# A Two-Stage Co-Evolution Multi-Objective Evolutionary Algorithm for UAV Trajectory Planning
## 4 Experiments and Analysis
### MOUTP Simulation Experiments Based on Classical DE Algorithm  
Complex terrain structures (e.g., mountain heights, slopes, occlusions, etc.) and radar obstacles can cause algorithms to be affected by a large number of local extreme points during operation, making it easy for individuals to fall into local optima. In this study, the classical DE algorithm was used to simulate MOUTP in different instances, and the purpose of this section is to analyze the performance of MOUTP based on the global search algorithm. Moreover, the classical DE algorithm has fewer parameter settings and stronger adaptability. Figure 6 shows the MOUTP simulation graphs for three different test instances, where the red circles indicate the trajectory points; the thin solid lines indicate the connectivity relationships between the UAV, the trajectory points, and the mission points; the red thick solid lines indicate the optimal UAV trajectory, fitted according to the key trajectory points; and the black circular dashed lines indicate that the trajectory segment crosses the obstacle region. In order to show the trajectory point evolution generated by the algorithm more intuitively during the iteration process, this study randomly shows the connectivity of 13 trajectory points in _Gen_ iterations. On the premise that the fitted trajectories based on the  
key trajectory points do not traverse the real terrain digital elevation model, the real terrain digital elevation model was hidden in Figure 6d-f in order to better observe whether the key trajectory points traversed the radar obstacles or not. Table 2 represents the coordinates of the key trajectory points generated via MOUTP based on the classical DE algorithm and the average time of its operation for the three instances. The grey numbered areas indicate key trajectory points that crossed the obstacles. Comprehensively, it can be seen in Figure 6 and Table 2 that the classical DE algorithm jumped out of the local optimum and generated the final UAV flight trajectory in different instances. The average response time was shorter, but the trajectory traversed the radar obstacle in both Instance 2 and Instance 3, and the fitted trajectory segments resulted in a certain collision risk to UAV flights. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**UAV**} & \multicolumn{4}{c}{**Coordinates of Key Trajectory Points**} & \multicolumn{4}{c}{**Target**} & \(\textbf{T}_{average}\) \\  & **(km)** & & & & & & & & & & & **(km)** & **(s)** \\ \hline \multirow{3}{*}{Test} & 17.0 & 23.3 & 27.5 & 38.9 & 48.4 & 57.6 & 75.3 & 89.3 & 105.7 & 109.4 & 114.3 & 122.6 & 140.0 & \\ \cline{2-13}  & 17.0 & 29.7 & 34.2 & 52.4 & 69.6 & 79.8 & 105.5 & 125.0 & 142.0 & 149.1 & 157.2 & 169.4 & 200.0 & 24 s \\ \cline{2-13}  & 20.0 & 23.4 & 24.8 & 27.9 & 29.9 & 28.3 & 28.5 & 28.1 & 29.0 & 28.6 & 30.1 & 28.5 & 20.0 & \\ \cline{2-13}  & 17.0 & 33.6 & 37.1 & 58.9 & 66.8 & 64.2 & **71.5** & 82.6 & 97.4 & **101.4** & **115.0** & 123.5 & 140.0 & \\ \cline{2-13}  & 17.0 & 29.2 & 44.9 & 66.5 & 79.4 & 80.4 & **110.5** & 110.4 & 130.4 & **150.4** & **168.4** & 189.0 & 200.0 & 26 s \\ \cline{2-13}  & 20.0 & 19.3 & 20.3 & 20.3 & 18.5 & 18.5 & **21.0** & 20.7 & 20.3 & **21.4** & **20.2** & 21.0 & 20.0 & \\ \cline{2-13}  & 17.0 & 20.8 & 32.9 & 39.4 & 48.8 & 71.3 & **74.7** & 99.1 & 107.0 & **116.2** & 124.2 & 131.4 & 140.0 & \\ \cline{2-13}  & 17.0 & 25.4 & 52.3 & 59.9 & 64.7 & 74.3 & 106.0 & 114.1 & 137.7 & **151.9** & 174.3 & 185.8 & 200.0 & 30 s \\ \cline{2-13}  & 20.0 & 23.2 & 25.3 & 25.5 & 24.8 & 25.6 & **24.7** & 25.1 & 24.9 & **24.8** & 25.0 & 25.2 & 20.0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MOUTP based on classical DE algorithm to generate coordinates of key trajectory points. Figure 6: Simulation of MOUTP based on classical differential evolutionary algorithm. (**a–c**) represent the simulation figures in the three test instances of the traditional DE algorithm respectively. (**d–f**) conceal the terrain data in the three test instances respectively.