1. Introduction.- 2. Concepts for the Analysis of the ES.- 3. The Progress Rate of the (1
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?)-ES on the Sphere Model.- 5. The Analysis of the (?, ?)-ES.- 6. The (?/?, ?) Strategies - or Why "Sex" May be Good.- 7. The (1, ?)-?-Self-Adaptation.- Appendices.- A. Integrals.- A.1 Definite Integrals of the Normal Distribution.- A.2 Indefinite Integrals of the Normal Distribution.- A.3 Some Integral Identities.- B. Approximations.- B.1 Frequently Used Taylor Expansions.- B.3 Cumulants, Moments, and Approximations.- B.3.1 Fundamental Relations.- B.3.2 The Weight Coefficients for the Density Approximation of a Standardized Random Variable.- B.4 Approximation of the Quantile Function.- C. The Normal Distribution.- C.3 Product Moments of Correlated Gaussian Mutations.- C.3.1 Fundamental Relations.- C.3.2 Derivation of the Product Moments.- D. (1, ?)-Progress Coefficients.- D.2 Table of Progress Coefficients of the (1, ?)-ES.- References.

Evolutionary algorithms, such as evolution strategies, genetic algorithms, or evolutionary programming, have found broad acceptance in the last ten years. In contrast to its broad propagation, theoretical analysis in this subject has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is deriving a qualitative understanding of why and how these ES algorithms work.