Evolutionary computation and Wright's equation

AbstractIn 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

Evolutionary Optimization and the Estimation of Search Distributions with Applications to Graph Bipartitioning

We present a theory of population based optimization methods using approximations of search distributions. We prove convergence of the search distribution to the global optima for the Factorized Distribution Algorithm FDA if the search distribution is a Boltzmann distribution and the size of the population is large enough. Convergence is defined in a strong sense -- the global optima are attractors of a dynamical system describing mathematically the algorithm. We investigate an adaptive annealing schedule and show its similarity to truncation selection. The inverse temperature beta is changed inversely proportionally to the standard deviation of the population. We extend FDA by using a Bayesian hyper parameter. The hyper parameter is related to mutation in evolutionary algorithms. We derive an upper bound on the hyper parameter to ensure that FDA still generates the optima with high probability. We discuss the relation of the FDA approach to methods used in statistical physics to approximate a Boltzmann distribution and to belief propagation in probabilistic reasoning. In the last part, we apply the algorithm to an important practical problem, the bipartioning of large graphs. We assume that the graphs are sparsely connected. Our empirical results are as good or even better than any other method used for this problem

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 p_i. 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

Effective mutation rate for probabilistic evolutionary design of analogue electrical circuits

The paper represents the approach to evolutionary analogue circuit design on the base of the univariate marginal distribution algorithm. In order to generate a new population the probability distribution is used instead of reproduction operators. It allows us to control evolvability of a population on mesoscopic level. Experimental results obtained have indicated that a high mutation rate increases the success rate, although computational costs are increased too. The effective mutation rate that supplies high success rate and small computational costs is examined for different weightings of the fitness function