While nonlinear phenomena in mechanical systems are well understood, strategies for designing structures that exhibit certain nonlinear responses have received little attention. Design optimization is a systematic and iterative process aimed at improving the performance and efficiency of a system. It involves exploring various design choices and parameters to find the best possible solution that meets specific criteria or objective, such as maximizing or minimizing nonlinearity. The use of design optimization techniques for tuning nonlinear dynamics has important implications for the development of micro- and nano-scale devices. By optimizing the nonlinear response of these devices, it is possible to achieve enhanced performance, and better control over their nonlinear behaviour. In my thesis, I have devised a novel methodology that empowers us to optimize the nonlinear vibration characteristics of devices. My work extends to the development of a versatile routine capable of defining complex geometries and facilitating design within a Finite Element Method (FEM) framework. This routine operates in tandem with optimization algorithms, enabling us to identify and refine the most optimal designs in terms of strength of nonlinearity, minimizing or maximizing it when desirable.