# Three-Dimensional Drone Cell Placement: Drone Placement for Optimal Coverage
## 5 Experiment and Results
### Experiments  
For the experiments, a height constraint has been taken into consideration based on the geographical location of the research conducted to make sure the maximum height of the DC placed does not exceed the maximum legal height of any drones in the United Kingdom [50]. Environment has been a main consideration for the experiments, since user coverage is greatly impacted with the change in environment. Looking at the recent contribution in the field of DC placement and DA-RAN in [29; 38; 42; 51], all available urban environments have been taken into consideration while conducting the experiments. The experimental parameters for the experiments conducted are listed in Table 2.  
Here, instead of iterations, function evaluation (FE) has been implemented as the main criteria for algorithm termination to make sure the implemented algorithms are more in line with the previous experiments conducted in the field. FE is calculated based on the number of times the algorithm calls the fitness function to calculate the potential solution (fitness) in the search space. Based on the research conducted in [38], the maximum the number of FEs allowed has been fixed at 2500, calculated by:  
\[FE=max1T*N \tag{18}\]  
where \(max1T\) is the number of iterations and \(N\) is the population size; the number of DCs is fixed at 10, making the obtained results parallel with the research conducted by pioneers in the field. Total FE has been divided into 10 segments, each having 250 FEs. The search agents (flies, particles or chromosomes) are deployed (initialized) in the search space for 250 FEs; upon reaching these criteria, the covered users along with their associated DC are removed from the search space, allowing every DC to be deployed one after the other rather than all at once. This process continues until all 10 DCs have been deployed. A fourth algorithm or Random Search (RS) has also been implemented on the basis of the same theory where one DC is randomly deployed in the search space and the covered users and the associated DC is removed from the search space, continuing until all 10 DCs are deployed in the same process. RS was implemented to visualize the complex nature of the problem and serve as a control to illustrate the potential improvements achievable with more sophisticated algorithms like DFO, PSO and DE, demonstrating the effectiveness when using a hyper-heuristic method. Each experiment has been executed 1000 times, and the means of those executions have been compiled into a graph showcasing the coverage probability of each algorithm. Figure 1 represents the structure of the experiments conducted. Figure 2 depicts the coverage probability for DE, DFO, PSO and RS for four different terrestrial environments for four path loss values using default parameters. During initial experimentation, some irregularities were found with PSO and DE, where these implementations were prone to being stuck in the local minima after initial users were identified and removed. This phenomenon can be due to low diversity in PSO and DE; the diversities of \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Environment & Urban, suburban, dense urban, high-rise urban \\ Path loss threshold & 90, 100, 110, 120 \\ Area & 5 km\({}^{2}\) \\ Population size & 25 \\ Function evaluation & 2500 \\ Number of DCs & 10 \\ Height min, max & 0, 120 \\ Carrier frequency & \(2\times 10^{9}\) Hz \\ Speed of light & 299,792,458 m/s \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental parameters. Figure 1: Experiment tree. said algorithms have been reported in [48].