This paper proposes an optimized transmission scheme for Energy Harvesting (EH)-based two-way multiple- relay systems. All relays are considered as EH nodes that harvest energy from renewable and radio frequency (RF) sources, then use it to forward the information to the destinations. The power-splitting (PS) protocol, by which the EH node splits the input RF signal into two components for information transmission and energy harvesting, is adopted in the relay side. The objective is to optimize the PS ratios and the relays' transmit power levels in order to maximize the total sum-rate utility over multiple coherent time slots. An optimization approach based on geometric programming is proposed to solve the problem. Numerical results illustrate the behavior of the EH-based two-way multiple-relay system with respect to various parameters and compare the performance of the proposed approach with that of the dual problem-based approach.