中文摘要：

为尽可能减少由于自然灾害导致铁路运输受阻甚至中断情况下受影响的列车数，提出了对现有列车运行方案以抗毁性优化为目标的量化分析方法。首先基于当前列车运行方案建立列车运行网络模型，该模型以实际铁路站点为节点，以实际铁路线为边，以每条边开行的列车数量为边权重；随后提出了一个称之为度权效应的抗毁性评价指标。并以该评价指标为目标函数，使用改进粒子群算法对网络权重进行优化。仿真结果得出了优化前后列车运行网络的抗毁性评价值分别为0．8881和0．9063，表明可通过量化分析方法来刻画列车运行网络的抗毁性能。

英文摘要：

In order to reduce the number of the train affected by the railway breakdown because of disasters as possible as, this paper proposed a quantitative analysis method on invulnerability optimization for train scheduling scheme. Firstly, proposed train scheduling network model based on present train scheduling scheme, in which the real railway station was described as a vertex, and the railway line was described as an edge, designed the number of trains on the railway lines as the weight of edge. Secondly proposed a new indicator of invulnerability measurement and regarded as the object function to be optimized by using improved particle swarm optimization （PSO） algorithm, and the invulnerability measurement value calculated results of the o- riginal scheme and the optimal scheme is 0. 888 1 and O. 906 3 respectively which show the proportionality of the optimal scheme is better than original scheme. Simulation resuhs show that the quantitative analysis method can be used to measure the invulnerability of train scheduling networks.