The Theory of Evolution Strategies

1. Auflage. Softcover version of original hardcover Auflage 2001
ISBN: 978-3-642-08670-0
Verlag: Springer

Buch, Englisch, 381 Seiten, Previously published in hardcover, Format (B × H): 156 mm x 234 mm, Gewicht: 611 g

Reihe: Natural Computing Series

Evolutionary Algorithms, in particular Evolution Strategies, Genetic Algorithms, or Evolutionary Programming, have found wide acceptance as robust optimization algorithms in the last ten years. Compared with the broad propagation and the resulting practical prosperity in different scientific fields, the theory 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 on understanding the functioning of these probabilistic optimization algorithms in real-valued search spaces by investigating the dynamical properties of some well-established ES algorithms. The book introduces the basic concepts of this analysis, such as progress rate, quality gain, and self-adaptation response, and describes how to calculate these quantities. Based on the analysis, functioning principles are derived, aiming at a qualitative understanding of why and how ES algorithms work.

Zielgruppe

Research

Autoren/Hrsg.

Beyer, Hans-Georg

Fachgebiete

• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Geisteswissenschaften Philosophie Naturphilosophie, Philosophie und Evolution
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Biowissenschaften Biowissenschaften Evolutionsbiologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.