This paper investigates the outage performance and optimization for the four-phase two-way transmission network with an energy harvesting (EH) relay. To enable the simultaneous information processing and energy harvesting at the relay, we firstly propose a power splitting-based two-way relaying protocol (PSTWR). Then, we discuss its outage performance theoretically and derive an explicit expression for the system outage probability. In order to find the optimal system configuration parameters such as the optimal power splitting ratio and the optimal transmit power redistribution factor, we formulate an outage-minimized optimization problem. As the problem is difficult to solve, we design a genetic algorithm (GA) based algorithm for it. Besides, we also investigate the effects of the power splitting ratio, the power redistribution factor at the relay, and the source to relay distance on the system outage performance. Finally, extensive simulation results are provided to demonstrate the accuracy of the analytical results and the effectiveness of the GA-based algorithm. Moreover, it is also shown that, the relay position greatly affects the system performance, where relatively worse outage performance is achieved when the EH relay is placed in the middle of the two sources.