A Two-Stage Distributionally Robust Optimization Framework for UAV-Based Dynamic Inspection with Joint Deployment and Routing

The growing scale and complexity of industrial infrastructure make efficient and reliable inspections a critical challenge. Inspection task demands often vary dynamically, requiring efficient and demand-responsive inspection strategies to ensure stable operation. However, existing UAV inspection approaches typically deploy UAV base stations (UAV-BSs) based on fixed inspection frequencies, which are inadequate for adapting to such dynamic demands and may reduce inspection efficiency. Moreover, these approaches often rely on historical inspection data, whose empirical distributions may deviate from the true distributions, thereby compromising solution robustness. To address these issues, this paper proposes a two-stage distributionally robust optimization (TDRO) framework for joint UAV-BS deployment and inspection routing in dynamic environments. The framework accounts for uncertainties in both inspection frequency and distributional perturbations. Uncertainty sets constructed based on probability metrics are employed to capture deviations between empirical and true distributions, forming the foundation of the two-stage distributionally robust optimization model. The resulting model is solved using column-and-constraint generation (C&CG) integrated with column generation (CG), yielding robust deployment decisions and an effective trade-off between total system cost and inspection efficiency. Simulation results show that the framework effectively addresses inspection frequency uncertainty, reducing the total objective by 5.50% on average, with a further 2.16% reduction when distributional perturbations are considered.