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The evolution strategy, an algorithm imitating the effect of the biological evolution, has already been presented in this journal [Bäck92]. The basic algorithm described there uses a single population with a fixed number of parents and offspring. The present paper shows an extended algorithm with a higher imitative level of biological evolution. In this hierarchically organized evolution strategy there exist several populations being in competition with each other. These populations differ from each other by varied strategy parameters. The number of offspring is such a strategy parameter which is different in each population and it is shown that it can be adjusted adaptively with the proposed algorithm.After derivating the theoretical values for the optimal number of offspring for the two exemplary testfunctions hyperplane and hypersphere the simulation results for these testfunctions are shown.

Evolution strategies with subjective selection of the offspring can be applied to optimization problems, when no objective evaluation of the offspring is possible. For this class of optimization problems, strategies with insensitivity towards incorrect selection decisions are necessary. With subjective selection, incorrect decisions are unavoidable and have the effect of noise being overlaid onto the fitness value. Three examples of different evolution strategies (ES) are presented which are resistant against wrong selection decisions.