驾驶、装载、飞行：带无人机的旅行小偷问题

摘要

在收集作业中，不断累积的有效载荷会逐渐减慢车辆速度，从而对路径规划效率产生累积性惩罚。车载无人机可以通过取回外围物品来抵消这种惩罚，从而缩短完工时间并提高运营利润。然而，行驶时间仍然依赖于载荷，且地面车辆每收集一件物品都会改变决定无人机起飞点与汇合点的到达时间。本文提出了带无人机的旅行窃贼问题（TTP-D），通过联合优化物品选择、车辆路径和飞行同步，最大化扣除基于时间的租赁成本后的收集利润。我们构建了一个混合整数线性规划模型，可将小规模实例求解至最优；针对更大规模的实例，我们开发了元启发式算法以及基于注意力的深度强化学习（DRL）策略。我们进一步提出一种学习器初始化的混合求解器，由DRL策略构造初始解，随后通过短时退火运行对其进行优化。在两个基准测试集上，该混合方法仅需一小部分计算预算即可达到元启发式基线的大部分质量，但最大规模的实例仍需基线方法在完整预算下运行。最后，敏感性分析表明，租赁比率是盈利能力的主要驱动因素，而车队参数仅对利润产生边际影响。

English

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.