A faster heuristic for the traveling salesman problem with drone

The Flying Sidekick Traveling Salesman Problem (FSTSP) consists of using one truck and one drone to perform deliveries to a set of customers. 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 the 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 an amount 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.