Efficient, large-scale, and cost-effective energy storage systems provide a means of managing the inherent intermittency of renewable energy sources and drastically increasing their utilization. Compressed air energy storage (CAES) and its derivative architectures have received much attention as a viable solution; however, optimization objectives for these systems have not been thoroughly investigated in the literature. A hybrid thermal and compressed air energy storage (HT-CAES) system is investigated that mitigates the shortcomings of the otherwise attractive conventional CAES systems and its derivatives-shortcomings such as strict geological locations, low energy densities, and the production of greenhouse gas emissions. The HT-CAES system allows a portion of the available energy to operate a compressor and the remainder to be converted and stored in the form of heat through joule/resistive heating in a high-temperature, sensible, thermal energy storage medium. Internally reversible and irreversible HT-CAES system assumptions were investigated, in addition to regenerative and non-regenerative design configurations. Several system optimization criteria were examined-including maximum energy efficiency, maximum exergy efficiency, maximum work output, and minimum entropy generation-with a focus on whether the latter may lead to conclusive design guidelines in a real system. It is shown that an HT-CAES system designed based on a minimum entropy generation objective may operate at a lower energy and exergy efficiency as well as lower output power than otherwise achievable. Furthermore, optimization objective equivalence is shown to be limited to certain design conditions.