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 defined by the average fitness of the population. The average fitness W is defined 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 specific fitness function defined 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 diversified replicator equation. We show that a fast version of Wright's equation gives very good results for optimizing a class of binary fitness functions.

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