Modelling Finite Populations

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Description/Abstract

It is common to model the dynamics of an evolutionary algorithm by considering a typical or representative population. We consider modelling a genetic algorithm using two different descriptions of this typical population. The first using cumulants describing the distribution of fitnesses, the second using the distribution itself. Empirically the cumulant description is found to give a much more accurate description of the evolution despite the fact that it gives a cruder description of the typical distribution. The reason for the success of the cumulant approach is because cumulants are self-averaging quantities. The meaning of this statement in this context is explored. The full distribution description is exact in the limit of an infinite population. It is shown that even in simple problems this limit is only approached for very large populations. Furthermore, the infinite population limit can give misleading predictions for the observable long time behaviour of an evolutionary algorithm.