This study focuses on 5G network, which deploys small cells to form multi-hop topologies using high capacity backhaul wireless links to provide localized capacity. Nowadays, high energy efficiency is very important because powering on unnecessarily a massive amount of macro cells or small cells may lead to increased expenses, CO2 emission and environmental destruction. Based on a given MILP that solves the energy consumption optimization problem in a 5G network, this research proposes a heuristic algorithm based on integer relaxation that accelerates the resolution of the MILP. The heuristic algorithm could diminish the route options by striking out the impossible links or links with lower possibility to be used. Our numerical evaluations demonstrate that the proposed algorithm can find very good solutions in short time and has similar performance in terms of energy efficiency over a large number of traffic scenarios.