The building sector accounts for 36% of energy consumption and 39% of energy-related greenhouse-gas emissions. Integrating bifacial photovoltaic solar cells in buildings could significantly reduce energy consumption and related greenhouse gas emissions. Bifacial solar cells should be flexible, bifacially balanced for electricity production, and perform reasonably well under weak-light conditions. Using rigorous optoelectronic simulation software and the differential evolution algorithm, we optimized symmetric/asymmetric bifacial CIGS solar cells with either (i) homogeneous or (ii) graded-bandgap photon-absorbing layers and a flexible central contact layer of aluminum-doped zinc oxide to harvest light outdoors as well as indoors. Indoor light was modeled as a fraction of the standard sunlight. Also, we computed the weak-light responses of the CIGS solar cells using LED illumination of different light intensities. The optimal bifacial CIGS solar cell with graded-bandgap photon-absorbing layers is predicted to perform with 18%–29% efficiency under 0.01–1.0-Sun illumination; furthermore, efficiencies of 26.08% and 28.30% under weak LED light illumination of 0.0964 mW cm−2 and 0.22 mW cm−2 intensities, respectively, are predicted.