Robustness optimization of aviation-high-speed rail coupling network

Recently, interactions between the real networks have received extensive attention from scholars in different fields. Considering the edge coupling relationship between aviation networks (AN) and high-speed rail networks (HRN), we established the aviation-high-speed-rail coupling network (AHSRCN) model of China according to the real database of flights and trains. We defined the initial load of each edge based on the importance index of edges obtained by importance evaluation method, and then established a nonlinear load capacity model. Furthermore, according to the actual situation, we applied two dynamic load distribution strategies for each network with different load capacity exponential parameters and load capacity coefficient parameters, and use network congestion factor defined to reflect the robustness of the networks to study optimization of robustness of AHSRCN. The results show that as the proportion of remained edges increases, the aviation network and the high-speed rail network’s congestion reach the peak when the proportion of remained edges is 6% and 2%, respectively. The increase of load capacity parameters can effectively reduce the congestion factor of networks in nonlinearity way. For the case that the load capacity exponential parameter is less than 0, the Load Balancing Distribution (LBD) strategy can reduce the network congestion to the maximum extent. However, for the case that the load capacity exponential parameter is greater than 0, the Load Extreme Distribution (LED) strategy can suppress the network congestion more effectively, while the change of load capacity coefficient parameter will not cause this difference.