Conclusions

In this book, we have studied the effects that noise has on the local performance of several variants of the (µ/ρ t λ)-ES. Our conviction that certain behaviors of evolution strategies can best be understood in the most simple environments in which they can be observed led us to the definition of the linear and of the spherical fitness environments in Section 3 of Chapter 2.Inherent to both fitness environments are symmetries that result in invariance properties that simplify substantially the analysis of the behavior of the strategies. After initialization effects have faded, the behavior of the strategies can be described by time-invariant probability distributions. Most of the analyses presented in this work followed the same basic pattern: identify the variables determining the strategies' state, determine the effects that variation and selection have on them, and infer information on those variables by means of invariance considerations. As the variables we sought to learn about are random variables, those steps required the handling of probability distributions of usually unknown shape, and frequently we had to resort to expanding the distributions in terms of derivatives of a normal distribution and to hope that they are well characterized by a number of lower-order moments. That hope and various modeling assumptions and simplifications made in the calculations made it necessary to verify the accuracy of our results by comparing them with results of computer experiments.