Air traffic network optimization via Laplacian energy maximization

Designing robust air traffic network is an ongoing research effort that seeks to improve the network robustness when one or more air routes are added to the existing network. We demonstrate that Laplacian energy is a fair and promising measure of network robustness based on a case study of a real air traffic network and extensive numerical experiments. Therefore, this paper aims at maximizing the Laplacian energy to enhance network robustness. The corresponding weighted Laplacian energy maximization problem is formulated as flight route addition problem to facilitate practical operations. Three methods are proposed to solve the flight route addition problem, including tabu search, greedy algorithm and integer program. Their trade-off between optimality performance and computational efficiency is demonstrated through the numerical results on a scale-free network. A case study on a real air traffic network is also included for further investigation.