This work addresses the topic of external gear pumps for automotive applications, which operate at high speed and low pressure. In previous works of the authors, a hybrid lumped-parameter/finite-element model has been developed, in order to foresee the pump dynamic behaviour in terms of gear and casing acceleration. The model includes the main important phenomena involved in the pump operation and it has been validated on the basis of experimental data. In this research, an original optimization process has been applied to such a hybrid model in order to reduce the pump vibration level, i.e. the acceleration of the external casing. The set up of the optimization process comprises a single objective (case accelerations) and some operational and geometrical input variables (oil viscosity, oil Bulk modulus, relief groove dimension and radial clearance in the journal bearings). This paper compares three optimization methodologies for the optimization of the pump vibration level. In particular common optimization processes based on simulations are compared with a combined analysis based, firstly, on Design Of Experiments (DOE) and Response Surface Modelling (RSM) and, secondly, on the application of evolutionary algorithms to reach the optimal variable combination. The different methodologies are compared in terms of time efficiency and accuracy in the solution. Finally, a robust design process has been carried out in order to consider the manufacturing tolerances of the real pump and assess their effect on the performance of the component. The results offer important information and design insights that would be very difficult to obtain without such procedures.© 2010 ASME