具有有效上、下界的双线多站能力铁路训练时刻表编制
Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds
摘要：
训练运行调度是近年来铁路行业的重要课题之一，它对铁路基础设施的效率有着重要的作用。本文讨论了多线路铁路网的调度问题。更具体地说，这里提出了一个通用模型，其中考虑了一组操作和安全要求。该模型处理车站内列车超车并考虑车站容量。目标函数是最小化总行程时间。不幸的是，这个问题是NP难的，实际大小的问题不能在可接受的时间内解决。为了减少处理时间，我们提出了一些启发式规则，减少了二进制变量的数量。这些规则是基于问题的参数，如旅行时间，停留时间和安全时间的车站，并试图消除不可行的区域的解决方案空间。此外，拉格朗日松弛算法模型，以找到一个下限。最后，全面的数值实验德黑兰地铁的情况下报告。结果表明，效率的启发式规则，也拉格朗日松弛法的方式，所有分析的问题，得到最优值。
英文摘要：
Train scheduling is one of the significant issues in the railway industry in recent years since it has an important role in efficacy of railway infrastructure. In this paper, the timetabling problem of a multiple tracked railway network is discussed. More specifically, a general model is presented here in which a set of operational and safety requirements is considered. The model handles the trains overtaking in stations and considers the stations capacity. The objective function is to minimize the total travel time. Unfortunately, the problem is NP-hard and real size problems cannot be solved in an acceptable amount of time. In order to reduce the processing time, we presented some heuristic rules, which reduce the number of binary variables. These rules are based on problem's parameters such as travel time, dwell time and safety time of stations and try to remove the impracticable areas of the solution space. Furthermore, a Lagrangian Relaxation algorithm model is presented in order to find a lower-bound. Finally, comprehensive numerical experiments on the Tehran Metro case are reported. Results show the efficiency of the heuristic rules and also the Lagrangian Relaxation method in a way that for all analyzed problems the optimum value are obtained.
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