Robustness Optimization of Air Transportation Network With Total Route Cost Constraint

Designing a robust air transportation network is critical for aviation activities to maintain highly efficient operations. Given certain total route cost, designing a strategy to improve the robustness of the network is a challenging issue. In this paper, first, a comparison experiment based on a small example shows the total effective resistance is a superior measure satisfying two critical criteria that other measures do not satisfy. Consequently, we explicitly formulate the network optimization problem as the minimization of total effective resistance under several constraints. The problem is often too time-consuming to solve to the optimal by exact methods. To achieve better efficiency, we propose a convex relaxation method for medium-scale networks making use of the problem properties. For large-scale networks, a clustering based convex relaxation method, reducing the dimensions of the network via selecting critical airports, is further proposed. To demonstrate the efficiency and efficacy of the proposed methods, simulations are performed on nine typical scale-free network and two real air transportation networks including Jetstar Asia Airway and domestic American Airlines. Note to Practitioners —The crucial need for designing robust air transportation networks in the aviation industry serves as the impetus for this work. The application scenarios range from the design of airport and flight operation networks for airlines, to air traffic networks with airways and waypoints, extending to drone cargo networks. An essential characteristic of a well-designed network is its ability to preserve connectivity, as much as possible, when it experiences disruptions such as flight cancellation or airway navigation equipment failure. The paper presents an argument for using total effective resistance as the key measure of network robustness, showing it to outperform other measures. We’ve developed specialized algorithms that leverage the unique properties of this optimization problem to minimize the total effective resistance of air transportation networks subject to certain total route cost to enhance the network structure. Although this study focuses on air transportation networks, the applicability of the algorithms extends beyond this field. Practitioners can apply them in other scenarios to design robust networks in various aviation operations.