Title: Graph transformer decision model for efficiently resolving the UAV-UGV joint routing problem

Authors: Ke Zhang; Yuelong Su

Addresses: School of Transportation Management, People's Public Security University of China, China ' The State Key Laboratory of Intelligent Green Vehicle and Mobility, Tsinghua University, China

Abstract: The integration of unmanned aerial vehicles with unmanned ground vehicles presents a promising solution for last-mile delivery in urban environments. However, current research often models vehicle movement as discrete nodes, rather than as the waypoint selection in continuous space. This paper proposes a novel framework named graph transformer decision model (GTDM), to address the challenging problem of joint routing problem for multiple drones and ground vehicles. The framework employs a graph transformer module for state encoding of the heterogeneous multi-agent system. Then, during the decision process, each agent computes task assignment probabilities for drones through an attention mechanism and generates optimal scheduling strategies using greedy decoding. Evaluated on the real-world road network of Xiong'an New Area, results demonstrate that the proposed method successfully balances solution quality with computational efficiency compared with heuristic algorithms, such as large neighbour search, showcasing its robustness and potential for practical deployment in future smart cities.

Keywords: unmanned aerial vehicles; UAVs; vehicle routing problem; transformer; urban logistics; reinforcement learning.

DOI: 10.1504/IJCSE.2026.155103

International Journal of Computational Science and Engineering, 2026 Vol.29 No.4, pp.417 - 425

Received: 26 Dec 2025
Accepted: 28 Feb 2026
Published online: 27 Jul 2026 *

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