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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (2): 279-293.doi: 10.3969/j.issn.1005-3085.2024.02.006

• • 上一篇    下一篇

拥挤网络下OD需求重构的双层规划模型

李高西1,2,  任  艺1   

  1. 1. 重庆工商大学数学与统计学院，重庆  400067;
    2. 经济社会应用统计重庆市重点实验室，重庆  400067
  • 收稿日期:2022-12-27 接受日期:2023-09-28 出版日期:2024-04-15 发布日期:2024-06-15
  • 通讯作者: 任艺 E-mail: ry991002@163.com
  • 基金资助:
    国家自然科学基金 (11901068)；国家应用数学中心项目 (ncamc2021-msxm01)；重庆市自然科学基金面上项目(CSTB2022NSCQ-MSX0606)；重庆市研究生导师团队建设项目 (yds223010).

A Bi-level Programming Model for OD Demand Reconstruction under Congested Network

LI Gaoxi1,2,  REN Yi1   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067;
    2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067
  • Received:2022-12-27 Accepted:2023-09-28 Online:2024-04-15 Published:2024-06-15
  • Contact: Y. Ren. E-mail address: ry991002@163.com
  • Supported by:
    The National Natural Science Foundation of China (11901068); the National Center for Applied Mathematics (ncamc2021-msxm01); the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX0606); the Graduate Tutor Team Construction Project of Chongqing (yds223010).

摘要：

提出了在拥挤网络下利用密度作为观测变量对 Origin-Destination (OD) 需求进行重构的双层规划模型。上层目标为极小化各个估计值与观测值之间的误差，下层为用户均衡模型。采用 KKT 条件法将该双层规划转化为相对容易求解的均衡约束规划模型，再用 Scholtes 松弛化方法求解转化后模型。数值实验结果表明，在拥挤网络下的 OD 重构问题中，利用密度作为观测变量优于流量作为观测变量，同时在求解方法上，利用 KKT 条件转换为单层模型的求解方法优于上下层交替求解法。

关键词: OD需求重构, 双层规划模型, KKT条件法, 路段密度, 路径密度

Abstract:

A bi-level programming model to reconstruct origin-destination (OD) demand by using density as the observed variable under congested network is proposed. The upper-levels minimize the errors on the estimated values and observed values, and the lower-levels are user equilibrium model. For a bi-level programming model, KKT condition method is adopted, it is transformed into a mathematical program with equilibrium constraints which is easier to solve, and then Scholtes relaxation method is used to solve the transformed model. The numerical results show that, using density as the observed variable is better than using flow in the OD reconstruction problem under congested network. Meanwhile, for solving method of bi-level programming model, the method of transforming KKT condition into single-level is superior to the upper-lower alternate algorithm.

Key words: OD demand reconstruction, bi-level programming model, KKT-approach, link density, route density

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