航空网络航路点布局的多目标优化设计

航路网络中航路点布局问题（CWLP）是航路网络规划的核心。基于此，从航路网络经济性和安全性出发，考虑航路运行成本和潜在冲突系数两个因素，建立航路点布局多目标优化模型，求解时采用动态递变权重系数的蝙蝠算法以保证运行成本和潜在冲突系数能同时获得较优解。最后对北京飞行情报区进行仿真实验，将蝙蝠算法（BA）与其他多目标算法对比，得到4种算法的非支配解，证明多目标蝙蝠算法在求解航路点布局的大规模优化问题上，能够获得更优解。同时，考虑偏好经济性和偏好安全性两种情况选择两组权重，数据显示，与初始网络相比，这两种情况下网络运行成本和冲突系数减少比例分别为9.99%、15.64%以及-3.97%、65.81%。实验结果表明，该方法能够在航路点布局规划上给决策者以多种优化方案。

A Multi-objective Optimization Design for Crossing Waypoints Location in Air Route Network

Crossing waypoints location problem (CWLP) is a core of air route network planning. Based on the situation, a model of multi-objective optimization for CWLP is built, judged by the two factors of total airline cost and total flight conflict coefficient and proceed from the economic and safe aspects of air route network. During the solution, multi-objective bat algorithm based on dynamic gradient weight coefficient is adopted to make sure that the cost and flight conflict coefficient can obtain optimal solutions at the same time. In the end, this paper takes Beijing flight information area as a simulation and gains four kinds of non-dominated solution by comparing BA with other algorithms. The result indicates that the BA in solving the problem can get a more optimal solution. Meanwhile, in consideration of two groups of weight according to the preference of economy or the safety, the data show that the proportional reductions of the network operation cost and conflict coefficient in these two situations respectively are 9.99%, 15.64% and -3.97%, and 65.81%, compared with the initial network. The conclusion of the simulation is that the method can provide various solutions for the decision makers in the design for crossing waypoints location.