# A Hybrid Metaheuristic Algorithm for the Efficient Placement of UAVs
## 2 Related Work  
Employing UAVs as aerial communication platforms has become a rising research topic. As mentioned before, UAV-aided wireless communications have found a wide range of applications during the last decade [12; 13; 14; 15] and, more recently, many authors have addressed the placement problem. In particular, in [15], the authors dealt with the UAV placement problem with non-orthogonal multiple access techniques and proposed a machine learning approach in order to adjust the UAVs' positions within the three-dimensional space, when the ground users are roaming. The Q-learning-based algorithm was applied when UAVs were moving. The authors tested two different scenarios: a single UAV case considering three users that were uniformly distributed within an area of 1 km \(\times\) 1 km, and a multiple-UAV case. Unfortunately, the work did not attempt to solve the problem for large network sizes. Besides, a unified spatial analytical approach for non-orthogonal-aided UAV networks is desired, as the authors themselves pointed out. The proposed machine learning framework left some open issues such as the time it takes the algorithm to be tested and the considerable delays if the number of users is large. In [16], the authors proposed a minimax facility location model for optimizing network delays that are caused by topological arrangements, which occur during UAV deployment in heterogeneous networks, and their mapping to a particular demand area. Instead of considering data link rates, the proposed model was aimed in the direction of the delay optimization by accurate positioning of the UAVs. The authors solved the question using entropy nets, which the authors considered to be the neural network version of decision trees. In that approach, a decision is taken while using fewer neural connections. The proposed approach was tested in a network of up to 500 users and six UAVs in an area of 10 km \(\times\) 10 km. Later, the same authors proposed a similar approach to overcome the two problems, namely, the Macro Base Station decision problem and the cooperative UAV allocation problem [17]. Howeber, the proposed approach proved to be time consuming and the delays varied with an increase of the size network, since more iterations were required to localize the additional UAVs. In [18], the authors studied the deployment of a Software Defined Network (SDN)-based UAV network, where the UAVs act as forwarding elements and the SDN controller manages the network. In particular, the issue of control overhead caused by the UAV-SDN controller communication was discussed. Here, the authors have not considered the delay due to data link rates, but, due to multi-hop communication, the UAVs are interconnected and each control packet between UAVs and the SDN controller will be transmitted multiple times. The authors proposed a scheme involving the buffering of update packets at intermediate nodes and merging of control packets to achieve a trade-off between control overhead and delay. The authors tested the proposed scheme in a network with a total of 36 UAVs deployed in an 1 km \(\times\) 1 km area, with the controller being placed at some specific corner. The simulations results have shown that, as buffering time increases, the delay increases, as expected, but overhead decreases. In [19], the authors investigated the problem of positioning UAVs in a wireless ad hoc network. They modeled the problem as a facility location problem and proposed a quadratic unconstrained binary optimization model. The main objective was to improve the connectivity at the shortest total distance and to maximize the linkage (downlink). The problem was solved using CPLEX's branch-and-cut optimizer. Test problems of size \(m=10\) to 100 for the wireless nodes, and \(n=3\) to 7 for the UAVs were generated and solved. Despite the effort of the authors for solving different scenarios varying the number of users and UAVs, large networks were not considered.