高速旅客列车开行方案的鲁棒优化模型

于预测客流与实际需求存在一定偏差，以单一预测值为基础的开行方案不 能与实际需求相匹配.将客流需求限定于预测均值与峰值所构成的区间，利用鲁棒理论建 立基于客流需求波动的开行方案鲁棒优化模型，并转化为线性混合整数规划模型.根据模 型特点，设计拉格朗日松弛的求解算法，通过松弛耦合约束，将原问题分解成更为简单的 子问题.以目标值增加率（相对于客流确定模型）变化的首个“拐点”对应的解为鲁棒解.最 后对武广高铁测算，在有效时间内获得了高质量的解，平均误差率为5.04%.结果表明,鲁 棒解能较好地平衡客流需求波动与开行方案计划.

The Robust Model for Line Planning Problems of High Speed Passenger Train

The estimated demand data are usually unreliable due to the actual demand, and train line planning based on estimated demand data might not match the actual demand. Assumes that each actual demand lies in an interval specified by mean value and peak value, a robust optimization model is built and translated into a linear mixed integer programming model. And the Lagrangian relaxation algorithm is developed according to the model structure. Then the original problem is decomposed into much simpler subproblems through relaxing the coupling constraints. According to the increment rate of the objective value (corresponding the model for determined passenger demand), the solution of its inflection points is the robust solution. Finally, the model is tested on the Wuhan- Guangzhou high speed railway in China, and a good solution can be achieved with an average gap of 5.04%. The result shows that the robust solution can balance the passenger demand fluctuation and line planning well.