## 5 Experimental Analysis
### Algorithm Performance
#### 5.2.4 Pareto Front Analysis
The minimum time solution facilitates rapid service delivery, yet it may result in increased costs and diminished coverage. The star-shaped points (*) on the coordinate axis denote the Ideal Point, which represents a hypothetical solution wherein all objectives are theoretically optimized, yet practically unattainable. Each objective value associated with the Ideal Point corresponds to the extreme values of the objectives within the Pareto solution set, including minimum delivery time, lowest cost, and maximum coverage. However, achieving these extreme values simultaneously in practice is infeasible. By designating the Ideal Point, one can visually illustrate the disparity between the results produced by the algorithm and the theoretical optimum. The series of Pareto front diagrams presented herein illustrates the interdependent and mutually restrictive relationship among the following three optimization objectives: demand coverage, distribution time, and distribution cost. In practical distribution scenarios, it is essential to prioritize actual needs and select the most appropriate distribution plan from the set of non-dominated solutions. 2.5 The Relationship Between Road Network Vulnerability and the Completion Rate of Air-Ground Collaborative Logistics Tasks  
The vulnerability of road networks serves as a critical metric for assessing the extent of performance degradation within a transportation system when nodes or road segments experience failure. In urban distribution contexts, an increase in the rate of node failures correlates with a gradual rise in the vulnerability value of the road network, which, in turn, leads to a significant decline in the task completion rate associated with traditional ground distribution methods. Conversely, the air-ground collaborative logistics model effectively addresses the challenges posed by road network vulnerability by incorporating unmanned aerial vehicles (UAVs) to facilitate auxiliary distribution. It is evident from Figures 16 and 17 that, as the node failure rate increases, the vulnerability of the road network escalates, reaching a value of 0.8. At this juncture, the task completion rate for the traditional ground distribution model is approximately 60%, whereas the air-ground collaborative logistics model sustains a significantly higher task completion rate of 95%, with a distribution time of approximately 120 min. More critically, when the node failure rate rises further to 70%, the vulnerability of the road network approaches 1.0. Under these conditions, the task completion rate for the traditional distribution model declines sharply to below 40%, while the air-ground collaborative logistics model continues to achieve a task completion rate of 90%, with a distribution time of around 150 min. Figure 16: Relationship between node failure rate and road network vulnerability. Figure 17: The correlation between road network vulnerability and the rate of task completion. The advantages of air-ground collaborative distribution are primarily responsible for its effectiveness. On one hand, unmanned aerial vehicles (UAVs) can directly access failed nodes without being impeded by obstructions in the ground transportation network. On the other hand, the collaborative distribution model involving both trucks and UAVs allows for dynamic adjustments to distribution strategies and the optimization of distribution routes based on the real-time conditions of the road network. In scenarios where the vulnerability of the road network is exacerbated by natural disasters, traffic accidents, or large-scale events, the air-ground collaborative logistics model offers a more reliable distribution solution. Notably, in extreme situations where the failure rate of nodes exceeds 50%, the task completion rate of traditional distribution methods declines significantly, whereas the air-ground collaborative approach is capable of maintaining a high level of service, thereby underscoring its critical value in emergency logistics.