## 4 Results
### Multiple Fire Points Location  
To accurately locate the continuous multiple mountain forest fire points, the particle swarm optimization algorithm is implemented for UAV swarm path planning. Firstly, the parameters of the particle swarm are initialized, including the particle population \(M\), the number of the iteration \(k\), the inertia weight \(w\), the individual learning factor \(c_{1}\), the group learning factor \(c_{2}\), the location boundary area, and the starting point of the UAV flight. It should be noted that those parameters are selected based on the standard PSO algorithm [36]. The specific parameters for initializing the particle swarm are detailed in Table 2.  
Secondly, to ensure the feasibility of the UAV flight trajectory and reduce the algorithm calculation time, the cubic B-spline interpolation algorithm is implemented to smooth the flight trajectory. To guarantee the effective execution of the cubic B-spline interpolation algorithm, each particle is set to consist of three positions, which means that there are three location points in each UAV flight path to connect the starting and ending points. Furthermore, in order to avoid collisions, UAVs should always fly higher than the terrain height in the flight path, which means that the height of a UAV flight should exceed the height of a mountain forest, according to Equation (7). Additionally, the distance between the starting and ending points is defined as fitness. In order to obtain accurate fitness and fire point locations, the models of mountain forests should be interpolated and refined. Based on the above settings and preparations, the results of the UAV flight path to locate the forest fire points are illustrated in Figures 8 and 9. As can be seen, with the height Z changes, the color of the mountain gradually changes from blue to yellow, the stars represent fire points and squares represent start point. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(M\) & 50 \\ \hline \(k\) & 100 \\ \hline \(w\) & 1.2 \\ \hline \(c_{1}\), \(c_{2}\) & 2, 2 \\ \hline location boundary area & (0, 0, 0) to (100, 100, 100) \\ \hline starting point & (0, 0, 0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for initializing the particle swarm. Figure 7: **(a)** Front view of the five modeled mountain forests and fire points; **(b)** Top view of the five modeled mountain forests and fire points. As shown in Figure 8, the UAV departs from the starting point (0, 0, 0), initially reaches Fire Point F1 at a relatively high position of the mountain forest M1, then proceeds to Fire Point F2 of the mountain forest M2, next proceeds to the Fire Point F3 at a relatively low position of the mountain forest M3, after that proceeds to the Fire Point F4 of the mountain forest M4, ultimately arriving at the Fire Point F5 of the mountain forest M5. As can be seen, the UAV flight path planning method realizes the detection of multiple continuous mountain forest fire points at different heights and locations. It is important to highlight that each path is connected by three location points, and all the paths successfully avoid the adjacent mountain forests. In order to show more detailed features of the method for detecting continuous multiple mountain forest fire points, Figure 9 illustrates the top view of the UAV flight path. As depicted in Figure 9, the UAV flight paths P1, P2, P3, P4, and P5 are shown more directly, highlighting the details of the flight trajectory successfully bypassing the adjacent mountain forests. It is important to note that all optimal fitness can be obtained after 62 iterations of the PSO algorithm. The computation times of the flight paths P1, P2, P3, P4, and P5 are 13.3 s, 7.9 s, 9.1 s, 11.2 s, and 13.1 s, respectively. Figure 10 illustrates how optimal fitness evolves with the number of iterations.