n practice, full-duplex (FD) transmission achieves better system outage performance than that of half-duplex (HD) transmission but suffers from strong self-interference (SI). In this paper, we provide performance analysis of relay selection (RS) schemes in multi-relay wireless networks, where we obtain the exact and approximate closed-form expressions for outage probability (OP) in the high signal-to-noise ratio (SNR) regime over in- dependent and identically distributed (i.i.d.) Rayleigh fading channels in three proposed optimal RS schemes, i.e., HD deploying maximal ratio combine (HDMRC) and FD deploying joint decoding (FDJD) and hybrid FD/HD relaying transmission scheme (HTS). Most importantly, these schemes operate in two proposed optimal power supply policies so-called optimal power under the individual power constraints (OPIPC) and optimal power with energy harvesting ability (OPEHA). Additionally, asymptotic expressions in high SNR regime are given to help gain better insights on the system performance. It is also shown that the proposed HTS scheme outperforms HDMRC and FDJD schemes in terms of outage performance, where OPEHA is better than OPIPC under the impact of SI. Besides that, HTS RS scheme significantly decreases the power consumption which helps enhance energy efficiency. The validity of the proposed analyses is proven by simulations.