We introduce and investigate several state-of-the-art shape deformation methods for their use in evolutionary design optimization problems. Starting from classical free-form deformation (FFD) we broaden our investigation to more flexible methods such as direct manipulation FFD and deformations based on radial basis functions. We integrate the different methods into a framework for evolutionary design optimization and apply them in a passenger car optimization scenario improving the drag of a simplified Honda Civic model. We evaluate the aerodynamic performance of different design variations utilizing computational fluid dynamics simulations. Based on this scenario we analyze and compare the strengths and weaknesses of the individual methods.