  The vehicle routing problem with drones (VRP-D) is to determine the optimal
routes of trucks and drones such that the total operational cost is minimized
in a scenario where the trucks work in tandem with the drones to deliver
parcels to customers. While various heuristic algorithms have been developed to
address the problem, existing solutions are built based on simplistic cost
models, overlooking the temporal dynamics of the costs, which fluctuate
depending on the dynamically changing traffic conditions. In this paper, we
present a novel problem called the vehicle routing problem with drones under
dynamically changing traffic conditions (VRPD-DT) to address the limitation of
existing VRP-D solutions. We design a novel cost model that factors in the
actual travel distance and projected travel time, computed using a machine
learning-driven travel time prediction algorithm. A variable neighborhood
descent (VND) algorithm is developed to find the optimal truck-drone routes
under the dynamics of traffic conditions through incorporation of the travel
time prediction model. A simulation study was performed to evaluate the
performance compared with a state-of-the-art VRP-D heuristic solution. The
results demonstrate that the proposed algorithm outperforms the
state-of-the-art algorithm in various delivery scenarios.
