To understand paths towards higher efficiency (η) for copper-indium-gallium-(sulfur)-selenide [CIG(S)Se] solar cells, we investigated a variety of absorber composition grading schemes for various back-side gallium (Ga), front-side sulfur (S), and double-graded Ga composition depth profiles in TCAD 1D/2D simulations. We fitted experimental results of a Back-Side Graded (BSG) solar cell with our TCAD models, prior to investigating other grading and interface schemes. The BSG solar cell was fabricated on a High Productivity Combinatorial (HPC™) platform based on sputtering Cu(In,Ga) followed by selenization. Our TCAD simulation methodology for optimizing CIG(S)Se solar cells started with a sensitivity analysis using 1D Solar-cell CAPacitance Simulator (SCAPS)  by selecting a typical range of key model parameters and analyzing the impact on η. We then used a 2D commercially-available Sentaurus simulation tool  to incorporate wavelength-dependent optical characteristics. As a result, we provide insight in the impact of grading schemes on efficiency for a fixed ‘material quality’ equal to an in-house BSG solar cell. We also quantify the effects of interface layers like MoSe2 at the Mo/CIG(S)Se interface, and an inverted surface layer at the CIG(S)Se/CdS interface.