## 4 Proposed Algorithm
So, LS algorithm is more suitable to solve the problem of high demand for customer satisfaction, VNS algorithm is more suitable to solve the problem of high demand for total completion time. From Figure 11 it is observed that when the parameter \(\omega\) changes, the result of SA algorithm is the most stable and there is almost no fluctuation. The result of VSN algorithm is relatively stable with small fluctuation, while the result of LS algorithm has large fluctuation, which is sensitive to the parameter, so its stability is poor. The experimental results demonstrate that VNS is feasible and effective for the considered problem. Figure 10: Routes of UAV\({}_{3}\). Figure 9: Routes of UAV\({}_{2}\). Table 3 shows the average operation times for the three specifications of radius of area \(r\). Figure 12 shows the convergence curves of the three algorithms LS, SA, and VNS simultaneously. The horizontal coordinate is the run time and the vertical coordinate is the ARPD value. From Figure 12 it is observed that LS has the fastest convergence, SA is second, and VNS has the slowest convergence, but VNS outputs the best results. Since it can escape from the local optimum by changing the neighborhood, it is possible to find a better solution compared with LS and SA. However, constant changes of neighborhood increase its cost of time. Based on the above experimental results and analysis, we determine that VNS performs better than the other two which are the most commonly used heuristics for optimization problems, although it converges the slowest. VNS is easy to implement and it can balance very well between diversity and \begin{table}
\begin{tabular}{c c c c} \hline \hline \(r\) & \(LS\) & \(SA\) & VNS \\ \hline
1000 & 7.63 & 19.72 & 50.26 \\
2000 & 14.82 & 38.13 & 98.57 \\
3000 & 28.74 & 74.05 & 189.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average operation time (s). Figure 12: The time convergence curve of the algorithms. convergence. We believe that there are many other metaheuristics which are suitable for solving the problem and may have better performance. Based on our preparatory work, GA and PSO converge slowly and their performances on TSP are good for small-size testing instances. If the computation time is not limited, we believe they can find better solutions than those of VNS in probability significance. NSGA-II is another potentially competitive algorithm which may be very suitable for the considered problem, since NSGA-II converges faster than GA and PSO and has promising performance on multiobjective optimization problems. We will further investigate these algorithms to improve our work on the considered problem based on these assumptions. ## 6 Conclusions

The delivery problem of logistics UAV in urban environment is considered to be a scheduling problem. We first present the automatic delivery system for logistics UAVs to improve the distribution efficiency and reduce costs. The Variable Neighborhood Search algorithm framework is proposed to address the scheduling problem of the system. We use the special method of two-stage optimization to solve the optimization problem with customer satisfaction and total completion time. The experimental results show that the proposed VNS is robust and has better performance. For future work, more multivariate heuristic algorithms will be incorporated, edge computing scenarios that are more realistic will be considered, more practical UAV volume models and energy consumption models will be applied, and the information interaction, multi-UAVs cooperation, and optimized operation mode in the distribution process will be further considered. There are also many other potential algorithms that may be more suitable for solving the considered problem. We will further investigate these algorithms to improve our work on the considered problem. Conceptualization and Methodology: [PERSON], [PERSON], [PERSON], [PERSON], and M.W. ; Validation: [PERSON], [PERSON], and M.W.