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Probabilistic analysis of the (1+1)-evolutionary algorithm

We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations for the mean and the variance represent the strongest of their kind. The approach we develop is also applicable to characterize the limit laws and is based on asymptotic resolution of the underlying recurrence. While most approximations have their simple formal nature, we elaborate on the delicate error analysis required for rigorous justifications.