adaptation has the potential to address both these limitations. We describe what we believe to be the impediments -- historic and analytic -- to the discovery of such a theory and highlight the negative role that the building block hypothesis (BBH) has played. We argue based on experimental results that a fundamental limitation which is widely believed to constrain the SGAs adaptive ability (and is strongly implied by the BBH) is in fact illusionary and does not exist. The SGA therefore turns out to be more powerful than it is currently thought to be. We give conditions under which it becomes feasible to numerically approximate and study the multivariate marginals of the search distribution of an infinite population SGA over multiple generations even when its genomes are long, and explain why this analysis is relevant to the riddle of the SGAs remarkable adaptive abilities.
Skepticism of the building block hypothesis (BBH) has previously been expressed on account of the weak theoretical foundations of this hypothesis and the anomalies in the empirical record of the simple genetic algorithm. In this paper we hone in on a
more fundamental cause for skepticism--the extraordinary strength of some of the assumptions that undergird the BBH. Specifically, we focus on assumptions made about the distribution of fitness over the genome set, and argue that these assumptions are unacceptably strong. As most of these assumptions have been embraced by the designers of so-called competent genetic algorithms, our critique is relevant to an appraisal of such algorithms as well.
