The optimization of non-linear functions is a common problem when designing technical systems. In many realistic optimization and decision problems, the evaluation of the objective function requires the solution of a complex simulation model or the conduction of one or more experiments, such as a destructive testing procedure. AdCo Engineering<sup>GW</sup> uses so-called Bayesian optimization for such problems. Bayesian optimization is a very powerful strategy for identifying extrema of objective functions. Bayesian optimization is particularly beneficial when either function evaluations are expensive or there is not any gradient information available or the problem is not convex or the function evaluations are contaminated with noise. Bayesian optimization techniques are among the most efficient methods in terms of the required number of function evaluations. A large part of the efficiency results from the ability of the Bayesian optimization scheme to incorporate a-priori assumptions and knowledge about the problem and to update this knowledge via specific function evaluations. In this context, the exploitation of the current knowledge is traded off against the exploration of the search space.