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针对铁路列车运行图优化模型精确解求解困难的问题,结合累积流变量模型的特点,提出基于累积流变量的列车运行图优化0-1整数规划模型,设计拉格朗日松弛求解算法,将复杂的列车组合优化问题转化为单列车的最短路径问题集合,从而降低求解难度。针对拉格朗日松弛子问题,设计具有状态空间的时空网络,实现车站作业方式的差异化处理。模型与算法以武广高铁为背景进行验证和分析。
In view of the difficulty of solving the exact solution of the optimization model of railway train operation diagram and combining the characteristics of the cumulative flow model, a 0-1 integer programming model of train operation diagram based on cumulative flow variables is proposed. Lagrange relaxation algorithm is designed, Of train combinatorial optimization problems into a single train shortest path problem set, thereby reducing the difficulty of solving. Aiming at the Lagrange slack issue, a space-time network with state space is designed to realize the differentiated processing of station operating modes. The model and algorithm are validated and analyzed in the context of Wuhan-Guangzhou high-speed rail.