基于分布鲁棒优化的城市轨道交通网络末班车衔接研究
作者:
作者单位:

1. 北京交通大学 轨道交通控制与安全国家重点实验室, 北京 100044;2. 北京交通大学 交通运输学院, 北京 100044;3.北京交通大学 轨道交通控制与安全国家重点实验室, 北京 100044;4.1. 北京交通大学 交通运输学院, 北京 100044;5.2. 北京交通大学 综合交通运输大数据应用技术交通运输行业重点实验室, 北京 100044

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中图分类号:

U231+92

基金项目:

国家杰出青年科学基金(771825004);中央高校基本科研业务费专项资金资助项目 (2020JBM031);北京交通大学基本科研业务费研究生创新项目 (2021YJS203);轨道交通控制与安全国家重点实验室(北京交通大学)开放课题(RCS2019K002)


Distributionally robust optimization for the last-train connection planning problem in urban rail transit networks
Author:
Affiliation:

1.State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China 2. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China;2.State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China 2. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China;3.1.School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China 2.Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China

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    摘要:

    随着我国城市轨道交通网络规模快速扩张,线路间协调配合的高度复杂性给城市轨道交通的运营组织与管理带来极大挑战。针对客流需求及其分布双重不确定条件下的城市轨道交通网络末班车衔接优化问题,提出一种分布鲁棒机会约束规划模型,即在给定容忍度下最小化最坏条件下换乘失败客流量。通过分析分布鲁棒优化模型与传统鲁棒优化模型之间的联系,证明该模型为鲁棒优化模型的推广形式。基于有限的期望和方差信息构造高斯分布非精确集,采用对偶理论将原模型转化为可利用CPLEX 求解的混合整数二阶锥规划形式,并通过数值试验验证所提模型的有效性。算例结果表明,分布鲁棒模型可利用CPLEX快速求得精确解;相比鲁棒模型可有效避免产生过于保守的优化结果;相比随机模型可有效降低最坏条件下换乘失败客流量,具有较强的鲁棒性。

    Abstract:

    With the rapid development of urban rail transit network in China, the number of lines and passenger demand are increasing sharply day by day. The coordination between lines brings great challenges to the operation due to its high complexity. In order to minimize the unsuccessful transfer-passenger flow transfer of last-train under worse case with given level of tolerance, a distributionally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand, in which the probability distribution of uncertain parameters is only partially known. By analyzing the relationship between the distributionally robust optimization model and the traditional robust optimization model, it is proved that the former is an extension of the latter. Furthermore, the original model is reformulated into a second-order mixed-integer conic programming form which can be solved by CPLEX under the Gaussian perturbations ambiguity set. The results of a numerical case indicate that the proposed model can be solved to optimality quickly by CPLEX, and can effectively avoid over-conservative optimization compared to the classic robust optimization model and reduce unsuccessful transfer-passenger flow in the worse case compared with the traditional stochastic programming model, which exhibits more robust performance.

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  • 收稿日期:2021-06-30
  • 最后修改日期:2021-09-22
  • 录用日期:2021-09-28
  • 在线发布日期: 2021-10-01
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