# A Hybrid Metaheuristic Algorithm for the Efficient Placement of UAVs
## 6 Conclusions  
In this paper, we have treated the UAV placement problem to deploy a wireless infrastructure for communications in the context of disaster relief, rescue operations, and providing user connectivity in remote or hostile environments. The UAVs serve as aerial relays to connect users on the ground, and we seek to maximize the total link capacity of the aerial communication infrastructure. The problem is recognized as a typical \(p\)-hub median problem, with a mathematical formulation developed in order to consider the air-to-ground and air-to-air propagation model.  
The mixed integer linear programming formulation is optimized via the classical CPLEX branch-and-cut algorithm and via a hybrid metaheuristic, the BR-ILS. The latter is proposed in order to obtain reduced computational cost in association with optimal or close-to optimal solutions. The experimental results show that BR-ILS largely outperforms CPLEX solver for small and large-sized instances, in terms of execution time, while achieving zero gap for the instances whose optimal solution could be obtained by CPLEX. Moreover, when compared to a naive heuristic allocation strategy, the BR-ILS algorithm is able to deliver an average improvement of about 12% for the total cost when different numbers of users are uniformly scattered on the ground. Finally, it is worth mentioning that the BR-ILS algorithm is relatively simple: it has been applied to the tested instances without requiring any special fine-tuning or set-up process, which makes it an appealing tool to support the solution of the UAV placement problem.  
Future work involves extending the problem formulation and experimental analysis to more diverse scenarios and parameters, considering flows of data packets between users and other wireless network setups. In fact, the formulation of the \(p\)-hub median problem allows for its extension to consider individual flows of packets between users, which is a quite useful feature of this optimization problem. This means that one can consider the actual traffic load that is imposed on each end-to-end connection established between two any users on the ground. However, to treat this problem, one needs to carefully address the impact of channel errors on packet transmissions within each link searched by the algorithm. Moreover, depending on the application scenario, the characteristics and statistics of the packet flows need to be carefully addressed, so they can be properly incorporated into the proposed framework. Furthermore, the adaptation of BR-ILS to other versions of the \(p\)-hub median problem is possible. One of the interesting variants of this problem is the capacitated version [41] and, therefore, another orientation for future research could be to consider a fixed link capacity for each UAV. Under these conditions, the mathematical model may include the capacity restrictions.  
Conceptualization, S.A.F., M.M.C. and D.G.S.; methodology, S.A.F., M.M.C. and D.G.S.; software, S.A.F.; validation, S.A.F.; formal analysis, S.A.F.; investigation, S.A.F.; resources, S.A.F. and D.G.S.; data curation, S.A.F.; writing--original draft preparation, S.A.F., M.M.C. and D.G.S.; writing--review and editing, S.A.F., M.M.C. and D.G.S.; visualization, S.A.F.; supervision, S.A.F., M.M.C. and D.G.S. All authors have read and agreed to the published version of the manuscript.  
This study was financed in part by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior--Brasil (CAPES)--Finance Code 001.  
The authors declare no conflict of interest.