Reducing the energy consumption of wireless communication systems with new technologies and solutions continues to be an important concern in developing future standards. In this paper, we study the routing strategies in multi-hop relaying networks. For a 2-way assignment routing method, an efficient feedback scheme is presented to minimize the power consumption over the whole system. Compared with the full channel information in traditional feedback scheme, only the backward accumulated feedback metrics are required. If the proposed routing calculation is used, there is no performance loss. When the number of the hops and the relays is large, the new scheme achieves a significant feedback overhead reduction. Moreover, we show a proof for the optimality of the presented routing strategy based on mathematical induction.