Evolution Strategies
The
Evolution-Strategist

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Evolution-strategic optimization is based on the hypothesis that during the biological evolution the laws of heredity have been developed for fastest phylogenetic adaptation. Evolution-Strategies (ES) imitate, in contrast to the genetic algorithms, the effects of genetic procedures on the phenotype. The presumption for coding the variables in the ES is the realization of a sufficient strong causality (small changes of the cause must create small changes of the effect). The climax of the theory of the Evolution-Strategy is the discovery of the Evolution Window: Evolutionary progress takes place only within a very narrow band of the mutation step size. This fact leads to the necessity for a rule of self-adaptation of the mutation step size.

The notations (1+1)-ES, (1+l)-ES, (1, l)-ES, (m/r, l)-ES ... characterize Evolution-Strategies with an increasing level of imitation of biological evolution. [1]. The letter m means the total number of parents, r marks the number of parents, which will be recombined, and l stands for the number of offspring. Selection takes place only among the offspring (komma notation) or among the offspring and parents together (plus notation). The algebra-like expansion of the notation scheme leads to Nested-Evolution-Strategies, written in the form [ml(ml)g]-ES. Within the outer brackets the l populations will be judged according to their convergence speed, after each of these population has run g-times through a (ml)-selection scheme (g = isolation number). The Nested Evolution-Strategy forms the basis for the evolutionary self-adaptation of strategic parameters. For the self-adaptation of a single mutation step size a simple (1, l)-ES may give suitable results. Nested Evolution-Strategies are qualified for multimodal optimization.

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[1] Ingo Rechenberg: Evolutionsstrategie '94. Stuttgart: Frommann-Holzboog 1994.
[2] Hans-Paul Schwefel: Evolution and Optimum Seeking: New York: Wiley & Sons 1995.

Left the classical experiment made in 1964:
Evolution of a flow-body with minimum drag. Application of a (1+1)-Evolution-Strategy in a windtunnel experiment.

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