In this paper, we introduce the multiple Traveling Salesman Problem with Drone Stations (mTSP-DS), which is an extension to the classical multiple Traveling Salesman Problem (mTSP). In the mTSP-DS, we have a depot, a set of trucks, and some packet stations that host a given number of autonomous vehicles (drones or robots). The trucks start their mission from the depot and can supply some packet stations, which can then launch and operate drones/robots to serve customers. The goal is to serve all customers either by truck or by drones/robots while minimizing the makespan. We formulate the mTSP-DS as a mixed integer linear programming (MILP) model to solve small instances. To address larger instances, we first introduce two variants of a decomposition-based matheuristic. Afterwards, we suggest a third approach that is based on populating a solution pool with several restarts of an iterated local search metaheuristic, which is followed by determining the best combination of tours using a set-partitioning model. To verify the performance of our algorithms, we conducted extensive computational experiments. According to the numerical results, we observe that the use of drone stations leads to considerable savings in delivery time compared to traditional mTSP solutions. Furthermore, we investigated the energy consumption of trucks and drones. Indeed, depending on the energy consumption coefficients of trucks and drones as well as on the distance covered by drones, the mTSP-DS can also achieve energy savings in comparison to mTSP solutions.

在本文中，我们介绍了无人机站的多旅行商问题(mTSP-DS)，它是经典多旅行商问题(mTSP) 的扩展。在 mTSP-DS 中，我们有一个仓库、一组卡车和一些承载给定数量的自动驾驶车辆（无人机或机器人）的数据包站。卡车从仓库开始执行任务，可以提供一些数据包站，然后可以启动和操作无人机/机器人为客户服务。目标是通过卡车或无人机/机器人为所有客户提供服务，同时最大限度地缩短制造时间。我们将 mTSP-DS 制定为混合整数线性规划(MILP) 模型来解决小实例。为了解决更大的实例，我们首先介绍了基于分解的两种变体数学的。之后，我们建议第三种方法，该方法基于通过多次重新启动迭代的局部搜索元启发式来填充解决方案池，然后使用集合分区确定最佳旅行组合模型。为了验证我们算法的性能，我们进行了广泛的计算实验。根据数值结果，我们观察到与传统的 mTSP 解决方案相比，使用无人机站点可以显着节省交付时间。此外，我们调查了卡车和无人机的能源消耗。事实上，根据卡车和无人机的能耗系数以及无人机覆盖的距离，与 mTSP 解决方案相比，mTSP-DS 也可以实现节能。