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In this paper, we derive models of the selection pressure in XCS for proportionate (roulette wheel) selection and tournament selection. We show that these models can explain the empirical results that have been previously presented in the literature. We validate the models on simple problems showing that, (i) when the model assumptions hold, the theory perfectly matches the empirical evidence; (ii) when the model assumptions do not hold, the theory can still provide qualitative explanations of the experimental results.
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