In this paper, robust optimization tool is proposed for nonlinear energy sinks used for the mitigation of friction-induced vibrations due to mode coupling instability in braking systems. The study is based on a mechanical system which is composed of two NESs coupled to the well-known two-degrees-of-freedom Hulten's model. ` In such an unstable system coupled with NES, it is usual to observe a discontinuity in the steady-state amplitude profiles which separates the parameters space into two parts which contain mitigated and unmitigated regimes respectively. We developed a methodology based on Multi-Element generalized Polynomial Chaos to identify this discontinuity which allows us to determine the Propensity of the system to undergo a Harmless Steady-State Regime (PHSSR). The objective of this work is, therefore, to maximize the value of PHSSR to obtain an optimal design of the NESs. For that, several stochastic optimization problems are presented taking into account the dispersion of the uncertain parameters.