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In this paper, the optimization of multilayer films consisted of alternating layers of material with different mechanical properties, following a triadic Cantor sequence, is performed. The extremely low thresholds for subharmonic generation of ultrasonic waves has a significant importance in the generation of the full band-gaps due to the nonlinear coupling between the phonon and the fracton vibration regimes. The optimization with respect to most important features of sonic composites, such as the localized modes around interfaces and the size of the full band-gaps is analysed. The case of a relevant uncertainty of the design parameters which may change over frequency is taken into consideration. Uncertain parameters are related to the local band-gaps and boundary conditions where the displacement and the traction vectors can be discontinuous. Maximizing the full band-gaps is taken as the objective function, while the constant volume of the structure is taken as the constraint. The results show an unexpected influence of discontinuities upon the generation of the full band-gaps.