駕駛、打包、飛行：配備無人機的旅行竊賊問題

摘要

在收集作業中，累積的載重會逐漸降低車輛速度，對路線規劃效率造成累積性懲罰。車上搭載的無人機可透過取回偏遠物品來抵銷此懲罰，進而縮短總完工時間並提高營運利潤。然而，行駛時間仍取決於載重，且地面車輛每收集一件物品，都會改變決定無人機發射點與會合點的到達時間。本文提出「帶無人機的旅行竊賊問題」（Travelling Thief Problem with Drone, TTP-D），在扣除按時間計費的租賃成本後最大化收集利潤，並同時最佳化物品選擇、車輛路線規劃與飛行同步。我們建構了一個混合整數線性規劃，可將小規模實例求解至最佳；同時針對較大規模實例，分別開發了元啟發式演算法與基於注意力機制的深度強化學習（DRL）策略。我們進一步提出一個學習器初始化的混合求解器，由 DRL 策略建構初始解，再以短暫的退火流程進行細部改良。在兩組基準測試集上，此混合求解器能以一小部分的計算預算恢復元啟發式基線的大部分解品質，儘管最大規模的實例仍需基線方法以完整預算執行。最後，敏感性分析顯示，租賃比率是獲利能力的主要驅動因素，而車隊參數僅在邊際上影響利潤。

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.