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An essential task for operation and planning of biogas plants is the optimization of substrate feed mixtures. Optimizing the monetary gain requires the determination of the exact amounts of maize, manure, grass silage, and other substrates. Accurate simulation models are mandatory for this optimization, because the underlying chemical processes are very slow. The simulation models themselves may be time-consuming to evaluate, hence we show how to use surrogate-model-based approaches to optimize biogas plants efficiently. In detail, a Kriging surrogate is employed. To improve model quality of this surrogate, we integrate cheaply available data into the optimization process. Doing so, Multi-fidelity modeling methods like Co-Kriging are employed. Furthermore, a two-layered modeling approach is employed to avoid deterioration of model quality due to discontinuities in the search space. At the same time, the cheaply available data is shown to be very useful for initialization of the employed optimization algorithms. Overall, we show how biogas plants can be efficiently modeled using data-driven methods, avoiding discontinuities as well as including cheaply available data. The application of the derived surrogate models to an optimization process is shown to be very difficult, yet successful for a lower problem dimension.
Computational intelligence methods have gained importance in several real-world domains such as process optimization, system identification, data mining, or statistical quality control. Tools are missing, which determine the applicability of computational intelligence methods in these application domains in an objective manner. Statistics provide methods for comparing algorithms on certain data sets. In the past, several test suites were presented and considered as state of the art. However, there are several drawbacks of these test suites, namely: (i) problem instances are somehow artificial and have no direct link to real-world settings; (ii) since there is a fixed number of test instances, algorithms can be fitted or tuned to this specific and very limited set of test functions; (iii) statistical tools for comparisons of several algorithms on several test problem instances are relatively complex and not easily to analyze. We propose a methodology to overcome these difficulties. It is based on standard ideas from statistics: analysis of variance and its extension to mixed models. This paper combines essential ideas from two approaches: problem generation and statistical analysis of computer experiments.