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Institute
Sequential Parameter Optimization is a model-based optimization methodology, which includes several techniques for handling uncertainty. Simple approaches such as sharp- ening and more sophisticated approaches such as optimal computing budget allocation are available. For many real world engineering problems, the objective function can be evaluated at different levels of fidelity. For instance, a CFD simulation might provide a very time consuming but accurate way to estimate the quality of a solution.The same solution could be evaluated based on simplified mathematical equations, leading to a cheaper but less accurate estimate. Combining these different levels of fidelity in a model-based optimization process is referred to as multi-fidelity optimization. This chapter describes uncertainty-handling techniques for meta-model based search heuristics in combination with multi-fidelity optimization. Co-Kriging is one power- ful method to correlate multiple sets of data from different levels of fidelity. For the first time, Sequential Parameter Optimization with co-Kriging is applied to noisy test functions. This study will introduce these techniques and discuss how they can be applied to real-world examples.
We propose to apply typed Genetic Programming (GP) to the problem of finding surrogate-model ensembles for global optimization on compute-intensive target functions. In a model ensemble, base-models such as linear models, random forest models, or Kriging models, as well as pre- and post-processing methods, are combined. In theory, an optimal ensemble will join the strengths of its comprising base-models while avoiding their weaknesses, offering higher prediction accuracy and robustness. This study defines a grammar of model ensemble expressions and searches the set for optimal ensembles via GP. We performed an extensive experimental study based on 10 different objective functions and 2 sets of base-models. We arrive at promising results, as on unseen test data, our ensembles perform not significantly worse than the best base-model.