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arxiv: 2606.30680 · v1 · pith:VJTRHSVGnew · submitted 2026-06-26 · 💻 cs.RO · cs.AI· cs.LG· physics.soc-ph

Locker-based Truck-Drone Routing with Integrated Considerations of Pickups, Deliveries, and No-Fly Zones

Xuanyu Liu , Hui Hu , Jiao Zhao , Ziliang Wang , Zhengbing He This is my paper

Pith reviewed 2026-07-01 06:19 UTC · model grok-4.3

classification 💻 cs.RO cs.AIcs.LGphysics.soc-ph
keywords truck-drone routingdeep reinforcement learninglast-mile deliveryno-fly zonesvehicle routing problempickups and deliveriesneural heuristiclocker-based operations
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The pith

A two-stage deep reinforcement learning method constructs coordinated truck-drone routes that minimize costs while respecting pickups, deliveries, battery limits, loads, and no-fly zones.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the locker-based truck-drone routing problem with pickups, deliveries, and no-fly zones, formulated as a Markov decision process whose goal is to minimize fleet operational cost. It solves the problem with a two-stage neural heuristic: the first stage uses an attention encoder and bidirectional GRU decoder to build truck routes as a capacitated vehicle routing problem; the second stage transfers policy and applies a hybrid dispatch heuristic to insert drone flights from lockers. Experiments on varied instance sizes show the approach beats metaheuristic and other neural baselines in solution quality for most cases while running in very short times. A sympathetic reader cares because last-mile operations must integrate physical constraints and restricted airspace, and a fast, scalable planner could enable wider adoption of hybrid fleets.

Core claim

The paper defines the LTDRP-PDNF and solves it by casting route construction as a Markov Decision Process solved via a two-stage deep reinforcement learning neural heuristic. Stage one applies an attention-based encoder and Bidirectional Gated Recurrent Unit decoder to the truck-only capacitated vehicle routing problem. Stage two combines policy transfer with a hybrid dispatch assignment heuristic to produce fully coordinated truck-drone routes that respect battery, load, pickup, delivery, and no-fly zone constraints while minimizing total cost.

What carries the argument

Two-stage DRL architecture consisting of an attention-based encoder plus BiGRU decoder for truck routing, followed by policy-transfer and hybrid dispatch heuristic for drone coordination.

If this is right

  • The method produces feasible coordinated routes on instances of varying scales while incorporating all listed operational constraints.
  • Computation times remain exceptionally short relative to metaheuristic and neural baselines.
  • Solution quality exceeds that of the compared baselines in the majority of tested cases.
  • The framework supplies a practical, scalable planning tool for locker-based operations under real airspace and vehicle limits.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same staged architecture could be retrained on different objective weights to prioritize emissions or service time instead of cost.
  • Embedding live weather or dynamic airspace data into the MDP state would allow the heuristic to react to temporary no-fly restrictions.
  • Extending the locker nodes to include charging stations or parcel sorting would test whether the dispatch heuristic still scales without redesign.
  • Deployment on city-scale graphs with thousands of lockers would reveal whether the policy-transfer step continues to avoid compounding errors across stages.

Load-bearing premise

The two-stage DRL architecture with policy transfer and hybrid dispatch heuristic can be trained and deployed to produce near-optimal coordinated truck-drone routes that correctly incorporate battery, load, no-fly zone, pickup, and delivery constraints without suffering generalization failure on unseen instances.

What would settle it

Generate a new collection of large-scale instances that include dense, irregular no-fly zones and compare the method's routes and runtimes against known lower bounds or exact solvers on the same instances; consistent large gaps or timeouts would falsify the claim of reliable near-optimality and scalability.

Figures

Figures reproduced from arXiv: 2606.30680 by Hui Hu, Jiao Zhao, Xuanyu Liu, Zhengbing He, Ziliang Wang.

Figure 1
Figure 1. Figure 1: A sketch for LTDRP-PDNF. to continue the delivery tasks. Once all services for delivery stations and lockers are completed, the drone can either return to the depot with its truck or fly back independently [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: 1) Encoder: Let V = {0, 1, . . . , n} denote the node set, where node 0 represents the depot and C = {1, 2, . . . , n} represents the customer set. Each node is described by its coordinate vector xi . For customer nodes, the demand is further normalized by the truck capacity P, i.e., δi = di/P. The initial representation of node i is obtained through a trainable embedding layer: z (0) i = ( A0xi + a0, i = … view at source ↗
Figure 2
Figure 2. Figure 2: Overall structure [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The encoder-decoder structure for solving CVRP [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Optimization process of the drone route is initiated at the delivery station. This operation continues until all lockers have received service. The tight constraints of the MBP method make its solutions susceptible to local optima. To further improve the initial solution, an improved local search (ILS) algorithm is utilized. We employ a 2-opt operation to swap the access order of two points, which helps re… view at source ↗
Figure 5
Figure 5. Figure 5: Training curves Gurobi obtains the optimal solution within the time limit, its result is used as the reference; otherwise, the best solution obtained by the tested heuristic or neural methods is used as the reference. Before comparing these methods in detail, we first present the training curves of the DRL method employed in the first stage [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Generalization to different sizes ALNS, PSO, and AM. The average total cost results are presented in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of representative LTDRP-PDNF solutions [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of drone maximum load capacity on total cost [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Impact of drone battery capacity on total cost [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

