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.

Different numerical optimization strategies were used to find an optimized parameter setting for the sheet metal forming process. A parameterization of a time-dependent blank-holder force was used to control the deep-drawing simulation. Besides the already well-established gradient and direct search algorithms and the response surface method the novel Kriging approach was used as an optimization strategy. Results for two analytical and two sheet metal forming test problems reveal that the new Kriging approach leads to a fast and stable convergence of the optimization process. Parallel simulation is perfectly supported by this method

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