地铁线路双向中断时长不确定下的列车运行调整

Train Rescheduling under Bi-Directional Interruption with Uncertain Duration of a Metro Line

针对地铁线路双向运营中断时长不确定的情况,提出以到发时刻偏差、区间车次取消数和运行间隔均匀性为目标函数的列车运行调整和车底周转一体化模型;为求解这一混合整数非线性规划模型,在模型线性化的基础上,采用2阶段法和滚动时域优化算法,按乐观预测和悲观预测2种策略,实现列车运行计划的滚动优化调整和快速求解;为证明该模型及求解方法应对运营中断持续时长不确定的能力,基于北京地铁7号线某工作日下的实际运营数据构建算例进行验证。结果表明:模型及求解方法能够在中断时长不确定的情况下生成接近最优解的列车运行调整计划;提出的求解方法有效提高了计算效率,算例中断30 min悲观预测的求解时间为157 s,为直接求解法的15.39%;2种策略均在预测值与实际值更接近时,得到更接近最优解的运行调整结果;悲观预测策略更适用于双向中断时长不确定且可能有多个预测时长时,而乐观预测策略更适用于中断时长信息较为准确时。

In view of the condition about the bi-directional interruption with uncertain duration of a metro line,an integrated model of train rescheduling and rolling stock circulation is proposed,which takes the deviation of arrival and departure time,the number of cancellations of interval train number and the uniformity of operation interval as objective functions.In order to solve this mixed integer nonlinear programming(MINLP) model,the two-stage approach and the rolling horizon optimization algorithm are adopted based on the linearization of the model.Moreover,on the basis of optimistic prediction and pessimistic prediction strategies,the rolling optimization rescheduling and rapid solution of train operation plan are realized.In order to prove the ability of the model and solution method to cope with the uncertain duration of operation interruption,an example is constructed based on the actual operation data of Beijing Subway Line 7 in a working day to verify it.The results show that the model and solution method can generate the train rescheduling plans close to the optimal solution under the condition of uncertain interruption duration.The proposed solution method effectively improves the computational efficiency,and the solution time of the pessimistic prediction is 157 s when the example is interrupted for 30 minutes,which is only 15.39% of that of the direct solution method.In addition,when the predicted duration is closer to the actual duration,the rescheduling results of the two strategies are closer to the optimal solution.Furthermore,the pessimistic prediction strategy is more suitable for the bi-directional interruption with uncertain duration and may have multiple predication duration,while the optimistic prediction strategy is more suitable for the interruption that has relatively accurate duration information.