双层规划在城市交通领域研究与应用的系统综述

doi:10.15960/j.cnki.issn.1007-6093.2023.02.001

摘要/Abstract

摘要：

双层规划是约束条件中含有优化问题，具有上下双层递阶结构的非凸优化问题，是典型的NP-Hard问题。本文系统性综述双层规划在城市交通领域的研究与应用，聚焦交通网络设计和OD(origin destination)反推调整两类问题。首先，利用文献计量法概述国内外研究主题与演变历程。其次，以开创性研究为线索溯源首次系统综述、首篇博士论文、首个TR-B专题和首篇中文综述关键研究。再次，梳理道路、公交、多模式网络设计问题与静态、动态OD反推问题的近期发展。从次，总结通用求解方法，讨论求解方法发展动向，阐述双层规划与平衡约束数学规划的关系。最后，指出未来发展的机遇与挑战：智慧交通探索揭示、建模架构模式优选和计算平台互动共享。

关键词: 双层规划, 网络设计问题, OD反推调整, 用户均衡, 平衡约束数学规划, 模型算法

Abstract:

Bi-level programming is a typical NP-Hard problem. It is a nonconvex optimization problem with upper and lower hierarchical structure and contains optimization problems in constraint conditions. This paper systematically reviews the researches and applications of bi-level programming in the context of urban transport, focusing on transportation network design problem and OD estimation/adjustment problem. Firstly, the domestic and international research topics and evolution progress are summarized by bibliometrics. Secondly, it takes pioneering research as the clue to look back upon important researches, the first systematic review paper, the first doctoral dissertation, the first Transportation Research Part-B's issue, and the first review paper in Chinese are introduced. Thirdly, the recent development of network design problems including road, transit and multi-modal, and the static and dynamic OD estimation problems are expounded. Fourthly, some general solutions are concluded, and the trends of solutions are discussed, the relationship between bi-level programming and MPEC is expressed. Finally, it points out three opportunities and challenges in the future should be addressed, including exploring and revealing of smart transportation, the optimization of modeling architecture, and building a computing platform to share and interact.

Key words: bi-level programming, network design problem, OD estimation/adjust -ment, user equilibrium, MPEC, model and algorithm

中图分类号:

O221.2

魏贺, 刘昊飞, 许丹丹, 韩雪华, 王良, 张晓东. 双层规划在城市交通领域研究与应用的系统综述[J]. 运筹学学报, 2023, 27(2): 1-26.

He WEI, Haofei LIU, Dandan XU, Xuehua HAN, Liang WANG, Xiaodong ZHANG. A systematic review of researches and applications of bi-level programming in the context of urban transport[J]. Operations Research Transactions, 2023, 27(2): 1-26.

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