Given a set of customers, the Flying Sidekick Traveling Salesman Problem (FSTSP) consists of using one truck and one drone to perform deliveries to them. The drone is limited to delivering to one customer at a time, after which it returns to the truck, from where it can be launched again. The goal is to minimize the time required to service all customers and return both vehicles to the depot. In the literature, we can find heuristics for this problem that follow the order-first split-second approach: find a Hamiltonian cycle h with all customers, and then remove some customers to be handled by the drone while deciding from where the drone will be launched and where it will be retrieved. Indeed, they optimally solve the h-FSTSP, which is a variation that consists of solving the FSTSP while respecting a given initial cycle h. We present the Lazy Drone Property, which guarantees that only some combinations of nodes for launch and retrieval of the drone need to be considered by algorithms for the h-FSTSP. We also present an algorithm that uses the property, and we show experimental results which corroborate its effectiveness in decreasing the running time of such algorithms. Our algorithm was shown to be more than 84 times faster than the previously best-known ones over the literature benchmark. Moreover, on average, it considered a number of launch and retrieval pairs that is linear on the number of customers, indicating that the algorithm's performance should be sustainable for larger instances.

翻译：给定一组客户，飞行副手旅行商问题（FSTSP）涉及使用一辆卡车和一架无人机为客户执行配送服务。无人机每次仅限于向一个客户配送，之后返回卡车，并可从卡车再次起飞。目标是最小化服务所有客户并使两辆车均返回仓库所需的时间。在现有文献中，我们可以找到遵循“先定序后拆分”方法的该问题启发式算法：首先构建包含所有客户的哈密顿回路h，随后移除部分客户交由无人机处理，同时确定无人机的起飞点与回收点。这些算法实际上优化求解了h-FSTSP——该变体要求在遵循给定初始回路h的前提下求解FSTSP。本文提出了惰性无人机特性，该特性保证h-FSTSP算法只需考虑部分无人机起飞与回收节点的组合。我们还提出了一种利用该特性的算法，并通过实验验证了其在减少此类算法运行时间方面的有效性。在文献基准测试中，我们的算法比先前最优算法快84倍以上。此外，该算法平均处理的起飞-回收节点对数量与客户数量呈线性关系，表明算法性能在更大规模实例上应具有可持续性。