*5.1. The Trade-Off between the Safety of UAVs and the Service Quality for Demands*

We observed that the distance gap between flying UAVs becomes decreased when most of the demand nodes in a service area are densely located in the center of the area, which is natural considering the distribution of the demand nodes. If the safety of UAVs should be placed before the service quality to customers, one can consider further restricting the zoning approach. For example, adding a constraint that restricts the allocation of neighborhood demand nodes to different zones or treating the neighborhood demand nodes as abstract nodes could be considered for the zoning approach. Figure 7 illustrates two zoning solutions obtained with and without such additional constraints for UAV safety.

It should be noted that the zoning approach can also be implemented to maximize the service quality for demands. For example, one may want a zoning solution that minimizes the total distance between demand nodes and their responsible bases. The workload balance between zones can also be considered to derive a zoning solution.

Following this idea, we obtain different zoning solutions by applying the objective functions—to minimize the weighted total distance between demand nodes and bases and to minimize the between-zone variance of the total weighted distance between demand nodes and bases. We apply a genetic algorithm (GA) to derive the solutions. By the nature of a meta-heuristic algorithm, the implemented GA can easily address different types of objective functions and additional constraints (e.g., the limited flight time of UAVs) of the zoning problem. Please refer to Appendix A for details of the GA implementation. Figure 8 shows the solutions obtained; differences to the solutions in Figure 7 are clearly observed.

**Figure 7.** Zoning solutions with and without additional safety constraints: (**a**) with safety constraints; (**b**) without safety constraints.

**Figure 8.** Illustrations of zoning solutions with the service quality-oriented objective functions: (**a**) a solution to minimize the total distance between demands and bases; (**b**) a solution to evenly distribute demands to bases.

Importantly, the shift in the objective function of the zoning problem (*Pzoning*), which leads a different zoning solution, can bring a different degree of trade-off between UAV safety and service quality to demands. This phenomena is conceptually visualized in Figure 9.

**Figure 9.** The performance trade-off between different zoning solutions.

In the figure, the performance of two different zoning solutions with different numbers of available UAVs is plotted. The solutions are distinguished by their line type (a solid line for a safety-oriented zoning solution and a dotted line for a service quality-oriented zoning

solution), and their performances with respect to different perspectives are represented with different colors (blue for UAV safety and red for service quality for demands).

As illustrated in Figure 9, the UAV safety and the service quality for demands are indeed difficult maximize at the same time. The degree of the trade-off would also vary by the objective function applied to the zoning problem and the number of available UAVs. Therefore, it is important to properly formulate a target zoning problem and tune a solution algorithm for the zoning based on the priority, preference, and constraints of a target service system, so that the proposed approach can produce a valid and effective zoning solution. A whole process to successfully implement the zoning approach is illustrated in Figure 10.

**Figure 10.** A process for zoning approach implementation.
