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列车运行过程中的运行干扰不可避免,提高鲁棒性是列车运行图优化的内在要求。可恢复鲁棒性优化是求解不确定性规划问题的一种新方法,结合问题在实际情况下的恢复算法,采用鲁棒算法生成的鲁棒解具有更强的适用性。本文将列车运行图的可恢复鲁棒性优化过程分为两阶段:第一阶段提出列车运行图优化模型(TP),评估不考虑鲁棒性要求下的最小列车旅行时间;基于TP模型提供的列车运行顺序,第二阶段提出两种采用不同恢复算法的可恢复鲁棒性优化模型(RRT-1和RRT-2),并给出模型转换方法,分析鲁棒算法的条件和鲁棒性代价。其中,RRT-1模型结合优化和评估两种过程,恢复算法基于列车晚点管理规则,偏重于减小列车晚点时间;RRT-2模型则主要考虑事件-活动网络图的结构,恢复算法基于恢复容量限制,恢复容量在一定程度上体现列车晚点传播范围。基于案例研究,总结两种可恢复鲁棒性优化模型的主要特点和不足。
The operation disturbance in the process of train operation is unavoidable. Improving the robustness is an inherent requirement of train operation diagram optimization. Recoverable robust optimization is a new method to solve the uncertain programming problem. Combined with the recovery algorithm of the problem under practical conditions, the robust solution generated by the robust algorithm has more applicability. In this paper, the process of recoverable robust optimization of train operation diagram is divided into two stages: the first stage proposes the train operation diagram optimization model (TP), the evaluation does not consider the minimum train travel time under the requirement of robustness; based on the TP model In the second phase, two kinds of recoverable robust optimization models (RRT-1 and RRT-2) with different recovery algorithms are proposed. The model transformation methods are given, and the conditions and the robustness of the robust algorithm are analyzed . Among them, the RRT-1 model combines optimization and evaluation. The recovery algorithm is based on the late train management rules, with emphasis on reducing the train delay time. The RRT-2 model mainly considers the structure of the event-activity network diagram. The recovery algorithm is based on the recovery capacity Restrictions, recovery capacity to a certain extent reflect the scope of train delayed transmission. Based on case studies, the main features and shortcomings of the two recoverable robust optimization models are summarized.