## 5 Experimental Results and Discussions
### Results  
#### 5.2.1 Convergence Analysis  
Figures 1-3 (corresponding to the three independent runs, as shown in the convergence curve subfigures on the left) illustrate the evolution of the optimal objective values over 50 iterations for each stage. Several observations can be made.  
* Rapid Decline in the Initial Phase  
There is a rapid decline in the initial phase followed by stabilization. In most stages, the objective values decrease rapidly within the first 10-20 iterations, indicating that the algorithm can quickly identify relatively good feasible solutions in its early phase. Thereafter, the curves gradually level off, suggesting that the combined effects of global and local search facilitate overall population convergence.
* Variations Among Different Runs  
Run 1: In stage 1, the initial value is approximately 25, eventually converging to 16.08; in stage 2, the value decreases from about 30 to 27.57; in stage 3, it declines from around 40 to 21.55.  
Run 2: In stage 1, the value drops from approximately 21 to 12.28, indicating a more effective utilization of the initial population and search direction in this run; in stage 2 and stage 3, the values converge to 21.03 and 26.62, respectively.  
Run 3: In stage 1, the initial value is higher (around 37), eventually converging to 26.41; stage 2 converges to 26.05; while in stage 3, the initial value is notably high (exceeding 50), ultimately converging to 45.75.  
These observations reveal that, under different random initialization and task environments, the convergence curves display certain fluctuations across stages, yet a clear reduction in objective values is achieved overall.  
* Overall Statistics  
Considering the final optimal values in stage 3 from the three runs (21.55, 26.62, and 45.75), the mean is 31.30 with a standard deviation of 12.77. This suggests that for stages with a larger scale or higher complexity, the algorithm may experience considerable fluctuations due to randomness in initialization and environmental factors. Nevertheless, on average, the algorithm demonstrates robust adaptability to dynamic environments.  
Figure 1: Convergence curve and UAV routes obtained with APSO-LS (run 1), where the blue line represents the path of UAV 1, the orange-red line represents the path of UAV 2, and the yellow line represents the path of UAV 3 in the right side sub-figures.  
In stages 2 and 3, as the number of task points or workload increases, the paths become more complex. Occasional crossings or sequential visits to charging stations among UAVs occur to satisfy energy constraints.  
The stage 1 paths in run 2 are the shortest (with a final makespan of only 12.28), indicating that the algorithm in this run achieved a more efficient task division and route design at the initial stage, thereby enabling the UAVs to complete all requirements with minimal flight and waiting times.  
* Charging Station Visits and Energy Management  
Some of the UAVs are observed to incorporate visits to charging stations prior to heading toward or executing new tasks. Since the algorithm's objective function integrates both energy consumption and completion time, mid-flight charging is performed only when necessary--either when endurance is insufficient or when it benefits the overall makespan.  
When tasks are more scattered or the workload is heavier (for example, stage 3 in run 3), UAVs may frequently shuttle between task points and charging stations, resulting in a relatively higher final makespan (45.75). This outcome reflects the adaptability of the rolling horizon strategy in complex environments, while also highlighting the influence of environmental or initialization challenges on the results.