Evolutionary computation and Wright's equation

In this paper, Wright's equation formulated in 1931 is proven and applied to evolutionary computation. Wright's equation shows that evolution is doing gradient ascent in a landscape deÿned by the average ÿtness of the population. The average ÿtness W is deÿned in terms of marginal gene frequencies pi. Wright's equation is only approximately valid in population genetics, but it exactly describes the behavior of our univariate marginal distribution algorithm (UMDA). We apply Wright's equation to a speciÿc ÿtness function deÿned by Wright. Furthermore we introduce mutation into Wright's equation and UMDA. We show that mutation moves the stable attractors from the boundary into the interior. We compare Wright's equation with the diversiÿed replicator equation. We show that a fast version of Wright's equation gives very good results for optimizing a class of binary ÿtness functions.