As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in mult...As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(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 program-ming 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 con-currently 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 solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.展开更多
The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery stage.To reach a balance between green transportation and competitiv...The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery stage.To reach a balance between green transportation and competitive edge,the collaborative routing of drones in the air and trucks on the ground is increasingly invested in the next generation of delivery,where it is particularly reasonable to consider customer time windows and time-dependent travel times as two typical time-related factors in daily services.In this paper,we propose the Vehicle Routing Problem with Drones under Time constraints(VRPD-T)and focus on the time constraints involved in realistic scenarios during the delivery.A mixed-integer linear programming model has been developed to minimize the total delivery completion time.Furthermore,to overcome the limitations of standard solvers in handling large-scale complex issues,a space-time hybrid heuristic-based algorithm has been developed to effectively identify a high-quality solution.The numerical results produced from randomly generated instances demonstrate the effectiveness of the proposed algorithm.展开更多
文摘As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(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 program-ming 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 con-currently 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 solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.
基金supported by the National Natural Science Foundation of China(No.61961146005)。
文摘The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery stage.To reach a balance between green transportation and competitive edge,the collaborative routing of drones in the air and trucks on the ground is increasingly invested in the next generation of delivery,where it is particularly reasonable to consider customer time windows and time-dependent travel times as two typical time-related factors in daily services.In this paper,we propose the Vehicle Routing Problem with Drones under Time constraints(VRPD-T)and focus on the time constraints involved in realistic scenarios during the delivery.A mixed-integer linear programming model has been developed to minimize the total delivery completion time.Furthermore,to overcome the limitations of standard solvers in handling large-scale complex issues,a space-time hybrid heuristic-based algorithm has been developed to effectively identify a high-quality solution.The numerical results produced from randomly generated instances demonstrate the effectiveness of the proposed algorithm.
