In this paper, we present a drone-based delivery system that assumes to deal with two different mixed-areas, i.e., rural and urban. In these mixed-areas, called EM-grids, the distances are measured with two different metrics, and the shortest path between two destinations concatenates the Euclidean and Manhattan metrics. Due to payload constraints, the drone serves a single customer at a time returning back to the dispatching point (DP) after each delivery to load a new parcel for the next customer. In this paper, we present the 1-Median Euclidean-Manhattan grid Problem (MEMP) for EM-grids, whose goal is to determine the drone's DP position that minimizes the sum of the distances between all the locations to be served and the point itself. We study the MEMP on two different scenarios, i.e., one in which all the customers in the area need to be served (full-grid) and another one where only a subset of these must be served (partial-grid). For the full-grid scenario we devise optimal, approximation, and heuristic algorithms, while for the partial-grid scenario we devise optimal and heuristic algorithms. Eventually, we comprehensively evaluate our algorithms on generated synthetic and quasi-real data.

翻译：本文提出了一种面向城乡混合区域的无人机配送系统，在该类混合区域（简称EM网格）中，距离度量采用两种不同标准，任意两个目的地之间的最短路径为欧几里得度量与曼哈顿度量的组合。受有效载荷限制，无人机每次仅服务单个客户，完成配送后需返回调度点装载下一客户的包裹。我们提出了面向EM网格的1-中位欧几里得-曼哈顿网格问题（MEMP），其目标是在待服务客户位置与调度点之间的总距离和最小化条件下确定无人机调度点的最优位置。针对两种场景展开研究：全网格场景（需服务区域内所有客户）与局部网格场景（仅需服务其中部分客户）。针对全网格场景设计了最优算法、近似算法及启发式算法；针对局部网格场景则提出了最优算法与启发式算法。最终通过在合成数据与准真实数据上的综合实验对所提算法进行了全面评估。