# Three-Dimensional Trajectory Optimization for UAV-Based Post-Disaster Data Collection
## 4 Numerical Analysis Methods  
The three-dimensional trajectory optimization is divided into 2 parts: hovering point placement and trajectory decision. The locations of the hovering points are decided by the distribution of the UEs. In our proposed approach, the optimization of the hovering points is conducted in two sequential phases, where the genetic algorithm and the hill climbing algorithm are applied separately but collaboratively as follows. First, to search for the 2D optimal location of the hovering points that cover the maximum number of UEs in an LSCP, a genetic algorithm (GA) is adopted and the search scope is the whole mission area. However, to keep the search scope manageable, we limited the search scope to the maximum altitude, which is 150m in this work. Once the 2D location of the hovering points are decided, the hill climbing (HC) algorithm, which is known as a local search algorithm, is used to search for better locations with lower altitude near the result of a location set covering problem (LSCP). This phase improves the spectral efficiency. While the GA focuses on the coverage efficiency that minimizes the number of hovering points, the HC attempts to improve spectral efficiency by reducing the transmission time while hovering. After the hovering points are decided, the trajectory which passes through all hovering points with the minimum time needs to be decided, which can be considered as a classic traveling salesman problem (TSP). The TSP is a well-known problem where a list of locations is given and there is a search for the shortest route that visits each location once and finally returns to the starting point. In our work, the UAV must visit all the hovering points in the search scope. The UAV can be used to search for the shortest route that visits each location once and finally returns to the starting point. The UAV can be used to search for the shortest route that visits each location once and finally returns to the starting point. In our work, the UAV must visit all the hovering points in the search scope.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Frequency \(f_{c}\) (MHz) & 2412 \\ Bandwidth \(B\) (MHz) & 22 \\ Boltzmann Constant \(k_{B}\) & \(1.38\times 10^{-23}\) \\ Temperature \(T\) (K) & 298 \\ Environment \(\mathcal{S}\)-Curve Parameter \(a\) & 9.61 \\ Environment \(\mathcal{S}\)-Curve Parameter \(b\) & 0.16 \\ LoS Additional Loss \(\eta_{\mathrm{L}\mathrm{G}}\) & 1 \\ NLoS Additional Loss \(\eta_{\mathrm{NLoS}}\) & 20 \\ UAV Antenna Type & Directional \\ UAV Antenna Half Width (rad) & \(\pi/4\) \\ UAV Forward Velocity \(\eta^{\mathrm{forward}}\) (m/s) & 14 \\ UAV Ascent Velocity \(\eta^{\mathrm{event}}\) (m/s) & 5 \\ UAV Descent Velocity \(\eta^{\mathrm{descent}}\) (m/s) & 4 \\ UE Antenna Type & Omnidirectional \\ UE Transmission Power \(P_{\mathrm{K}}\) (m/W) & 200 \\ UE Maximum Data Size \(\Phi_{\mathrm{max}}\) (MB) & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 6: Connection status between the UAV and the UE.  
points to collect data from the UEs, and our goal is to minimize the mission completion time. Considering a constant flying speed of UAV, the scenario in our work closely resembles that of the TSP and can be solved with similar approaches used to solve the TSP.