# A Hybrid Metaheuristic Algorithm for the Efficient Placement of UAVs
## 5 Experimental Study  
The proposed approach for the optimization aims at the efficient positioning of the UAVs in order to obtain the best possible coverage while maximizing link capacity. The proposed model was numerically analyzed for its efficiency on the basis of the parameters and configurations that are presented in this section. Test problems of size \(n=\{10,20,30,50,100,200\}\) and \(p=\{3,10\}\) were generated and solved. Each instance was generated spreading the nodes in a 5 km \(\times\) 5 km area following a Uniform spatial distribution. For each problem, the capacity was calculated according to Equation (6) and the parameters for simulations are presented in Table 1. A complete list with the generated instances can be downloaded from github.com/[PERSON]/p-UAV-instances. The proposed BR-ILS algorithm was implemented while using Java(r) 7 SE applications. The vast amount of tools available in the standard API of Java and its object-orientation made the development process easy. A standard personal computer was used to perform all tests, an Intel(r)Core(r)17-3520M CPU @ 2.90 GHz and 12 GB RAM running the Windows(r)10 operating system. During the implementation process of the BR-ILS, some of the details that required attention were found, especially: (_i_) The meticulous design of the different classes so that a convenient level of coupling and cohesion was reached; (_ii_) The quality of the Random Number Generator to perform random choices during the exploration of the space, which impacts directly the performance of our algorithm. We used the LFSR113 from the SSJ library created by [PERSON] et al. (2019) in order to overcome this situation. This generator provides a period of \(2^{113}\), compared to the period \(2^{48}\) of the generator provided by the standard Java library; and (_iii_) The level of precision used to store and operate with numerical values was key to reach the fastness of the proposed BR-ILS. The necessary algorithm parameters to complete the tests were specified, as follows: the maximum time during the ILS block was set to \(maxTime=900\) s; the Geometric distribution parameter \(\beta\) and the percentage _per_ were randomly chosen in the interval \((0.1,0.3)\). In the following, a complete analysis of the results is presented and, for that purpose, a test-bench that runs the BR-ILS algorithm was set for running a total of ten times, collecting information regarding the performance of the algorithm, each of them running with a different simulation seed. To assess the \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Description** \\ \hline Carrier frequency \(f_{c}\) & 2 GHz \\ UAVs altitude \(h\) & 2000 m \\ Transmission gain \(G_{t}\) & 0 dBi \\ Reception gain \(G_{r}\) & 0 dBi \\ Thermal noise power \(\sigma\) & –90 dBm \\ UAV transmission power & 20 dBm \\ User transmission power & 20 dBm \\ Channel bandwidth & 20 MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. performance obtained, a gap is defined as the percentage difference between the (potentially) optimal solution, previously found by CPLEX, and the one found by the algorithm. In addition, run-time information is used to compare the efficiency of both methods. Table 2 shows a comparison of the results obtained by using both our proposed BR-ILS algorithm and the branch-and-cut algorithm, whose implementation is provided by the optimization software ILOG CPLEX Version 12.10.0 by IBM(r). This software tool was chosen due to its wide adoption among operations research community and its reliability [40]. The optimizer automatically determines smart settings for a wide range of algorithm parameters, usually resulting in optimal linear programming solution performance.