Truck-drone delivery is an emerging last-mile logistics mode combining the long-haul capacity of trucks with the flexible service capability of drones. In locker-based operations, smart lockers serve not only as temporary parcel storage facilities but also as automated drone docking and service nodes. These automated nodes support drone takeoff, landing, parcel handover, and battery replacement, thereby significantly extending the service range and operational flexibility of drone-assisted delivery networks. However, practical locker-based delivery systems face complex real-world challenges, requiring the integrated coordination of not only parcel delivery, return pickup, battery-constrained and load-dependent drone flights, but also necessary detours around restricted airspace. To address this practical and multifaceted challenge, this paper introduces a locker-based truck-drone routing problem with integrated considerations of pickups, deliveries, and no-fly zones (LTDRP-PDNF), with the objective of minimizing the total operational cost of a fleet of drone-equipped trucks. We formulate the route construction process as a Markov Decision Process and develop a two-stage deep reinforcement learning-based neural heuristic. The first stage utilizes an attention-based encoder and a Bidirectional Gated Recurrent Unit decoder to solve the truck-only routing problem, formulated as a capacitated vehicle routing problem. The second stage combines a policy-transfer strategy with a hybrid dispatch assignment heuristic to construct fully coordinated truck and drone routes for LTDRP-PDNF. Experiments on instances of different scales demonstrate that the proposed method outperforms metaheuristic and neural heuristic baselines in most cases while maintaining exceptionally short computation times, offering an effective, scalable solution framework under practical operational constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript defines the locker-based truck-drone routing problem with pickups, deliveries, and no-fly zones (LTDRP-PDNF) and minimizes total operational cost for a fleet of drone-equipped trucks. Route construction is cast as an MDP; a two-stage DRL heuristic is proposed in which stage 1 solves the truck-only CVRP via an attention encoder plus BiGRU decoder, and stage 2 applies policy transfer together with a hybrid dispatch heuristic to produce coordinated truck-drone routes that respect battery, load, and no-fly-zone constraints. Experiments on instances of varying scales are reported to show outperformance versus metaheuristic and neural-heuristic baselines while retaining short run times.

Significance. If the performance claims are substantiated by reproducible experiments, the work supplies a scalable neural-heuristic framework for a practically relevant constrained routing problem that simultaneously handles pickups, deliveries, battery limits, and airspace restrictions. The two-stage architecture with policy transfer is a concrete contribution to the literature on hybrid truck-drone logistics.

major comments (1)
  1. [§5] §5 (Computational Experiments): the abstract and available description state that the method “outperforms metaheuristic and neural heuristic baselines in most cases,” yet no information is supplied on instance-generation procedure, how the battery, load, and no-fly-zone constraints are encoded inside the MDP, training hyperparameters, ablation studies, or statistical significance tests. Without these details the central empirical claim cannot be verified or reproduced.
minor comments (1)
  1. [Abstract] The abstract refers to “exceptionally short computation times” without quantitative comparison (e.g., wall-clock seconds versus baseline run times on the same hardware).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and the opportunity to improve the manuscript. The concern about insufficient experimental details is valid, and we will revise Section 5 to provide full reproducibility information while preserving the core contributions of the two-stage DRL framework.

read point-by-point responses

  1. Referee: §5 (Computational Experiments): the abstract and available description state that the method “outperforms metaheuristic and neural heuristic baselines in most cases,” yet no information is supplied on instance-generation procedure, how the battery, load, and no-fly-zone constraints are encoded inside the MDP, training hyperparameters, ablation studies, or statistical significance tests. Without these details the central empirical claim cannot be verified or reproduced.

    Authors: We agree that the current version of Section 5 omits critical details required for reproducibility. In the revised manuscript we will add: (i) the full instance-generation procedure, specifying how pickup/delivery demands, locker locations, battery capacities, load-dependent flight times, and no-fly zones are sampled and encoded; (ii) the precise state, action, and reward definitions that embed battery, load, and airspace constraints inside the MDP; (iii) complete training hyperparameters (learning rates, batch sizes, network dimensions, episode counts, and random seeds); (iv) ablation results isolating the attention encoder, BiGRU decoder, policy-transfer stage, and hybrid dispatch heuristic; and (v) statistical significance tests (paired t-tests or Wilcoxon signed-rank tests with p-values) across 10 independent runs per instance size. These additions will directly substantiate the performance claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes a two-stage DRL heuristic (attention encoder + BiGRU for truck CVRP, followed by policy transfer and hybrid dispatch) for the LTDRP-PDNF routing problem. No derivation chain, equations, or first-principles results are presented that reduce claimed performance or solutions to quantities defined by fitted parameters or self-citations within the paper. The approach is positioned as an empirical heuristic evaluated on test instances against baselines, with no self-definitional mappings, fitted-input predictions, or load-bearing self-citation chains detectable from the provided material. The central claims rest on external empirical comparisons rather than internal reduction to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the MDP formulation and neural components are treated as standard tools applied to the new problem.

pith-pipeline@v0.9.1-grok · 5838 in / 1202 out tokens · 24824 ms · 2026-07-01T06:19:49.627524+00:00 · methodology

discussion (0)

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    2019