## 4 Proposed Algorithm
The increase of \(r\) widens the differences between these RPD values, making it easier for the algorithm to find better solutions. Figure 6 illustrates that the following parameters: the maximum weight of packages \(g\), the total weight of packages \(G\), and the number of UAVs \(h\) have little influence on the execution of SA algorithm framework. Furthermore, their differences in RPD values are not statistically significant. This is because these three parameters hardly affect the ability of the algorithm to search for the global optimal solution. After comparing the robustness of LS with SA, we compared SA with Variable Neighborhood Search algorithm (VNS). From Figure 5, it can be observed that although the robustness of SA and VNS is similar, VNS optimizes the solution better especially for the following parameters: the radius of area \(r\) and the number of express cabinet \(m\). Figure 6 shows that the robustness of the two algorithms is not different, but VNS has better search performance. The differences in RPD values are statistically significant for the following parameters: the maximum weight of packages \(g\) and the total weight of packages \(G\). These experiments illustrate that there is little difference in robustness between algorithms SA and VNS, but the execution performance of VNS is better. This is because VSN algorithm framework can calculate the optimal solution in different neighborhoods to avoid falling into the local optimal situation, so it can frequently get the global optimal solution. Figure 4: The mean plot of the three compared algorithms with 95.0 percent Tukey HSD intervals. Figure 5: Interactions between area-related parameters with 95.0% Tukey HSD intervals. For each of the 243 instance combinations, five different values of initial temperature \(t\) of SA framework are chosen, i.e., in total there are 1215 instances for the algorithms to compare. Average Relative Percentage Deviations (ARPDs) on all instance combinations are shown in Table 2. This table not only shows the execution effect of different algorithms in each test instance, but it also depicts the influence of these instance parameters on different algorithms. From Table 2, it can be illustrated that VNS has the lowest ARPDs with different parameter settings and SA has the highest ARPDs. VNS performs better than the others mainly because it can escape from the local optimum by restructuring the neighborhood, and the explored solution space is larger than the other two. From the analysis of the results, it can be seen that the proposed VNS algorithm framework is robust for most parameters. In order to better show the structure of the result and system flow, the test based on a small-scale example is executed. The calculation results of the UAV flight tasks are described in detail. Figure 7 shows the path scheduling results of three isomorphic UAVs in a small-scale scenario. For this type of UAV, the upper limit of load is 5 kg, the average flight speed is 48 km/h, and the total flying time of single charging is 0.67 h. In this experiment, the coordinates (abscissa/km, ordinate/km) of each express cabinet are as follows: \(s_{0}\)(1.604, 1.720), \(s_{1}\)(1.163, 3.585), \(s_{2}\)(1.220, 2.153), \(s_{3}\)(2.467, 3.623), \(s_{4}\)(0.519, 3.264), \(s_{5}\)(0.714, 2.742).