Robust Optimization of UAV Inspection in Mountainous Expressway Networks Under Flight Time and Energy Consumption Uncertainty

Abstract

Unmanned aerial vehicle (UAV) inspection of mountainous expressway networks involves continuously distributed tasks, coordination among multiple base stations, and uncertain flight time and energy consumption induced by no-fly-zone detours. This study develops an offline robust planning framework that jointly determines base-station locations, fleet allocation, and inspection routes. The network is modeled as a task-arc coverage problem with constraints on coverage, station capacity, individual-UAV endurance, and takeoff–landing balance. A budgeted uncertainty set represents coupled time and energy deviations, and duality yields a linear robust counterpart. A branch-and-price algorithm dynamically generates robustly feasible routes through resource-constrained shortest-path pricing. In the Kunming case study, the baseline solution opens 46 of 77 candidate stations, deploys 75 UAVs, covers all 94 task arcs, and yields a robust cumulative inspection time of 3259.16 min. Sensitivity analysis characterizes the effects of the disturbance budget and uncertainty amplitudes. Additional validation shows that the robust plan eliminates endurance violations in two 10,000-scenario within-budget tests at an 18.0% deployment-cost premium relative to the deterministic plan, while local warm-start experiments support rapid operational route replanning after deployment. The framework therefore supports reliable offline network planning together with route-level operational adjustment under changing conditions.