基于时变小世界模型的航空网优化评估

航空网的优化设计对于优化资源配置、改善航运效率、提高航空公司竞争力等具有重要的现实意义.而航线结构与航班计划密不可分.本文首先讨论了航空网的时变特征,揭示了航班频率与航线距离之间的时空耦合关联.通过构建时变空间小世界模型,揭示了时变条件下网络的最优结构指数与时空耦合强度的惟一约束关系.以运行总成本最小化为主要优化目标,提出了一种可以快速评估航线结构优化情况的方法.该方法能根据网络客流分布情况快速推算出航线网络的最优拓扑及相应的航班频率分布.并用2001—2010年中国航空网络数据对此方案进行实证研究,发现预测与实际数据基本符合,并逐渐趋于稳定.这一方法能把复杂问题简单化,对各个航空公司每年的航线航班调整是否合理,现有的航空网络是否在逐步优化做出动态评估.分析航空网络的发展趋势,从而对未来的优化提供建议.

An assessment method for aviation network optimization based on time-varying small world model

The optimization of aviation networks is of great significance for optimizing the allocation of resources, improving transport efficiency, and enhancing the competitiveness among airline companies. There have been a lot of researches which combine the theory of complex network and the actual situations to analyze the air transportation system. The present work provides a certain theoretical basis for the plan of airline schedule. Firstly, we regard an airport as a node, flight frequency as a link weight, and build a heterogeneous network. Through empirical analysis, we find that the aviation network has small-world and scale-free properties. In addition, considering that the instant network consists of current flights changing over time, time-varying is another important characteristic of aviation network. Also, a spatiotemporal correspondence between the flight frequency and route geometric distance is demonstrated to be τ_ij~r_ij^-C. Secondly, by Monte Carlo simulation, we know that the time-ordered topologies influence the optimal navigation structure and make it different from those from traditional static models. Specially, we can obtain a unique restriction between C and optimal structural exponent α, which unveils a new optimization principle in route design and schedule arrangement. Applying these features to the cost-minimized optimization model, a method to evaluate the optimization of network is proposed, by which we can directly predict the overall optimal distribution of flight distances and corresponding flight frequencies only based on the information about the passenger flow assignment. Thirdly, China aviation network data from 2001 to 2010 are used for empirical study. It is found that the predictions consist with the actual data. Compared with traditional optimization methods, it can simplify the computational complexity, and therefore it takes full advantage of the structural convenience and provides a new perspective for the overall scheduling of air transportation system. In this case, companies are able to estimate route adjustments easily to see whether they are reasonable and analyze the development trend of network to provide suggestions for future optimization.