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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.
List of contents
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.
Summary
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.
Additional text
From the reviews:
"He gives an extensive mathematical treatment of idealised models of behaviour for several types of EA … . The detail is extensive enough to guide and educate graduate students … . The figures are clear and convincing. Part of the quality of the book is its aesthetically pleasing layout, for both figures and mathematics. … The book is a desirable resource for all those, students and others, who need or wish to have a single portable source for the mathematically-based fundamentals of the subject." (John Campbell, Expert Update, Vol. 6 (1), 2003)
"Evolutionary algorithms (EA) have found a broad acceptance as robust optimization algorithms in the last ten years. … The aim of this monograph is to provide a theoretical framework for the ES research field. … The book contains references to open problems, to new problem formulations, and to future research directions at the relevant places." (Horst Hollatz, Zentralblatt MATH, Vol. 969, 2001)
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From the reviews:
"He gives an extensive mathematical treatment of idealised models of behaviour for several types of EA ... . The detail is extensive enough to guide and educate graduate students ... . The figures are clear and convincing. Part of the quality of the book is its aesthetically pleasing layout, for both figures and mathematics. ... The book is a desirable resource for all those, students and others, who need or wish to have a single portable source for the mathematically-based fundamentals of the subject." (John Campbell, Expert Update, Vol. 6 (1), 2003)
"Evolutionary algorithms (EA) have found a broad acceptance as robust optimization algorithms in the last ten years. ... The aim of this monograph is to provide a theoretical framework for the ES research field. ... The book contains references to open problems, to new problem formulations, and to future research directions at the relevant places." (Horst Hollatz, Zentralblatt MATH, Vol. 969, 2001)
