Energy Efficiency (EE) is a key performance metric to design future wireless networks. Since Directional Antennas (DAs) focus the transmission energy towards the destination, it has been shown as a cost-effective solution when used in a backhaul network. In this paper we propose a new joint optimization framework of energy consumption and throughput in backhaul Wireless Mesh Networks (WMNs) equipped with DAs. We first formulate the joint optimization problem as a Mixed Integer Linear Problem (MILP) using a weighted objective function of both the consumed energy and the throughput. Then, we propose to use the Ant-Q algorithm, a Reinforcement Learning (RL) based approach, to reduce the solution complexity and enhance its convergence. Considering a discrete power control scheme, we define a new routing scheme based on the Ant-Q heuristic to select jointly the transmission beam and the transmission power. Using ILOG Cplex to find the optimal solution and NS-3 to conduct extensive simulations, we show the effectiveness and the accuracy of the proposed routing algorithm. Moreover, we analyze the optimization tradeoff depending on the beamwidth, the network topology, the gateway position and the optimization weight factor.

能源效率 (EE) 是设计未来无线网络的关键性能指标。由于定向天线 (DA) 将传输能量集中到目的地，因此在回程网络中使用时，它已被证明是一种具有成本效益的解决方案。在本文中，我们提出了一种新的能量消耗和吞吐量联合优化框架，用于配备 DA 的回程无线网状网络 (WMN)。我们首先使用消耗能量和吞吐量的加权目标函数将联合优化问题表述为混合整数线性问题 (MILP)。然后，我们建议使用基于强化学习 (RL) 的方法 Ant-Q 算法来降低解决方案的复杂性并增强其收敛性。考虑离散功率控制方案，我们定义了一种基于 Ant-Q 启发式的新路由方案，以联合选择传输波束和传输功率。使用 ILOG Cplex 寻找最优解和 NS-3 进行广泛的模拟，我们展示了所提出的路由算法的有效性和准确性。此外，我们根据波束宽度、网络拓扑、网关位置和优化权重因子分析优化权衡。