One of the two types of engines under consideration for the Space Station Solar Dynamic Power System is the Closed Brayton Cycle (CBC). The primary requirement of the system is to produce electrical power on orbit, in sufficient quantity and quality, at the lowest possible cost. The heat rejection system for the Closed Brayton Cycle plays an important role since the power generation efficiency is strongly dependent on the heat rejection temperature. The lower the rejection temperature, the higher the efficiency. However, the radiator area requirement increases as the rejection temperature is reduced. Consequently, for various rejection temperatures. studies must be performed to optimize the heat rejection system with respect to weight, volume and cost.This paper presents the results of an optimization study performed on the heat rejection system for a space based electrical power system using a CBC. The effect of varying system parameters on the radiator area and weight requirement has been analyzed. The result of this analysis indicates that the radiator area requirement is strongly dependent on the physical design characteristics of the radiator. The radiator sizing depends on the arrangement, size and design point heat rejection capability of the radiator panels as well as the radiator properties such as the fin effectiveness, emissivity and absorptivity. The optimization analysis to evaluate the effect of each of these parameters on the system weight and area is presented.