Drone routing problem with swarm synchronization

Abstract

The advantages of rotary-wing drone (RWD) delivery modes have already been delineated. However, single-unit RWDs do not completely solve real problems in last-mile parcel deliveries because of limited payload capacity and flight endurance. Currently, drone swarm technology is being rapidly developed. An RWD swarm can deliver heavy or multiple packages to customers; therefore, the RWD swarm strategy can address the payload capacity limitation of RWDs. Herein, an RWD delivery mode that involves dynamic swarms of RWDs in addition to single-unit RWDs is explored. The “dynamic” characteristic permits the RWD members in swarms to vary by coupling/decoupling operations at nodes. From the routing plan perspective, using RWD swarms for last-mile parcel deliveries is challenging; accordingly, we introduce a swarm synchronization mode that involves interactions among RWD routes. We formally define the drone routing problem with swarm synchronization (DRP-SS) and develop a mixed-integer linear programming model, which considers the decision on RWD swarms and multi trips. An adaptive large neighborhood search heuristic with specific operators is proposed. In the computational experiments, both small- and large-scale instances are used to validate the effectiveness of the mathematical formulation and the heuristic. Several managerial insights are obtained regarding the influence of detours, the utilization of RWD swarms, and the benefits of multi trips. The DRP-SS model and solution method can be used to estimate the performance of the selection of RWD swarms in practical situations.