多模式枢纽网络中高铁与航空均衡优化模型

Equilibrium optimization model of high-speed rail and airline in multi-modal hub network

在高铁与航空共存的多模式客运枢纽网络中,考虑机场容量限制,通过多项式Logit模型,模拟行者对交通方式、交通方式运营商和出行路线的选择行为,建立竞争情形下运营商各自利润最大化的Nash均衡优化模型。利用约束优化的KKT条件,设计基于非线性互补问题的求解算法,并通过实例验证模型的合理性和算法的有效性。研究结果表明:机场容量的变化对运营商的决策和出行者的出行选择有影响;通过关闭或开启某些航段,可使航空运营商的利润变大,或使得社会效益增加;此外,通过求解模型,得到机场容量扩容时带来的边际社会效益,可以为机场扩容提供一定的决策参考。

In view of airport capacity constraint in a multi-modal transportation hub network, a multinomial Logit model was used to describe the travelers＇ selection about the travel modes, travel operators and the travel routes. A Nash equilibrium optimization model was presented for both high-speed rail（HSR） and airline operators to maximize their individual profits in a competitive environment. Utilizing the KKT condition of constraint optimization, an algorithm was designed based on the nonlinear complementary problem, and an empirical network was used to illustrate the applicability of the model and the rationality of the algorithm. The results show that the change of airport capacity has impact on the operators＇ operative strategy and the travelers＇ travel selection. Closing or opening certain flight segments can increase the profit of air carriers or make the social welfare rise. Furthermore, the marginal social welfare gain of airport capacity expansion can be calculated by the model, which can potentially serve as a benchmark indicator for airport expansion.