Chains of resonators in the form of spring-mass systems have long been known to exhibiting interesting properties such as band gaps. Such features can be leveraged to manipulate the propagation of waves such as the filtering of specific frequencies or, more generally, mitigate vibrations and impact. Adding nonlinearities to the system can also provide further avenues to manipulate the propagation of waves and enhance vibration mitigation. This work proposes to optimally design such a chain of nonlinear resonators to mitigate vibrations in a robust manner by accounting for various sources of uncertainties. The stochastic optimization algorithm explicitly accounts for the non-smoothness of the nonlinear response of the system due, for instance, to its amplitude-dependent behavior. In addition, the approach introduces a formulation based on a field representation of the design variables, thus making the optimization approach scalable.