The optimal design of complex structures with nonlinear vibration is a significant concern for the industry. This work presents a numerical strategy relying on Bayesian Optimization for the parametric optimization of such structures with the aim of lowering the computational cost compared to classical global optimization algorithm. A specific focus is given on the mechanical solver for the resolution of the nonlinear dynamical problem using the Harmonic Balance Method combined with an Alternating Frequency/Time approach and a scheme for the numerical continuation of the solution path. This mechanical solver is then employed to build and enrich a Gaussian Process within a Bayesian Optimization procedure. The whole strategy is applied to the parametric optimization of a gantry crane.