The vibrational behavior of bladed-disks is known to be particularly complex in reason of mistuning amplifications but also in reason of geometrical nonlinear effects (use of lighter materials). In such a context, methodologies for the dynamical analysis based on the nonparametric probabilistic approach [1] odf the random mistuning combined to nonlinear reduced-order models allows for a better understanding of uncertainty propagation through the forced response [2]. The difficulty related to this unavoidable mistuning effects has led to consider the detuning (alternating between several blade types) as a way for inhibiting the amplifications. A computational methodology adapted to the detuning context of nonlinear dynamics of mistuned bladed-disks developed in [3] has shown very encouraging results. In this context, the present research deals with a novel formulation for the detuning optimization of a bladed-disk structure using a 12 bladed-disk computational model issued from [4]. The dynamical amplification is defined with respect to the pure mistuned configuration and involves scalar quantities that are defined from the extreme values of the maximum displacements occurring in the structure. The numerical procedure allows for obtaining a full data basis. Its analysis shows the existence of a few number of detuned configurations that reduce the mistuning amplification effects. A second part of this work consists in proposing a formulation of the combinatorial optimization problem for which a surrogate model of the cost function is constructed using the PLoM method [5], as a machine learning tool from a small training set. The optimal solution obtained is compared to the one obtained with the data basis. [1] M.P. Mignolet, C. Soize, Stochastic reduced order models for uncertain nonlinear dynamical systems. Computer Methods in Applied Mechanics and Engineering, 197(45-48):3951--3963 (2008). doi:10.1016/\break j.cma.2008.03.032. [2] E.~Capiez-Lernout, C.~Soize, M.~Mbaye, Mistuning analysis and uncertainty quantification of an industrial bladed disk with geometrical nonlinearity. Journal of Sound and Vibration, 356(11):124--143 (2015). doi:10.1016/j.jsv.2015.07.006 [3] A. Picou, E. Capiez-Lernout, C. Soize, M. Mbaye, Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities. Computational Mechanics, 65(3):711--730 (2020). doi:10.1007/s00466-019-01790-4. [4] R. Bladh, M. Castanier, C. Pierre, Component-mode-based reduced order modeling techniques for mistuned bladed disks-part 2: Application. ASME Journal of Engineering for Gas Turbines and Power, 123(1):100-–108 (2001). doi:10.1115/1.1338948. [5] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold. Journal of Computational Physics, 321:242-258 (2016). doi:10.1016/j.jcp.2016.05.044.