One major industrial challenge is to consider the detuning as a technological means to reduce the dynamical amplifications induced by mistuning. Due to technological evolutions, the nonlinear geometrical effects induced by the large displacements cannot longer be neglected. Recently, methodologies for the robust analysis of detuned/mistuned bladed-disks in presence of geometrical nonlinearities have been developed. A full analysis of the detuning optimization of mistuned bladed-disks with finite displacements is carried out on a 12 bladed-disk finite element model. The paper is based on a computational methodology previously developed by the authors. It insists on the necessity to carefully optimize all the involved numerical parameters to get the nonlinear mistuned response of each considered detuned configuration with an optimal balance between response accuracy and computational costs. We then have to be very careful with the construction of an adapted scalar quantity of interest for defining the detuning optimization problem. Direct computations allowing for all possible detuned configurations to be considered allow for obtaining a full data basis. A meticulous post-processing shows the existence of a few detuned configurations, that inhibits the mistuning amplification effects of the pure mistuned bladed-disk.