铁路枢纽内快运班列车流组织的鲁棒优化研究

Optimal Train Flow Robust Organization for Cargo Express Train in Railway Hub

针对当前生产运营中较少考虑货运站点货物需求不确定性以及客户对货物运到期限的要求,设计双层时空服务网络描述枢纽内快运班列车流组织过程。该网络分为货源层和编组层,货源层中带有方向别的车流选择延迟弧或运输弧在相应时段到达编组层中的编组站。同时考虑编组站办理方向总数和车流组织基本约束,构建了铁路枢纽内快运班列车流组织鲁棒优化模型(CR),使用IBM ILOG Cplex软件对模型进行精确求解。通过算例和大规模测试进行验证分析,结果表明,当ω=0.03时,鲁棒模型的目标函数值比随机优化模型(CS)的目标函数值降低5.10%,发送车数提高5.66%,最长求解时间为82s,鲁棒性强于随机优化模型。虽然确定性模型(CD)在一些情景下可以获得较优的解,但是在需求不确定的条件下,确定性模型目标函数值要差于随机优化模型和鲁棒模型。当枢纽内货运站点数设为50时,时空网络服务弧段数达317,模型的求解时间为1 375.4s,在可以接受的时间范围内。

Considering the uncertainty of transportation demand and timing requirement of transport from the shippers at railway freight stations,a space-time service network at rail hubs is developed to describe the organization process of express train flows.The network consists of a cargo layer and a marshaling layer.The train flows in the cargo layer will follow either the delay arc or transport arc to arrive at the marshaling yard in the marshaling layer.Taking account of both departure directions of the marshaling yard and other basic constraints related to marshalling operation,a robust optimization model（CR）for train organization of cargo express train at rail hubs is formulated and solved by using the IBM ILOG Cplex software.A case study and a numerical test are applied to verify the effectiveness of this model.According to the study results,Whenω=0.03,compared to that of the random optimization model（CS）,the objective function value of the proposed robust optimization model（CR）reduces by 5.10%,departure train number increase the by 5.66%,and the longest time for obtaining the solution is 82 s,which show a higher robustness than the random optimization model（CS）.Although using the deterministic model（CD）for train organization can receive better solutions in some cases,but its optimized value of objective function is lower in the case of uncertain transport demand.When the number of freight stations in railway hubs is 50 and the number of service arcs of the network is 317,the computing time for the solutions of the model is 1 375.4s,which is found to be acceptable.