We focus on a shape optimization problem in hydrodynamic stability control. The goal is to minimize the drag in a flow regime by modification of the underlying geometry while ensuring hydrodynamic stability. We propose an extension of a numerical scheme to speed up the computations and avoid the solving of the original PDE model. Therefore, a metamodel is used as approximation of the original model. A Particle Swarm Optimization algorithm is used in conjunction with a Nash game to consider both objectives simultaneously, with a split of design variables established from a sensitivity analysis accounting for first and second derivatives of functionals related to the metamodel.