A coupled optoelectronic model was implemented along with the differential evolution algorithm to assess the efficacy of grading the bandgap of the CZTSSe layer for enhancing the power conversion efficiency of thin-film CZTSSe solar cells. Both linearly and sinusoidally graded bandgaps were examined, with the molybdenum backreflector in the solar cell being either planar or periodically corrugated. Whereas an optimally graded bandgap can dramatically enhance the efficiency, the effect of periodically corrugating the backreflector is modest at best. An efficiency of 21.74% is predicted with sinusoidal grading of a 870-nm-thick CZTSSe layer, in comparison to 12.6% efficiency achieved experimentally with a 2200-nm-thick homogeneous CZTSSe layer. High electron-hole-pair generation rates in the narrow-bandgap regions and a high open-circuit voltage due to a wider bandgap close to the front and rear faces of the CZTSSe layer are responsible for the high enhancement of efficiency.