考虑双重不确定性的公交时刻表分布鲁棒优化模型
作者:
作者单位:

1. 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 2. 北京交通大学 交通运输学院, 北京 100044

作者简介:

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中图分类号:

U231+92

基金项目:

国家自然科学基金(71961137008;71621001)


A distributionally robust optimization model for the bus timetabling problem under two-fold uncertainties
Author:
Affiliation:

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

Fund Project:

National Natural Science Foundation of China (71961137008;71621001)

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    摘要:

    城市公交系统由于受外界干扰,其需求和运行环境在时空上呈现高度不确定性,给日常运营组织带来了巨大挑战。为增强公交系统对于客流需求和运行场景双重不确定性的应对能力,提出了一种权衡服务质量和服务鲁棒性的单一线路时刻表优化方法。方法采用离散场景集来刻画需求的不确定性,并以滞留人数的期望值和条件风险值最小化为目标,综合考虑多方面约束,构建了多场景耦合的分布鲁棒优化模型(DRO)。为方便模型求解,特运用模糊集来描述场景发生概率的不确定性,再借助对偶理论和常规线性化方法将原模型转化为等价的混合整数线性规划形式。最后通过实际案例对方法进行了分析,结果表明:等价转换得到的线性形式可由GUROBI优化软件快速求得最优解;DRO模型所得时刻表能有效应对双重不确定性;随着不确定性的上升,分布鲁棒优化方法相较于传统随机规划方法体现出更强的鲁棒性,因此可望切实改善公交系统运营的稳定性。

    Abstract:

    The passenger demand and operating environment of the urban public transport system are highly uncertain in time and space due to external disturbance, bringing great challenges to the operating organization. To enhance the ability of the bus system to deal with the impact of the two-fold uncertainties rooted in the passenger demand and the operating scenarios, a distributionally robust optimization method of the single-line bus timetabling problem is proposed in this paper. A discrete set of scenarios is used to describe the uncertain demand, and a multi-scenario distributionally robust optimization model (DRO) is established to minimize the excepted number of detained passengers and conditional-value at risk (CVaR) by taking account of wide-ranging constraints. For the convenience of computing, a fuzzy set of uncertain quantities is constructed with the limited known distribution information. On this basis, the dual theory and conventional linearized approaches are then employed to transform the original model into a mixed-integer linear programming form. Finally, a case study of a bus line in Beijing is conducted to demonstrate the effectiveness and efficiency of the proposed model. The results show that the linear model obtained from equivalent transformation can be quickly solved to optimality by the GUROBI optimization soft package, and the timetable obtained based on the DRO model can effectively deal with the double uncertainties. In addition, compared to the SO model, with the increase of uncertainty, the distributionally robust optimization approach is insensitive to various possible uncertain scenarios, which is expected to improve the stability of the public transport system.

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历史
  • 收稿日期:2021-09-29
  • 最后修改日期:2022-01-13
  • 录用日期:2022-01-28
  • 在线发布日期: 2022-03-01
  • 出版日期: