# 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
By combining Figure 7 and Table 3, it was found that the MOUTP fitted trajectories based on the TSCEA in three different instances did not cross the obstacles. The third of these instances, i.e., the location of the key trajectory point near the radar [110,140,4] in Figure 7c,f and the fitted trajectory segments fit the shape of the radar, indicating that the TSCEA had a better performance in balancing the constraints and objectives. Meanwhile, the average planning time of MOUTP based on the TSCEA was higher than that of the DE algorithm but still within a limited time. (2) MOUTP based on different COOEAs  
As described in this section, three different COOEAs were used to simulate MOUTP under different instances, as shown in Figure 8. Table 4 displays the HV, IGD, FP, and average planning time performance metrics for different COOEAs. From the MOUTP simulation graph based on different COOEAs in Figure 8 and the metrics of different COOEAs in Table 4, the following was shown:  
* In Test Instance 1, the HV values of the TSCEA were all larger than those of the other COOEAs, and the values of the IGD were all smaller than those of the other algorithms, indicating that the TSCEA had better diversity and convergence than the other COOEAs. The values of the FP of the DD-CMOEA, the TSCEA, and the DPCPRA algorithm were all 100%, and part of the key trajectory points of the cDADSEA crossed the obstacles, so there were a small number of infeasible solutions. Although the average running time of the TSCEA was longer than that of the DD-CMOEA and the TSCEA, the difference was small. * In Test Instance 2, the HV values of the TSCEA were lower than those of the DPCPRA, suggesting that the TSCEA was less diverse than the DPCPRA; however, the values of the IGDs were still superior to those of the other COOEAs. The lower FP values of the DD-CMOEA and the cDADSEA suggest that some of the key trajectory points traversed the obstacles. Meanwhile, the average time of the algorithms in Test Instance 2 was longer than that in Test Instance 1 because the simulation environment was more complex in Test Instance 2; however, the planning time was still shorter. * The TSCEA's HV and IGD values were superior to those of the other algorithms in Test Instance 3. The FP of each COOEA in Test Instance 1 remained at 100%, but as the difficulty of the simulation environment in other instances increased further, the FP value of the other two COOEAs gradually decreased. The FP value of the TSCEA did not change. This indicates that the performance of the TSCEA metrics was more stable. Meanwhile, the average planning time of the TSCEA in Example 3 was also more stable. Figure 9 is a graph of the Pareto fronts for MOUTP based on different COOEAs. Figure 9a-c represent the COOEA Pareto fronts for Test Instance 1, Test Instance 2, and Test Instance 3, respectively. Since the simulation environment in Instance 1 was relatively simple, the distribution of each COOEA Pareto front was relatively uniform. However, the TSCEA had a more uniform distribution, and the two optimization objective values were smaller than those of the other algorithms, which indicates that the TSCEA was able to effectively balance the UAV range distance and the threat value of the distance to the obstacle. From Figure 9b,c, it can be seen that the UAV range distance and the UAV distance to the obstacle threat values of MOUTP based on the TSCEA were smaller than those of the other COOEAs, which was mainly due to the TSCEA's global search and constraint-processing abilities.