While historically limited by a lack of suitable materials, rapid advancements in manufacturing techniques, including 3D printing, have caused renewed interest in gradient-index (GRIN) optics in recent years. Further increasing the desire for GRIN devices has been the advent of Transformation Optics (TO) which provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by “transforming” it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. These transformations generally result in 3D GRIN lenses which often possess better performances than traditional radial GRINs. By decomposing TO-GRIN solutions into a 2D-polynomial basis to analyze their behavior, it can be determined which terms govern their performance improvements. However, TO is a computationally intensive evaluation and a comprehensive study of this sort could take weeks to perform. But, by training a surrogate model to approximate the TO calculation, the procedure can be greatly accelerated, dramatically reducing the time of this study from weeks to hours. Moreover, the obscure GRIN terms present in the TO solutions can be mapped to specific aberrations by decomposing the resulting wavefronts into a Zernike polynomial basis and performing multivariate regression analyses. This yields a surrogate model which approximates the full numerical ray-trace and offers an avenue for rapid GRIN lens design and optimization. Meanwhile, to aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as spot size, field-of-view, and Δn.