  Quantification and minimization of uncertainty is an important task in the
design of electromagnetic devices, which comes with high computational effort.
We propose a hybrid approach combining the reliability and accuracy of a Monte
Carlo analysis with the efficiency of a surrogate model based on Gaussian
Process Regression. We present two optimization approaches. An adaptive
Newton-MC to reduce the impact of uncertainty and a genetic multi-objective
approach to optimize performance and robustness at the same time. For a
dielectrical waveguide, used as a benchmark problem, the proposed methods
outperform classic approaches.
