In reflector system design, achieving high stability of phase center position with changes in frequency in reflector feed antennas is highly desired. However, obtaining highly stable phase center is not possible for UWB feed antennas, specially for planar ones. Thus, an optimum positioning for the UWB feed antenna should be defined. Optimization of the positioning of the feed antenna is essential since this process lowers resulting phase error losses significantly. In this work, a novel method for optimizing the UWB feed position of a prime focus reflector antenna from phase and amplitude recordings of the measured radiated field is introduced. An automatic and fast design procedure, based on Genetic Algorithms, is described. The proposed methodology has been numerically and experimentally assessed. The procedure is introduced by an application example to one of the most commonly used UWB feed antennas in high-performance reflector antenna systems: Linear Tapered Slot Antenna (LTSA). A LTSA antenna operating in 6-25GHz frequency band is designed and manufactured. The performance of the method is quantified in terms of its phase error losses in E- and H-planes for reflector illumination.