The exponential growth of traffic in mobile networks is leading to an increased pressure on the infrastructure of mobile networks and in particular on their backhaul networks. It is more critical than ever to carefully plan backhaul networks. In this paper, we formulate and solve the problem of hierarchical wireless backhaul network design. In our problem, we cover different requirements, namely: topology simplicity, network resiliency and link reliability. We formulate the problem as an Integer Linear Programming (ILP) problem, allowing us to solve the problem to optimality. Furthermore, we provide a graph theory based algorithm that allows to solve the problem overlarge scale. The proposed algorithm exploits the properties of the graph representing the network. The results of our evaluations in various network scenarios demonstrate the efficiency of our ILP formulation and the provided algorithm in keeping the backhaul network simple, resilient and reliable. Using a practical channel propagation model and different node densities that are representative of small-scale and large-scale urban environments, our results also show that even with high resiliency requirements, the network traffic can be backhauled with only5−10%of the nodes for the considered densities. Our results also demonstrate that our algorithm leads to near-optimal solutions in different scenarios.

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO’s profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.