Time-Dependent Path Optimization for Vehicles and UAVs Under Urban Dynamic Traffic and Restricted Zones

Current urban logistics models often struggle to reconcile diurnal traffic dynamics with rigid spatial–temporal regulations. This decoupling causes “cascading infeasibility,” where traffic delays trigger structural regulatory violations and UAV energy depletion. This study formulates a time-dependent vehicle–UAV joint routing problem that strictly couples time-varying speeds with vehicle-restricted zones and no-fly zones. The mixed-integer program minimizes a composite cost by integrating speed curves, geometric detour models, and coupled energy functions. To solve large-scale instances, we propose a hybrid metaheuristic solver (IHGA-VNS-SL) combining genetic algorithms, variable neighborhood search, simulated annealing, and self-learning. Tested on calibrated Wuhan instances, IHGA-VNS-SL quantitatively outperforms baseline heuristics (GA and ALNS). It achieves a tight 2.31% optimality gap against exact solvers (CPLEX) and up to a 20% cost reduction over ALNS, alongside near-zero tardiness. Results demonstrate that this strict coupling effectively mitigates synchronization failures, confirming the framework’s robustness for megacity distribution.

https://doi.org/10.3390/drones10060443

Cite as:

@article{Ji_2026,
  title={Time-Dependent Path Optimization for Vehicles and UAVs Under Urban Dynamic Traffic and Restricted Zones},
  volume={10},
  ISSN={2504-446X},
  url={http://dx.doi.org/10.3390/drones10060443},
  DOI={10.3390/drones10060443},
  number={6},
  journal={Drones},
  publisher={MDPI AG},
  author={Ji, Yuxuan and Liu, Linya and Wang, Yong and Wang, Xi Vincent and Wang, Lihui},
  year={2026},
  month=June,
  pages={443}
}