The Theory of Evolution Strategies

1. Front Matter

   Pages I-XIX

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2. Introduction

   • Hans-Georg Beyer

   Pages 1-24

3. Concepts for the Analysis of the ES

   • Hans-Georg Beyer

   Pages 25-50

4. The Progress Rate of the \(\left( {1\mathop ,\limits^ + \lambda } \right)\)-ES on the Sphere Model

   • Hans-Georg Beyer

   Pages 51-111

5. The (\(1\mathop + \limits_, \lambda \)) Quality Gain

   • Hans-Georg Beyer

   Pages 113-142

6. The Analysis of the (µ, λ)-ES

   • Hans-Georg Beyer

   Pages 143-201

7. The (μ/μ, λ) Strategies — or Why “Sex” May be Good

   • Hans-Georg Beyer

   Pages 203-256

8. The (1, λ)-σ-Self-Adaptation

   • Hans-Georg Beyer

   Pages 257-326

9. Back Matter

   Pages 327-381

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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.

• Evolution Strategy
• Evolutionary Algorithms
• Evolutionary Alorithm Theory
• Evolutionary Programming
• Evolutionsstrategie
• Evolutionäre Algorithmen
• Genetic Algorithms
• Genetische Algorithmen
• Optimization
• algorithms
• evolution
• evolutionary algorithm
• genetic algorithm
• algorithm analysis and problem complexity

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)

• Department of Computer Science, University of Dortmund, Dortmund, Germany

  Hans-Georg Beyer

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