Centrifugal compressor stages with high rotor stiffness (i.e. impeller hub-to-outer-diameter ratio) may represent a crucial element to cope with tight rotordynamic requirements and constraints that are needed for certain applications. On the other hand, high-stiffness has a detrimental effect on the aerodynamic performance. Thus, an accurate design and optimization are required to minimize the performance gap with respect to low-stiffness stages. This paper shows a redesign and optimization procedure of a centrifugal compressor stage aimed at increasing the impeller stiffness while keeping high aerodynamic performance. Two different optimization steps are employed to consider a wide design space while keeping the computational cost as low as possible. At first the attention is focused on the impeller only, then the diffuser and the return channel are taken into account. The multi-objective and multi-operating point optimization makes use of artificial neural networks (ANNs) as a surrogate model to obtain the response surfaces. RANS calculations are carried out using the TRAF code and are employed to create the training dataset. Once the ANN has been trained, an optimization strategy is used to find the constrained optimum geometries for the impeller and the static components. The optimized high-stiffness stage is finally compared to the low-stiffness one to assess its applicability.