A design optimization strategy for rotary desiccant cooling (RDC) systems integrated with a photovoltaic thermal collector-solar air heater (PVT-SAH) and a phase change material based thermal energy storage (TES) (named RDC-PVT-SAH-TES) is presented in this paper. The optimization method was developed using a multilayer perceptron neural network (MPNN) and a genetic algorithm to maximize the specific net electricity generation (SNEG) of RDC-PVT-SAH-TES systems while maintaining the required cooling demand with the assistance of an electric heater. A dimension reduction method was used to determine the main design parameters of the RDC-PVT-SAH-TES system. An RDC-PVT-SAH-TES system was simulated using TRNSYS and the simulation data were utilized for training and validation of the MPNN model and for dimension reduction analysis. A comparison of the design solution identified by this optimization method with a baseline design showed that the SNEG and the solar thermal contribution of this RDC-PVT-SAH-TES system can be increased from 3.77 kWh/m2 to 10.32 kWh/m2 and from 91.5% to 99.4%, respectively. The optimization method developed could be potentially adapted to facilitate optimal design and size of other engineering systems with onsite energy generation and thermal storage.