The Theory of Evolution Strategies

1. Introduction.- 2. Concepts for the Analysis of the ES.- 3. The Progress Rate of the (1% MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8% qadaqadaWdaeaapeGaaGyma8aadaWfGaqaa8qacaGGSaaal8aabeqa% a8qacqGHRaWkaaGccqaH7oaBaiaawIcacaGLPaaaaaa!3C4E!$$left( {1mathop ,limits^ + lambda } right)$$?)-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.