Evolutinary algorithms (EA) have found a broad acceptance as robust optimization algorithms in the last ten years. The idea of optimizing systems through imitating nature and applying the genetic operators such as selection, mutation, and recombination has a certain appeal. The fundamental algorithms are attractively simple, and quite universal. The aim of this monograph is to provide a theoretical framework for the ES research field. The analysis is based on understanding the evolutionary algorithm as a dynamical system. The central quantity of such an analysis is the progress rate \(\varphi\), introduced by Rechenberg (1973). This is a measure for the state change of the system toward the optimum.
The monograph contains seven chapters. In the first chapter the author gives his personal EA philosphy as an introduction to the evolutionary algorithms in general and particularly to the Evolution Strategies (ES). Different EA variants are handled under a unified approach and way of thinking. The views presented here results essentially from the analysis of ES models. In chapter 2 the theoretical framework will be defined in which the analysis of ES will be conducted in the following chapters. The progress measures will be defined here, which can be used in the evaluation of the optimization performance of an EA. The third chapter is dedicated to the progress rate of the \((1{+\atop ,}\lambda)\)-evolution strategies for the sphere model. The fourth chapter follows with the analysis of the quality gain of some strategies. The fifth chapter is devoted to the theoretical problem of population formation in \((\mu,\lambda)\)-strategies. In chapter 6 the recombination operator is investigated. The question of the actual use of ‘sex’ is followed here. The seventh chapter is devoted to the analysis of \(\sigma\)-self-adaptation using \((1,\lambda)\)-ES as an example.
The book contains references to open problems, to new problem formulations, and to future research directions at the relevant places.