The paper deals with the nonlinear stochastic dynamics concerning the detuning optimization in presence of random mistuning of bladed-disks with geometrical nonlinearities. We present an efficient computational methodology for reducing the computational cost, an analysis of the detuning, and the detuning optimization, based on the use of a high-fidelity computational model. A deep computational analysis is presented for a 12-bladed-disk structure that is representative of industrial turbomachines in order to understand the role played by the geometrical nonlinearities on the dynamical behavior and to exhibit the consequences on the detuning effects. For the detuning optimization with a very large number of possible detuned configurations, we propose a reformulation of the combinatorial optimization problem in a probabilistic framework, which is adapted to a probabilistic machine learning tool in order to limit the number of evaluations of the cost function with the high-fidelity computational model. The methodology proposed is validated for the 12-bladed-disk structure for which the exact optimal detuned configuration has been identified. A very good prediction is obtained.