分车模式下地铁客货协同运输与时刻表联合优化
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华东交通大学交通运输工程学院,江西 南昌 330013

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通讯作者:

邸振(1979—),男,副教授,博士,硕士生导师,研究方向为交通运输系统优化。E-mail:3126@ecjtu.edu.cn。

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U121

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国家自然科学基金项目(72161010)


Joint Optimization of Metro Passenger-Freight Cotransportation and Timetable Under Train-Dedicated Mode
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School of Transportation Engineering, East China Jiaotong University, Nanchang 330013 , China

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    摘要:

    目的】为了研究分车模式下地铁客货协同运输与时刻表联合优化问题,对列车、需求与潜在的时空轨迹之间的关系进行了重构,从而构建了整数线性规划模型,替代了传统的非线性规划模型。【方法】该模型的目标函数包含了货运列车的运用数量、客运需求的等待时间以及货运需求的滞留时间,所需满足的限制条件主要包括客货需求的流平衡约束、客货列车的容量约束、客运需求的最长等待时间约束以及货运需求的最长滞留时间约束等。通过松弛表示客货流量分配的整型变量,原始模型可等价地转化为混合整数规划模型,这可提高模型的求解效率。以北京地铁原八通线为场景构造一系列算例,并利用商业求解器Gurobi对其进行求解。【结果】实验结果表明:相较于原始模型,Gurobi能够更快地求解松弛模型;相较于原时刻表, 优化后的时刻表能够减少系统的广义成本。【结论】所提出的方法不仅能够满足分车模式下的地铁客货协同运输需求,而且可以有效控制分车模式下的地铁货运对客运需求的影响。

    Abstract:

    Objective】In order to study the joint optimization problem of metro passenger-freight cotransportation and timetable under the train-dedicated mode, the relationships between trains, demands and potential spacetime trajectories are reconstructed and an integer linear programming model is formulated instead of the traditional nonlinear programming model.【Method】The objective function of this model includes the number of freight trains in use, the waiting time of passenger demand as well as the detention time of freight demand. The restriction conditions to be met mainly include the flow balance constraints of passenger and freight demands, the capacity constraints of passenger and freight trains, the longest waiting time constraint of passenger demand and the longest detention time constraint of freight demand. By relaxing the integer-type variables of passenger and freight flows, the primal model could be equitably transformed into a mixed integer programming model, which can improve the solving efficiency of the model. Taking the original Batong Line of Beijing Metro as the background information, a series of numerical examples were designed and then solved by commercial solver Gurobi.【Result】The experimental results show that Gurobi can solve the relaxation model faster than the primal model; and compared with the original timetable, the optimized timetable can reduce the generalized cost.【Conclusion】The proposed method can not only meet the needs of subway passenger and freight cotransportation in the split mode, but also effectively control the influence of metro freight on passenger demand under this mode.

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邸振,左晗锜,罗俊.分车模式下地铁客货协同运输与时刻表联合优化[J].华东交通大学学报,2024,41(6):81-89.
Di Zhen, Zuo Hanqi, Luo Jun. Joint Optimization of Metro Passenger-Freight Cotransportation and Timetable Under Train-Dedicated Mode[J]. JOURNAL OF EAST CHINA JIAOTONG UNIVERSTTY,2024,41(6):81-89

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  • 收稿日期:2024-05-31
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  • 在线发布日期: 2025-02-10
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