## 4 Simulation Experiment and Result Analysis
### The Impact of a Planned Path Length on Search Effectiveness  
The straight-line distance flown by a UAV between two consecutive decision points, referred to as the planned path length, corresponds to the first waypoint interval \(D_{wp,1}\) mentioned earlier. This section conducts a simulation analysis of the swarm's collaborative search effectiveness under different \(D_{wp,1}\) values without \(Cost_{turn}\), using the influence of UAV quantity \(N_{UAV}\) on search effectiveness as a reference. Figure 6 illustrates the variation trends of area coverage rate \(r_{cover}^{ij}\) under the conditions \(N_{UAV}=i,i\in\{2,4,\ldots,8\}\) and \(D_{wp,1}=j,j\in\{1000,1500,\ldots,4000\}\). To intuitively represent the influence of \(N_{UAV}\) and \(D_{wp,1}\) on \(r_{cover}^{ij}\), two variables, \(r_{cover}^{\overline{D}}\) and \(r_{cover}^{\overline{D}}\), are defined:  
\[r_{cover}^{\overline{D}}=\sum_{j=1000,1500,\ldots}^{4000}r_{cover}^{ij}, \tag{21}\]  
\[r_{cover}^{\overline{D}}=\sum_{i=2,4,\ldots}^{12}\frac{r_{cover}^{ij}}{6}. \tag{22}\]Figure 7 presents the variation trends of \(r_{cover}^{\overline{D}}\) and \(r_{cover}^{\overline{D}}\) with respect to \(N_{UAV}\) and \(D_{wp,1}\), respectively. As shown in the figure, when \(N_{UAV}\) increases from 2 to 12, \(r_{cover}^{\overline{D}}\) exhibits a variation range of 0.541, whereas \(D_{wp,1}\) shows a significantly smaller variation range of only 0.056 as it increases from 1000 m to 4000 m.  
Figure 8 illustrates the overall trends of target capture rate \(r_{capture}^{i,j}\) with respect to \(N_{UAV}\) and \(D_{wp,1}\). Following the approach used for \(r_{cover}^{\overline{D}}\) and \(r_{cover}^{\overline{D}}\), two variables, \(r_{capture}^{\overline{D}}\) and \(r_{capture}^{\overline{D}}\), are defined for analyzing \(r_{capture}^{i,j}\), and their corresponding variations are presented in Figure 9. Similar to the case of \(r_{cover}^{i,j}\), \(r_{capture}^{\overline{D}}\) exhibits a significant variation range of 0.457 when \(N_{UAV}\) increases, whereas \(r_{capture}^{\overline{D}}\) shows a much smaller variation range of only 0.044 when \(D_{wp,1}\) increases. When evaluating target search effectiveness, both the number of targets captured and the time spent on the search must be considered. Therefore, the variable of average capture time \(\overline{t}_{capture}^{i,j}\) is introduced, defined as the average time elapsed from the start of the mission until target capture, with simulation results shown in Figure 10. Following the analytical approach used for \(r_{cover}^{i,j}\) and \(r_{capture}^{i,j}\), two variables, \(\overline{t}_{capture}^{\overline{D}}\) and \(\overline{t}_{capture}^{\overline{D}}\), are defined, and their variation trends are illustrated in Figure 11. When \(N_{UAV}\) increases, \(\overline{t}_{capture}^{\overline{D}}\) decreases significantly from 202.4 s to 79.8 s, a reduction of 122.6 s, whereas \(\overline{t}_{capture}^{\overline{D}}\) shows no clear trend as \(D_{wp,1}\) increases, with a much smaller variation range of only 28.2 s.  
Figure 6: Search coverage rate under different \(N_{UAV}\) and \(D_{wp,1}\). Figure 7: Comparison of coverage rate trends: (a) \(N_{UAV}\); (b) \(D_{wp,1}\). We define the average decision frequency per UAV as a metric to quantify communication and decision-making consumption:  
\[N_{D,\overline{J}}=\frac{100N_{D}}{N_{U}\cdot t_{s}}, \tag{23}\]  
where \(N_{D}\) represents the total number of decisions made by all UAVs, \(N_{U}\) denotes the number of UAVs, and \(t_{s}\) is the total search duration. Figure 8: Capture rate under different \(N_{UAV}\) and \(D_{up,1}\). Figure 10: Average capture time under different \(N_{UAV}\) and \(D_{up,1}\). As shown in Figure 12, \(N_{UAAV}\) has little impact on \(N_{D,\overline{J}}\), whereas when \(D_{wp,1}\) increases from 1000 m to 4000 m, \(N_{D,\overline{J}}\) decreases from approximately 1.903 to 0.997, a reduction of about 47.6%. The decrease in \(N_{D,\overline{J}}\) implies a slowdown in the Observation-Orientation-Decision-Action (OODA) cycle.