Two-Phase Heuristic for Vehicle Routing Problem with Drones in Multi-Trip and Multi-Drop Mode

As commercial drone delivery becomes increasingly popular, the extension of the vehicle routing problem with drones (VRPD) is emerging as an optimization problem of interests. This paper studies a variant of VRPD in multi-trip and multidrop (VRP-mmD). The problem aims at making schedules for the trucks and drones such that the total travel time is minimized. This paper formulate the problem with a mixed integer programming model and propose a two-phase algorithm, i.e., a parallel route construction heuristic (PRCH) for the first phase and an adaptive neighbor searching heuristic (ANSH) for the second phase. The PRCH generates an initial solution by concurrently assigning as many nodes as possible to the truck-drone pair to progressively reduce the waiting time at the rendezvous node in the first phase. Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase. Numerical tests on some benchmark data are conducted to verify the performance of the algorithm. The results show that the proposed algorithm can found better solutions than some state-of-the-art methods for all instances. Moreover, an extensive analysis highlights the stability of the proposed algorithm.