Shell structures are highly demanded structures in civil and aerospace engineering. Their curved shape allows a slender structural design with low dead weight and high load-bearing capacity. The curvature form, imperfections, boundary conditions, material and loading have a major influence on the load-bearing behavior. An optimization-based design of shell structures with deterministic models implies precision. In reality, all data and information are characterized by various types of uncertainty, e.g., natural variability, incompleteness (ack of knowledge), and imprecision (measurement errors). These uncertainties have not been sufficiently considered in traditional design concepts for shells so far. In the presented contribution a multi-objective optimization of shells with polymorphic uncertain parameters is performed. Based on available data the uncertainty quantification of a priori and design parameters with appropriate polymorphic uncertainty models is discussed. To show the procedure, a stiffened cylindrical shell is investigated. However, the uncertainty should not only be quantified, but also reduced by a subsequent optimization procedure improving the robustness, economy and safety of the shell designs. Therefore, several uncertainty reducing measures are evaluated. An optimization procedure with polymorphic uncertainty models leads to a nested-loop problem which is - from a computational point of view - very expensive. Finally, a surrogate model strategy is discussed for replacing complex shell models to reduce the numerical effort.