## 7 Discussion  
As shown above, varying \(\mu\) affects the objective functions, though we have computed the convex hull to reduce the search space to some extent. However, this parameter may still reduce or increase the number of candidate points to place UAVs in the target area. The choice of \(\mu\) depends on the requirement such as the area to be covered, the maximum transmission range, and also the number of available UAVs to cover the GNs to meet the QoS requirements.  
In this work, varying the flying altitude would not significantly affect the objective functions given the order of magnitude between the communication range of omni-directional antennas considered in the simulations and the allowed flying altitudes from the set \(\mathcal{H}\), i.e., picking uniformly any value from the set \(\mathcal{H}\), there will be a slight difference between the covered areas.  
The use of NSGA-II as an optimization tool allows us to produce a set of solutions that are better and spread as observed in our simulations results. It enables us to have options to select a solution according to the requirement of the application or problem at hand. For instance, if it is not acceptable that any GN communicates beyond 75% of the degree of dissatisfaction and there are no more than 60 available UAVs, then they can easily be configured with solutions that respect these requirements from our Pareto-optimal (non-dominated) set chosen from Figure 7.  
The experimental results presented in the previous section are specific to the proposed scenarios and assumptions that were considered in our system model. In a realistic environment, one should take into account additional constraints such as the effect of interference, GN mobility, number of GNs to be covered, terrain conditions, etc.  
* Interference: Nodes may be positioned within an acceptable distance for the required data rate, but may fail to achieve it due to interference caused by ongoing transmission of their neighboring nodes.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Max. UAVs** & **Degree.Dissat(\%)** & **Min. UAV** & **Degree. Dissat (\%)** \\ \hline \(\mu=0.15\) & 38 & 55.55 & 34 & 83.33 \\ \(\mu=0.30\) & 43 & 55.55 & 35 & 88.88 \\ \(\mu=0.45\) & 56 & 33.33 & 43 & 87.50 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Maximum and minimum No. of UAVs for each scenario.  
Figure 7: Trade-off between the number of UAVs and the degree of dissatisfaction of the GNs.  
* GN mobility: Although the mobility is not considered in this work, it is worth mentioning that it would at least demand scheduling of periodic updates and computation of new solutions due to topology changes. As was previously mentioned, that is a challenging issue, namely because of the need to minimize temporary connectivity disruption due to UAV position changes.
* Number of GNs: UAVs have a limited capacity to service a certain number of GNs efficiently, and if this capacity is exceed, additional UAVs may be needed.
* Terrain conditions/ structure: UAVs may not fly at the desired altitude due to the existence of obstacles (e.g., trees, mountains, buildings, etc.), which may require the addition of more UAVs to maintain the connectivity among the nodes.  
Algorithm 1 was used to ensure the connectivity of the network and produce valid solutions. We used the Breadth First Search (BFS) algorithm to check if there is a path to the destination. If a path is not found, it adds a new UAV to connect it, as explained in Section 4.2.1. This procedure is not optimized, which may conflict with the objective of minimizing the number of UAVs. However, it may eventually reduce the degree of dissatisfaction of the GNs.