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This research introduces the Travelling Thief Problem with Drone (TTP-D), a novel optimization framework for logistics that jointly coordinates ground vehicle routing, payload management, and autonomous drone retrieval to maximize operational profit. The study demonstrates how an attention-based Deep Reinforcement Learning policy can efficiently construct high-quality initial solutions for large-scale instances, significantly reducing computational costs compared to traditional metaheuristics while maintaining solution quality through hybrid annealing refinement.
Drive, Pack, Fly: The Travelling Thief Problem with Drone
arXiv:2608.16435v1 Announce Type: new 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.
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.
Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE); Optimization and Control (math.OC)
arXiv:2608.16435 [cs.AI]
(or arXiv:2608.16435v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.16435 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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