In this work, a hybridized 2-D finite element method (FEM) with modal analysis is used to study a flat 3-D gradient-index dielectric lens with a diameter of 10λ0. The use of this memory-efficient and fast method allows parametric studies or even optimization of the lens, which is generally not feasible using commercial full-wave simulators. Thanks to this tool, in a first study, the effect of the number of rings constituting the lens on its performance is analyzed while in a second step, a genetic algorithm is used to optimize the width of each ring to obtain a higher gain at three frequencies within the frequency band. Finally, the focal distance, lens thickness, and maximum permittivity are optimized to maximize the realized gain, while imposing constraints on the sidelobe level and reflection coefficient levels.