Optimizing multi-drone patrol path planning under uncertain flight duration: A robust model and adaptive large neighborhood search with simulated annealing

When conducting drone path planning, the flight duration of drones is a critical factor influencing the planning solution. Given the characteristics of drone batteries, accurately predicting the actual flight duration is challenging. It is crucial to reduce the impact of uncertain flight duration on path feasibility. To solve this problem, this paper proposes a robust optimization method that constructs a budget uncertainty set to describe the uncertain flight duration. To facilitate the solution process of the model, the strong duality theorem is employed to transform the robust model into a mixed integer linear programming model. To efficiently handle large-scale path planning problems, a hybrid heuristic algorithm with robust feasibility check (ALSA-RFC) is proposed. This algorithm combines the advantages of adaptive large neighborhood search and simulated annealing. Furthermore, to ensure the robustness of the solution, a method for generating robust initial solutions quickly and a robust feasibility checking method for solutions are constructed. Numerical experimental results demonstrate that ALSA-RFC can quickly find high-quality robust solutions. Additionally, through Monte Carlo simulations, the impact of robust parameters on the robustness of the solution scheme is analyzed, evaluating the performance of the algorithm in different scenarios. Comparisons with chance-constrained programming methods revealed that ALSA-RFC can significantly reduce the sensitivity of path planning results to fluctuations in flight duration without substantially increasing flight costs. Finally, a case study is conducted to further validate the practicality of ALSA-RFC in real-world applications.