地铁网络节能时刻表的两步线性规划模型
A Two-Step Linear Programming Model for Energy-Efficient Timetables in Metro Railway Networks
摘要：
本文提出了一种新的两步线性最优化模型来计算地铁网络的节能时刻表。所得到的时刻表最小化所有列车消耗的总能量，并最大化制动列车产生的再生能量的利用率，受到铁路网络的约束。与其他现有的模型，这是NP难的，我们的模型是计算上最容易处理的一个线性规划。我们将我们的最优化模型应用于上海地铁8号线PES 2-SFM 2的不同服务实例，该服务跨越了一天（18小时）的完整服务期，具有数千个活动列车。对于每一个实例，我们的模型都能非常快速地找到一个最佳时间表（最大运行时间小于小于13 s），有效能耗显著降低（最坏情况为19.27%）。基于该模型的代码已与泰雷兹公司的工业时间表编译器泰雷兹时间表编译器集成，泰雷兹公司拥有全球最大的基于通信的训练控制系统安装基础。
英文摘要：
In this paper we propose a novel two-step linear optimization model to calculate energy-efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and maximizes the utilization of regenerative energy produced by braking trains, subject to the constraints in the railway network. In contrast to other existing models, which are NP-hard, our model is computationally the most tractable one being a linear program. We apply our optimization model to different instances of service PES2-SFM2 of line 8 of Shanghai Metro network spanning a full service period of one day (18 hours) with thousands of active trains. For every instance, our model finds an optimal timetable very quickly (largest runtime being less than 13s) with significant reduction in effective energy consumption (the worst case being 19.27%). Code based on the model has been integrated with Thales Timetable Compiler - the industrial timetable compiler of Thales Inc that has the largest installed base of communication-based train control systems worldwide.
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