Evolution strategies are general, nature-inspired heuristics for search and optimization. Supported both by empirical evidence and by recent theoretical findings, there is a common belief that evolution strategies are robust and reliable, and frequently they are the method of choice if neither derivatives of the objective function are at hand nor differentiability and numerical accuracy can be assumed. However, despite their widespread use, there is little exchange between members of the “classical ” optimization community and people working in the field of evolutionary computation. It is our belief that both sides would benefit from such an exchange. In this paper, we present a brief outline of evolution strategies and discuss some of their properties in the presence of noise. We then empirically demonstrate that for a simple but nonetheless nontrivial noisy objective function, an evolution strategy outperforms other optimization algorithms designed to be able to cope with noise. The environment in which the algorithms are tested is deliberately chosen to afford a transparency of the results that reveals the strengths and shortcomings of the strategies, making it possible to draw conclusions with regard to the design of better optimization algorithms for noisy environments. 1

Many variants of evolutionary algorithms have been designed and applied. The

Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.

Iterative algorithms for numerical optimization in continuous spaces typically need to adapt their step lengths in the course of the search. While some strategies employ fixed schedules for reducing the step lengths over time, others attempt to adapt interactively in response to either the outcome of trial steps or to the history of the search process. Evolutionary algorithms are of the latter kind. One of the control strategies that is commonly used in evolution strategies is the cumulative step length adaptation approach. This paper presents a first theoretical analysis of that adaptation strategy by considering the algorithm as a dynamical system. The analysis includes the practically relevant case of noise interfering in the optimization process. Recommendations are made with respect to the problem of choosing appropriate popula- tion sizes.