# A Two-Stage Co-Evolution Multi-Objective Evolutionary Algorithm for UAV Trajectory Planning
## 4 Experiments and Analysis
### Experimental Settings  
(1) Test instances and model parameters In this section, three different test instances are designed with the aim of examining the UAV's traversal of mountainous terrain and radar scanning areas, as shown in Figure 5. Specifically, only the digital elevation model of real terrain was considered in Instance 1, as shown in Figure 5a. Instance 2 contained the real terrain digital elevation model and three radar models, as shown in Figure 5b. Instance 3 added three radar models to Instance 2, and its main purpose was to analyze the effect of increasing radar density on the performance of MOUTP. Instance 3 is shown in Figure 5c. In Figure 5, the yellow circle indicates the location of the UAV, the yellow pentagram indicates the location of the mission point, and the yellow hemisphere indicates the location of each radar model. Table 1 shows the real terrain digital elevation model dimensions and the coordinates and scanning radius of each radar model for different instances. sanfranciscos.dem.gz denotes the real terrain digital elevation model dataset [180; 230; 50], denotes the terrain dimensions, \(Rc\) denotes the radar's coordinates, and \(Rr\) denotes the radar's scanning radius. (2) Parameters for comparison algorithms  
The classical DE algorithm reduces the limitations of UAV constraints through the mutation operator, crossover operator, and other perturbation strategies, which makes it easier for individuals to jump out of the local optima. The DE algorithm is more suitable for solving optimization problems with complex environments and more constraints. The DD-CMOEA adopts a dual-population co-evolutionary approach, which uses two populations, mainPop and auxPop, to explore the feasible and infeasible domains, respectively, and the algorithm uses infeasible solutions that violate the constraints to participate in the evolution, which enhances the diversity of the populations. The cDADSEA employs a competing-constraint dual-archive two-stage evolutionary algorithm, which evolved in different evolutionary stages by means of a convergence-driven archive (CA) and diversity-driven archive (DA). The DDPCPRA designs a dynamic constraint-handling mechanism and a resource allocation mechanism whose main and assistant populations directly optimize all constraints. The basic parameters of each comparison algorithm in our experiment were set as follows:  
* Population size: \(N=100\);
* Number of iterations of the algorithm: \(Gen=500\);
* Probability of mutation: \(Pm=0.9\);
* Number of independent runs of the algorithm: 30. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Terrain-Type Obstacles** & **Terrain-Type Obstacles\_3 Radars** & \multicolumn{3}{c}{
\begin{tabular}{c} **Terrain-Type Obstacles\_6** \\ **Radars** \\ \end{tabular} } \\ \hline \multirow{5}{*}{\(\begin{array}{c}\text{sanfranciscos.dem.gz}\\ \text{[180,230,50]}\end{array}\)} & \# & \(Rc\) (km) & \(Rr\) (km) & \(Rc\) (km) \\ \cline{2-6}  & 1 & [120,70,4] & 30 & [120,70,4] & 30 \\ \cline{2-6}  & 2 & [110,140,4] & 26 & [110,140,4] & 26 \\ \cline{2-6}  & 3 & [52; 103,5] & 30 & [52,103,5] & 30 \\ \cline{2-6}  & 4 & - & - & [80,30,5] & 25 \\ \cline{2-6}  & 5 & - & - & [140,160,5] & 25 \\ \cline{2-6}  & 6 & - & - & [40,160,5] & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Scope of DEM of real terrain and parameters for modeling radar obstacles. Figure 5: Schematic representation of different test instances. (**a**) denotes terrain-type obstacles; (**b**) denotes terrain-type obstacles_3 radars; (**c**) denotes terrain-type obstacles_6 radars. The remaining specific parameters corresponded to those described in the respective original literature. 1. Evaluation indicators for CMOEAs
2.