基于鲁棒接续时间的铁路空车调运优化

Optimization on Railway Empty Wagon Allocation Based on Robust Connecting Time

空车调运是铁路运输的关键环节,其方案具有一定的鲁棒性,可以避免车站技术作业时间以及站间旅行时间等不确定因素对调运方案实施的影响.基于固定的车站技术作业时间和站间旅行时间,提出了空车供应站到达列车与发出列车、空车供应站发出列车与空车需求站发出列车间的空车接续时间关系判别方法.以空车调运收益最大化为目标,建立了确定情形下考虑车种替代的空车调运模型,在此基础上,引入波动率描述车站技术作业时间和站间旅行时间的不确定性,并通过设置波动下限调整模型的鲁棒性,建立了不确定情形下的空车调运鲁棒优化模型;结合模型性质,以车流关系变化为依据,设计了鲁棒优化模型的快速求解算法,将非线性优化问题转化为易求解的鲁棒等价模型.结果表明:求得的空车调运方案可以得出列车间的空车配流和车种替代情况,不确定因素的波动率和波动下限会影响空车调运方案的效益值,绝对鲁棒下站间旅行时间、供应站技术作业时间和需求站技术作业时间3个不确定因素导致方案效益值较确定模型分别下降了16.2%、12.1%和28.1%.

Empty wagon allocation is the key link in railway transportation.The scheme of empty wagon allocation should have robustness to avoid the influence of uncertain factors.Based on the fixed technical operation time of stations and travel time between stations,the connection time relationships between arrival and departure trainsin supply stations,and between departure trainsin supply stations and in demand stations are identified.To maximize the revenue of empty wagon allocation,an empty wagon allocation model involving vehicle type substitution is established.On this basis,the fluctuation rate is introduced to describe the uncertainty due to the technical operation time of stations and travel time between stations,and the lower limit of fluctuation is set to adjust the model robustness.A robust optimization model is established for empty wagon allocation under uncertain conditions.Combined with model properties,a fast algorithm for solving the robust optimization model is designed in terms of the change of traffic flow relationship,and the nonlinear problem is transformed into a robust equivalent model that is easy to solve.The results show the empty wagon allocation scheme can accurately obtain the empty wagon flow and vehicle type substitution,and the fluctuation rate and lower limit of uncertain factors affect the revenue of the scheme.Under absolute robustness,compared with the certain model,the revenue of the scheme is decreased by 16.2%,12.1%and 28.1%,respectively,due to the uncertain factors,including the travel time between stations,technical operation time of supply stations and technical operation time of demand stations.