城市轨道交通乘务计划优化编制研究综述

doi:10.13229/j.cnki.jdxbgxb.20231138

摘要/Abstract

摘要：

乘务计划是城市轨道交通运营计划的重要组成部分，其优化编制方法已成为交通运输领域的研究热点。为推动城市轨道交通乘务计划优化编制的研究进程，本文对国内外相关文献进行了全面梳理。针对数学模型，系统总结了基于“集合关系”和基于“网络构建”这两类典型的建模方法；针对求解算法，分为传统整数规划算法、基于列生成的数学规划方法、图与网络相关算法和智能启发式算法进行了详细评述。最后，针对现存不足和挑战，提出该领域未来的研究方向。

关键词: 城市轨道交通, 乘务计划, 数学模型, 优化算法

Abstract:

The crew schedule is a crucial component of urban rail transit operation plannings， and its optimization methods have become a hot research topic in the field of transportation. To promote the research progress in crew planning optimization for urban rail transit， reviewing relevant literatures from both domestic and international sources. Regarding mathematical models， systematically summarizing two typical modeling approaches which are respectively based on "set relations" and "network graph construction"； Concerning solution algorithms， provideing detailed assessments of traditional integer programming algorithm， mathematical programming method based on column generation， graph and network-related algorithm， and intelligent heuristic algorithm. Finally， addressing current research deficiencies and challenges to propose future research directions.

Key words: urban rail transit, crew planning problem, mathematical model, optimization algorithm

中图分类号:

U292.8

户佐安,周姝,张宇昂. 城市轨道交通乘务计划优化编制研究综述[J]. 吉林大学学报(工学版), 2025, 55(2): 401-418.

Zuo-an HU,Shu ZHOU,Yu-ang ZHANG. Review on crew planning optimization for urban rail transit[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 401-418.

图/表 7

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对比特点		普速铁路	高速铁路	城市轨道交通（以地铁为例）
线路条件	乘务基地	两端和中间	线路两端	线路两端
线路条件	站间距离	很长	较长	很短
运营情况	时刻表安排	较灵活	固定	固定
	运行交路	长	较长	短
	开行频率	较低	较高	高
乘务管理	人员类型	工种多	工种多	主要为司机
	乘务片段长度	长	较长	短
	班次所含片段数	少	较少	多
	冗余时间	很长	较长	较短
	跨夜值乘	常有	较少	一般没有

文献	计划阶段	建模方法	求解算法					文献	计划阶段	建模方法	求解算法
文献	计划阶段	建模方法	IPM	GNA	H	CG	Other	文献	计划阶段	建模方法	IPM	GNA	H	CG	Other
［33］	CS	NFP		√				［32］	CR	NFP	√
［34］	CS	SPP			√			［35］	CS	other			√
［36］	CS	SPP		√				［37］	CS	-			√
［38］	CS	SPP		√				［39］	CS	SCP			√
［40］	CS	SCP				√		［41］	CS	SCP			√
［42］	CS	SPP				√		［43］	CS	SCP				√
［44］	CR	SPP				√		［45］	CS	SCP			√
［46］	CR	SPP			√			［47］	CS	SCP			√
［48］	CR	SPP			√			［49］	CS	NFP				√
［50］	CS	SPP， NFP						［51］	CS	SPP			√
［52］	CS⊕CR	SCP， NFP	√			√		［53］	CS⊕CR	NFP			√
［54］	CS	SCP， NFP	√			√		［55］	CS⊕CR	NFP		√		√
［56］	CS	other			√		CP	［57］	CS	other			√
［58］	CS	SPP				√		［59］	CS	NFP	√
［60］	CS	SPP			√			［61］	CS	SCP，NFP		√		√
［62］	CS	other		√				［63］	CS⊕VS	SCP，SPP， NFP	√			√
［64］	CS	NFP			√			［65］	CS	SCP，NFP	√		√	√
［66］	CR	SPP， NFP	√					［67］	CS∪CR	NFP			√		ADMM
［30］	CS	NFP			√			［9］	CS⊕CR	NFP					ADMM
［31］	CS	SPP， other		√	√

文献	智能启发式算法（H）					（最大）求解规模	算法特点
文献	GA	TS	PSO	ACO	Other	（最大）求解规模	算法特点
［35］	√					814个乘务片段	基于贪婪机制的交叉和变异算子；染色体分为表达和未表达两部分
［41］	√					830个乘务片段	染色体长度可自适应改变
［38］	√					求解得到20个乘务班次	遗传算法中嵌套双向匹配法
［60］	√	√				686个乘务作业段	遗传禁忌混合搜索算法
［31］		√				高峰时段开行列车77列非高峰时段开行列车41列	夜班编制采用二分匹配算法；日班编制采用禁忌搜索算法
［34］		√				138个乘务作业段（日班）	夜班编制采用Hungarian算法日班编制采用禁忌搜索算法
［37］		√			EM；GM	900个乘务片段	对比了3种启发式算法
［46］		√				每日早班10个，白班15个，夜班10个轮转周期：1周，可用司机：48名	初始方案通过贪婪算法生成
［36］			√			9列车底 182个乘务片段	下层模型采用改进Dijkstra算法；上层模型采用离散粒子群算法
［48］			√		SE	每日100个值乘班次，20个休息班次轮转模式：六班五运转	粒子群与模拟进化的混合算法
［67］			√			686个乘务作业段轮转周期：7天轮转模式：四班三运转	排班阶段采用基于ADMM的对偶分解算法；轮班阶段采用改进粒子群算法
［64］				√		248个乘务作业段	将问题转换为类TSP问题
［51］				√		724个乘务作业段	基于蚁群路径选择策略的优化算法
［39］					√	830个乘务片段	考虑中国就餐和休息制度，基于启发式思想的班次生成与选择方式
［53］					LR	2030个乘务作业段（1周）	拉格朗日松弛启发式算法
［45］					GM	830个乘务片段	灰色关联分析融入可变迭代贪婪算法
［59］					F&R	日开行车次超300趟	进行聚类操作简化模型

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