# Three-Dimensional Drone Cell Placement: Drone Placement for Optimal Coverage
## 5 Experiment and Results
### Results  
Figure 6 represents the final coverage probability of the algorithms with all the above experiments accounted for. There has been a noticeable improvement in user coverage among most of the environments. Figures 7-10 visualize the difference between the coverage probability of the implemented algorithm for the default and tuned parameter values. DFO, due to the restart mechanic with higher diversity, has the least improvement in user coverage probability. However, with DFO's advantage in diversity from the disturbance threshold, the coverage probabilities of DFO and DE are very similar in all instances. The DC placement problem on its own, although being a complex problem, can be converted to a simpler one when broken down into multiple sub-parts. In the case of the problem presented in this paper, its complexity has been minimized. It is hypothesized that for DE implementation with its 250 FEs per segment, the search agents are not converging fast enough to the local minima  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Algorithms**} & \multicolumn{2}{c}{**DFO**} & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**DE**} \\ \hline \hline \multirow{2}{*}{**EnvironmentParameter**} & **N** & \(\Delta\) & **N** & **W** & **c1** & **c2** & **Wd** & **N** & **F** & **CR** \\ \cline{2-10}  & 83 & 0.089 & 102 & 0.52 & 0.96 & 0.87 & 0.55  
and the scattered agents are leading to its higher diversity, while PSO converges faster, initially leading to its less than optimal user coverage. Given increased FEs or iterations, DE will converge to the local minima, leading to less than optimal coverage. Any additional constraints or changes in the parameter tuning process for finding the user coverage could affect the algorithms' performance. In some cases, Figures 7(a),7(b) and 7(b),7(c), mainly in the case of DFO and DE, the base coverage sometimes exceeds the coverage with tuned parameters. This behavior could be accounted for by the heuristic nature of the algorithms. A Wilcoxon Signed-Rank test was conducted between the two sets of results; the result of the statistical test in Table 5 illustrates the lack of any significant difference between the performance of the standard and tuned algorithms. Although there has been a noticeable improvement in user coverage in some environments, the paired test illustrates that the different implementations of PSO are significantly different (highlighted in red) than those of DFO and DE. Figure 8: User coverage for urban environments. Figure 7: User coverage for suburban environments. Not all scenarios have seen an improvement in user coverage. The major factors affecting the improvement in user coverage can be separated into two parts  
* Path loss threshold: Scenarios with a low path loss threshold have had the most improvement. Lower path loss dictates a smaller coverage radius and vice versa. Due to the smaller coverage area, there is a greater possibility for improvement in such scenarios. Figures 7a,b, 8a,b, 9a,b and 10a are such cases where parameter tuning had a bigger impact, except for Figure 10b where the type of environment also affects the coverage. Scenarios with a higher threshold such as Figures 7c,d, 8c,d and 9d have had the least improvement in user coverage because most available users are already covered by a large coverage radius (with a few exceptions). However, it is to be noted that a higher threshold does not always dictate a greater coverage radius; as we change the environment type, the coverage radius is also affected. * Environment: Environments such as suburban and urban are considered as easy environment since there are a limited number of factors obstructing LoS, while environments such as high-rise urban and dense urban are considered as hard environments where multiple artificial structures can easily obstruct LoS, with high-rise urban being considered the hardest of all the given environments.