Contributions to the optimization of particle design under uncertainty

Nanoparticles as well as polyethylene glycol, which are considered in the application of this thesis, are extremely small. Thus, already small fluctuations in their size have an enormous impact on their other properties. Therefore, during their production or extraction, great attention must be paid to imperfections in order to achieve the desired results. Hence, optimization under uncertainty is an useful tool. In this thesis, two basic processes, synthesis and chromatography, are optimized. For synthesis, reformulations and simplifications at the model level are used in order to find the optimum reactor length with an uncertain growth rate. Furthermore, a bundle method is incorporated to optimize the inflow rate of the feed for processes, which are based on non-linear partial differential equations. The optimization of the fractionation times with uncertain acetonitrile ratio of an analytical chromatography process serves as an application for an approach from distributional robust optimization. For this approach, we discretize a semi-infinite problem and define additional constraints to obtain an inner approximation of the feasible set. For the uncertainty set, we use bounds on the first two moments as well as an envelope function. It should be emphasized that non-convex indicator functions in the constraints can also be considered. If process data is available and can be integrated into the model, the approach can also be used for preparative chromatography. In both, synthesis and chromatography, uncertainties due to external factors such as temperature or inaccuracies, e.g., of the mixing pump for the eluent, are taken into account.