Evolutionary algorithms are a common probabilistic optimization method based on the model of natural evolution. One important operator in these algorithms is the selection scheme, for which in this paper a new description model, based on fitness distributions, is introduced. With this, a mathematical analysis of tournament selection, truncation selection, ranking selection, and exponential ranking selection is carried out that allows an exact prediction of the fitness values after selection. The correspondence of binary tournament selection and ranking selection in the expected fitness distribution is proved. Furthermore, several properties of selection schemes are derived (selection intensity, selection variance, loss of diversity), and the three selection schemes are compared using these properties.

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