北京交通大学学报2026，Vol.50Issue(3)：22-30,9.DOI:10.11860/j.issn.1673-0291.20250128
可售无座票条件下的高铁列车开行方案优化
Optimization of high-speed train operation plan considering the availability of unreserved tickets
摘要
Abstract
To improve the adaptability of high-speed train operation plans to daily passenger flows,this paper proposes an optimization method for high-speed train operation planning that considers the avail-ability of unreserved tickets.Recognizing that not all passengers are willing to accept unreserved tick-ets,it is first necessary to identify the target demographic for this ticket type.A Logit model is estab-lished to analyze passenger acceptance of unreserved tickets when reserved tickets are sold out.Simul-taneously,Origin-Destination(OD)passengers are categorized into two groups:those who exclusively accept reserved tickets and those who are willing to accept unreserved tickets.Passenger flow is allo-cated separately for these two groups during the subsequent solution process.Second,an optimization model is constructed with the dual objectives of minimizing passengers'generalized travel time and rail-way operational costs.This is subject to constraints ensuring that the quantities of both ticket types meet diverse travel demands and that the ticket allo-cation in each section complies with train capacity limits.To account for generalized travel time,a time penalty coefficient is applied to the travel time of passengers purchasing unreserved tickets;this penalization aims to minimize unreserved ticket pur-chases,thereby safeguarding passenger comfort while satisfying the load factor requirement.Given the multitude of variables and the large scale of the decision-making model,a hybrid approach combining a Genetic Algorithm(GA)and the Gurobi solver is developed.The Gurobi solver is utilized to separately allocate passenger flow for reserved and unreserved ticket holders,simultaneously determining the ticket allocation scheme and the objective function values.These results then serve as fitness values for the subsequent GA operations.Finally,a case study based on the Beijing-Shanghai high-speed rail-way is conducted.The results demonstrate that,compared to operation plans that do not offer unre-served tickets,the proposed plan reduces total passenger travel time by 3.15%and railway operation costs by 8.71%.Furthermore,the ticket allocation scheme aligns closely with passenger demand,veri-fying the effectiveness of the proposed model and algorithm.关键词
高速铁路/列车开行方案/无座票/Logit模型/遗传算法Key words
high-speed railway/train operation plan/unreserved tickets/Logit model/genetic algorithm分类
交通工程引用本文复制引用
查伟雄,胡佳伟,李剑,石俊刚..可售无座票条件下的高铁列车开行方案优化[J].北京交通大学学报,2026,50(3):22-30,9.基金项目
国家自然科学基金(72161010) National Natural Science Foundation of China(72161010) （72161010）
