Centrifugal pumps, being used nowadays for many applications, must be suited for a wide range of pressure ratios and flow rates. To overcome difficulties arising from the design and performance prediction of this class of turbomachinery, many researchers proposed the coupling of CFD codes and optimization algorithms for a fast and effective design procedure. However, uncertainties are present in most engineering applications such as turbomachines, and their influence on turbomachinery performance should be considered. In this work we apply some advanced optimization techniques to the blade optimization of an ERCOFTAC-like pump, and we assess the robustness of the optimal profiles through an uncertainty propagation study. The main source of uncertainty is constituted by the uncertainty of the operating conditions, primarily the rotational speed of the pump shaft that affects also the flow rate.