<p>This paper introduces a general computational framework for optimizing the performances and mitigating the adverse dynamics of nonlinear energy sinks (NESs) under harmonic external forcing. It is well known that attaching small, essentially nonlinear, subsystems to a linear host system can provide efficient passive vibration mitigation. However, the introduced nonlinearity can induce adverse dynamics, in the form of isolated response curves, which are detrimental to the performances of the system. Several multi-objective optimization problems are formulated, which consist in minimizing objective functionals derived from bifurcation and singularity theory in order to control such phenomena and improve the performances of NESs. The methodology is demonstrated on a two-degree-of-freedom system consisting of a linear oscillator coupled to a nonlinear energy sink with cubic stiffness. However, its fully computational nature makes it applicable to arbitrarily complex NES configurations and lays the foundation for extending the design optimization of NESs to full finite element models. These results are compared to those obtained with the inclusion of a nonlinear damping term, which is a common way of mitigating the issue of isolated response curves in the literature. We report significant computational speed-ups compared to existing methodologies for controlling isolated response curves induced by nonlinear energy sinks.</p>