Relay selection scheme in cooperative communication systems has been known as an effective technique that provides full diversity with efficient use of bandwidth in literature. Generally, the total power is shared equally between the source and the selected relay in relay selection schemes. However, the power allocation between the source and the selected relay is critical to further improve the error performance. In this study, we utilize Artificial Neural Networks (ANNs) to determine the optimum power allocation in Amplified-and Forward (AF) relay selection schemes for a minimum Bit Error Probability (BEP) performance over various channel gains. Since the analytical solution for an optimum power allocation in relay selection schemes is very complicated, the use of ANNs is an efficient and quick solution to further improve the performance.