CAJ | 학술논문

针对编制开行方案涉及因素多、建模及求解困难的特点，结合有容量限制的多商品流网络设计问题，建立确定列车开行对数、开行区段、停站方案及编组形式的多目标整数规划模型，运用权重法将多目标规划转化为单目标规划。鉴于标准的列生成算法难以协同处理网络设计与网络配流问题，设计综合使用列生成与行生成策略的启发式算法确定列车的运行路径及停站方案，采用改进分支策略的分支定界算法求解最终模型。最后，以京沪高铁为例进行验证，在有效时间内获得较高质量解，该解与最优解的误差率为2.13%，且优于京沪高铁实际采用的开行方案。
침대편제개행방안섭급인소다、건모급구해곤난적특점，결합유용량한제적다상품류망락설계문제，건립학정열차개행대수、개행구단、정참방안급편조형식적다목표정수규화모형，운용권중법장다목표규화전화위단목표규화。감우표준적렬생성산법난이협동처리망락설계여망락배류문제，설계종합사용렬생성여행생성책략적계발식산법학정열차적운행로경급정참방안，채용개진분지책략적분지정계산법구해최종모형。최후，이경호고철위례진행험증，재유효시간내획득교고질량해，해해여최우해적오차솔위2.13%，차우우경호고철실제채용적개행방안。
To address the characteristics of line planning problem that involves many factors and is difficult to model and solve,considering multi-commodity network design problem with capacity constraints,a multi-ob-jective integer programming model was formulated to determine the train line planning,including the service frequency,train route,train stopping patterns and train length.Thereafter the model was converted into single objective programming model using the priority method.Due to the fact that the standard column generation algorithm is difficult to handle the network design and network flow assignment problems simultaneously,an heuristic algorithm with comprehensive use of column and row generation approaches was designed to deter-mine the train route and train stopping patterns.Then the branch and bound algorithm with an improved branching strategy was put forward to solve the final model.Finally,the model was tested against the data of the Beijing-Shanghai high speed railway in China,to deliver a better quality solution within the effective time, while the error rate between the solution and the optimal solution was only 2.13%.As a result,the solution outperformed the line plans in use at Beijing-Shanghai high speed railway.