## 5 Experimental Results and Discussions
### Results
#### 5.2.4 Discussions  
From the above results and analysis, the following findings can be drawn. Convergence behavior: The convergence curve drops rapidly in the early iterations, indicating a strong global search capability of the particle swarm. This is attributed to the global search ability of the PSO algorithm combined with the local search operator designed in this study. In the middle and later stages, the curve flattens while still achieving improved solutions, reflecting the effectiveness of the adaptive perturbation strategy. This strategy helps the algorithm to escape local optima and continuously refine solutions without introducing excessive disturbance that could harm convergence. Figure 5: Convergence curve and UAV routes obtained with standard PSO (run 2), 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. Figure 6: Convergence curve and UAV routes obtained with standard PSO (run 3), 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. Adaptability to dynamic task updates: Since task numbers and loads are updated at each stage, static planning would struggle to accommodate sudden or incremental demands. By reapplying PSO optimization at each stage, the algorithm can dynamically adjust path planning and task assignments based on new task requirements or UAV energy states, reducing ineffective scheduling. Energy-aware scheduling: By incorporating energy consumption weights in the objective function and inserting necessary charging operations when detecting low UAV energy levels, the algorithm minimizes the impact of charging delays and excessive flight distances on the makespan while ensuring task completion. In multiple experiments, UAVs successfully returned to charging stations for replenishment before energy depletion. Robustness of the algorithm: Although there is significant variation in stage 3 across three independent runs (21.55 vs. 45.75), the overall results consistently converge to feasible solutions within a limited number of iterations. The algorithm demonstrates good scheduling efficiency at an average makespan of 31.30. Given the high-dimensional, strongly nonlinear, and stochastic nature of UAV scheduling problems, these results validate the algorithm's robustness in general cases. Trade-off between makespan and energy consumption: In this study, makespan and energy consumption are merged into a single objective function, with a weighting coefficient \(\alpha\) to balance the trade-off. If a particular application prioritizes endurance and energy efficiency, a larger \(\alpha\) can be used; conversely, if minimizing completion time is critical, reducing \(\alpha\) will emphasize time-based objectives. Impact of random initialization and dynamic configurations: The results from three independent runs suggest that random initialization and varying dynamic task configurations significantly influence the final outcome. To mitigate this dependency, parallelized or multi-population strategies could be introduced. Additionally, reinforcement learning or other adaptive methods could be incorporated to quickly determine superior initial solutions at each stage, further improving convergence speed and solution quality. In summary, the results from three independent runs fully demonstrate the effectiveness and robustness of the improved PSO (APSO-LS) when applied to multi-UAV dynamic scheduling within a rolling time-domain framework. Whether observed from the rapid decline and stable convergence of the convergence curve or from the UAVs' flexible access to task points and charging stations in the visualized paths, the algorithm exhibits a comprehensive advantage in balancing task completion time and energy consumption.