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铁路网车流分配需要解决的关键问题是如何确定车流路径,而同一终点的车流具有合而不分的特点,即呈现“树状结构”径路。以多商品网络流理论为基础,构建铁路网车流分配与树状径路综合问题的混合整数规划模型,优化结果可得到铁路网中流量分布情况及符合“树状结构”的车流走行路径。设计拉格朗日松弛算法求解模型,通过松弛掉模型中弧段能力约束进而将原问题分解为求解多个单支车流分配子问题,采用传统次梯度优化算法求解对偶问题;上界计算方面设计基于车流排序的可行解求解方法。算例表明:该算法可有效求解模型,实现车流径路“树状结构”要求;求解效果和计算空间方面优于商业软件ILOG CPLEX。
The key problem to be solved in the distribution of railway network traffic is how to determine the traffic flow path, while the traffic flow of the same destination has the same characteristics, that is, the “tree structure” path is presented. Based on the theory of multi-commodity network flow, a mixed integer programming model of traffic flow distribution and tree track synthesis in railway network is constructed. The optimization results can get the flow distribution in the railway network and the traffic flow path in line with the “tree structure”. The Lagrangian relaxation algorithm is designed to solve the model. The original problem is decomposed to solve the multiple subcarrier allocation problem by loosening the arc capacity constraint in the model. The traditional sub-optimal gradient optimization algorithm is used to solve the dual problem. The upper bound design A feasible solution method based on traffic flow ordering. The example shows that this algorithm can effectively solve the model and achieve the requirements of traffic flow routing and tree structure. It is better than the commercial software ILOG CPLEX for solving the effect and computing space.