🤖 AI Summary
This study addresses the vehicle-drone collaborative collection and profit maximization problem under load-dependent travel times by proposing a Traveling Thief Problem with Drones (TTP-D) model that jointly optimizes item selection, route planning, and flight synchronization. A hybrid solution framework integrating mixed-integer programming, metaheuristics, and attention-based deep reinforcement learning is developed, featuring a learner-initialized hybrid solver to balance solution quality with computational efficiency. Experimental results demonstrate that this solver recovers baseline performance under low computational budgets and identifies the rental-to-profit ratio as a critical determinant of system profitability. These findings provide efficient decision support for complex collaborative scheduling in logistics applications where operational costs and payload dynamics significantly impact overall economic performance.
📝 Abstract
In collection operations, accumulating payload progressively slows the vehicle, imposing a cumulative penalty on routing efficiency. An onboard drone can offset this penalty by retrieving outlying items, thereby shortening the makespan and increasing operational profit. However, travel time remains load-dependent, and each item collected by the ground vehicle shifts the arrival times that govern the drone's launch and rendezvous points. This paper introduces the Travelling Thief Problem with Drone (TTP-D), which maximises the collected profit, net of a time-based rental cost, by jointly optimising item selection, vehicle routing, and flight synchronisation. We formulate a mixed-integer linear program that solves small instances to optimality, and develop both metaheuristics and an attention-based Deep Reinforcement Learning (DRL) policy for larger instances. We further propose a learner-initialised hybrid solver, in which the DRL policy constructs an initial solution that a short annealing run subsequently refines. On two benchmark sets, this hybrid recovers most of the metaheuristic baseline's quality at a fraction of its computational budget, although the largest instances still require the baseline at its full budget. Finally, a sensitivity analysis reveals that the rental ratio is the primary driver of profitability, whereas the fleet parameters affect profit only at the margin.