Viewing the selection process in a genetic algorithm as a two-step procedure consisting of the assignment of selection probabilities and the sampling according to this distribution, we employ the χ2 measure as a tool for the analysis of the stochastic properties of the sampling. We are thereby able to compare different selection schemes even in the case that their probability distributions coincide. Introducing a new sampling algorithm with adjustable accuracy and employing two-level test designs enables us to further reveal the intrinsic correlation structures of well-known sampling algorithms. Our methods apply well to integral methods like tournament selection and can be automated.

In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basis algorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basis algorithm is only suboptimal. We apply methods from the field of evolutionary computation (EC) to test the quality of the near-best-basis results. We observe a phenomenon: the results of the near-best-basis algorithm are inferior in terms of cost-function optimization but are superior in terms of rate/distortion performance compared to EC methods.

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Currently, the most efficient numerical techniques for evaluating high-dimensional integrals are based on Monte Carlo and quasi-Monte Carlo techniques. These tasks require a significant amount of computation and are therefore often executed on parallel computer systems. In order to keep the communication amount within a parallel system to a minimum, each processing element (PE) requires its own source of integration nodes. Therefore, techniques for using separately initialized and disjoint portions of a given point set on a single PE are classically employed. Using the so-called substreams may lead to dramatic errors in the results under certain circumstances. In this work, we compare the possible defects employing leaped quasi-Monte Carlo and Monte Carlo substreams. Apart from comparing the magnitude of the observed integration errors we give an overview under which circumstances (i.e. parallel programming models) such errors can occur.

Abstract. In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi-Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically demonstrate the speed-up and the quality loss obtained by the LLL reduction, and we present important applications for parameter selections.