# Energy-Efficient Multi-User Routing in a Software-Defined Multi-Hop Wireless Network
## 1 Introduction
In the SDMWN model, the routing strategy is designed in the logical control layer and sent to each node by the controller to complete the deployment of the entire data transmission layer. The SDMWN allows the packet switches to have a centralized interface, like OpenFlow, to provide a real-time QoS assurance of certainty [10]. During the data transmission, the nodes transmit the current residual energy and other information back to the logical centralized controller without delay. Subsequently, the controller draws a new global network topology and adjusts the routing to get the shortest path of the next transmission process. In this paper, we focus on the balance between transmission time and energy consumption, based on the energy model and delay model, which are suitable for practical application, aiming at studying the routing of providing data transmission for multiple users in the context of SDMWN. It is different from the previous research on the QoS minimum cost routing for a single user. In this paper, not only the routing algorithm conforming to constraints should be developed for multiple users, but also the global energy consumption of all users should be optimized, which is more consistent with the application scenarios. Therefore, the routing algorithm is designed for multiple users to minimize the total energy consumption of all transmission paths. In the proposed algorithm, users must specify their destinations, the size of data, and the maximum delay they can accept. To avoid transmission queuing and reduce transmission failures, we assume that the intermediate nodes do not transfer data for multiple users repeatedly. Hence, the technology of this paper is as follows: In the first place, the Lagrange relaxation-based aggregated cost (LARAC) is adopted to aggregate delay and energy consumption variables. The LARAC algorithm is based on the Lagrange relaxation technique, which allows the routing problem to be solved in polynomial time. Then, owing to our goal being to solve simultaneously the problem of global minimum energy consumption and no duplicate nodes in the paths, the above conditions may not be satisfied when all users choose the optimal path. Therefore, combining the LARAC algorithm with K-Dijkstra, we develop the K-LARAC algorithm to find the alternative path set for each user. Finally, we map the alternative paths to chromosomes in the genetic algorithm (GA) and use it to quickly find the routing scheme that meets the global minimum energy consumption and does not have duplicate intermediate nodes. Simulation results show that the proposed global routing can not only be solved in polynomial time, but also obtain approximate optimal solutions, in which the validity of the algorithm is further demonstrated. This paper is organized as follows: the related work is introduced in Section 2. In Section 3, we introduce the system model, including the network model, energy model, and delay model. In Section 4, the expression of global energy consumption minimization under constraint conditions and the optimization algorithm to solve the problem are introduced. Sections 5 shows the simulation results, and Section 6 gives the conclusions.