The improved unmanned aerial vehicle (UAV, or drone) delivery systems allow an unattended truck to pair two or more drones to accelerate delivery. Although such systems have been addressed in the literature, the extent to which approach can design a robust truck-drone schedule under uncertainty is not yet understood. This paper introduces a robust traveling salesman problem with multiple drones (RTSP-mD), in which a truck coordinates with a heterogeneous fleet of drones to make deliveries under uncertain navigation environments. The RTSP-mD is first formulated as a second-order cone programming (SOCP) to minimize makespan and synchronization risk simultaneously. To solve this complex problem, a three-phased adaptive large neighborhood search (ALNS) algorithm is proposed. The experiment results show that nominal optimal solution generally has a lower expected makespan but rarely remains efficient or feasible under a small perturbation to schedules. About one-third of robust optimal solutions can be against a large reduction of synchronization risk at a negligible price in makespan. And we demonstrate that the drone number remains stable for robust (near-)optimal solutions rather than growing along with customer density increase.

改进后的无人驾驶飞行器（UAV，或无人机）交付系统允许无人值守的卡车配对两架或更多无人机以加速交付。尽管此类系统已在文献中得到解决，但尚不清楚这种方法在多大程度上可以在不确定的情况下设计出稳健的卡车-无人机时间表。本文介绍了多无人机 (RTSP-mD) 的稳健旅行推销员问题，其中一辆卡车与异构无人机舰队协调，在不确定的导航环境下进行交付。RTSP-mD 首先被制定为二阶锥规划 (SOCP)，以同时最小化完工时间和同步风险。为了解决这个复杂的问题，提出了一种三阶段自适应大邻域搜索（ALNS）算法。实验结果表明，名义最优解通常具有较低的预期完工时间，但在对时间表的小扰动下很少保持高效或可行。大约三分之一的稳健最优解决方案可以以可忽略不计的完工时间价格大幅降低同步风险。我们证明无人机数量对于稳健（接近）最优的解决方案保持稳定，而不是随着客户密度的增加而增长。