Handling Uncertainty in Higher Dimensions with Potential Clouds towards Robust Design Optimization

Robust design optimization methods applied to real life problems face some major difficulties: how to deal with the estimation of probability densities when data are sparse, how to cope with high dimensional problems and how to use valuable information in the form of unformalized expert knowledge. We introduce the clouds formalism as means to process available uncertainty information reliably, even if limited in amount and possibly lacking a formal description. We provide a worst-case analysis with confidence regions of relevant scenarios which can be involved in an optimization problem formulation for robust design.