| In recent years,with the rapid development of high-speed railway in China,the network structure based on "four vertical and four horizontal" and "eight vertical and eight horizontal" as the goal has been constructed.According to the “Long-term railway network planning” compiled in 2016,it is estimated that the scale of high-speed railway network will reach about 38000 km by 2025.In the face of such a large-scale high-speed railway network,the operation organization of high-speed railway trains is facing unprecedented challenges at the strategic,tactical and operational levels.The operation of China's high-speed railway is complex,and the main-line train and cross-line train with different speed are scheduled at the same time.However,the influence of cross-line trains on capacity calculation and capacity optimization is mostly ignored,which is inconsistent with the actual situation in China.Considering that the capacity of high-speed railway in China is mostly calculated by drawing lessons from existing lines or foreign capacity calculation methods,therefore,two capacity calculation methods are proposed for Chinese high-speed railway.Secondly,in order to alleviate the increasingly tense high-speed railway capacity and meet the strategic and tactical needs of Chinaese high-speed railway operation organization,this paper puts forward the collaborative optimization of train stopping plan and timetable based on statistical data of passengers and time-dependent passenger demand respectively,so as to improve the capacity utilization rate and run more trains in the limited space-time resources.The main work of this paper is as follows:(1)Based on the analysis of the existing calculation methods for the capacity of highspeed railway,a new carrying capacity calculation method was proposed.The new method virtualized a station into a section,which can also transform the calculation of station capacity into the calculation of virtual section capacity,to realize the integration of station and section for the study of high-speed railway capacity.On the basis of station virtualization,the minimum headway of different train groups was calculated,and the average minimum headway method was used to calculate the virtual section capacity.By comparing the capacity of virtual section corresponding to each large passenger station,the minimum capacity was chosen as the capacity of the section.The new method can deal with the influence caused by cross-line trains and various operations of stations on the average minimum headway more conveniently.It can also simplify the structure of the train diagram as well as the calculation process.Finally,the Beijing-Shanghai highspeed railway was taken as an example to verify the feasibility of this method.(2)This paper analyzes the real scenario of high-speed railway in China,and finds that the operating trains including cross-line trains and main-line trains,but most of the existing studies ignore the influence of the cross-line train on the timetable generation.An integer programming model is proposed,the objective is to maximize the number of operating trains.The model considers trains of different speed,and the conflict between each train in different directions at the cross-line station is expressed by the headways of trains,which is dependent on the yard layout of cross-line station.Using the alternating direction multiplier method(ADMM)to solve the model,the complex train combination optimization problem is decomposed into the shortest path problem of a single train.Finally,adopting Taiyuan—Dezhou and Zhengzhou—Beijing high-speed railway as the case study,the feasibility of the model and algorithm is verified and the effect of different proportions of cross line trains and the layout of station yard on the timetable is analyzed,then the calculation results are compared with the capacity analysis method proposed by the author,which shows that the calculation results of the two methods is consistent.(3)This paper analyzed the current capacity optimization methods of high-speed railway,and built the space-time network based on the time-discrete physical network of high-speed railway.Therefore,the train stopping and train off-line operation was represented by stopping arc and off-line arc respectively with different time weights.Considering the constraint of minimum train headway time,an integer programming model was proposed based on the line planning.The capacity optimization of high-speed railway was realized by collaboratively optimizing main-line and off-line train timetable and stopping plans of some trains,aiming at maximizing the number of service trains and minimizing the total travel time.Alternating direction method of multipliers(ADMM)was used to solve the problem and improve the solving efficiency.Finally,the case study of the Beijing-Shanghai high-speed railway was conducted to test the model and the algorithm.(4)Based on the time-dependent passenger demand of high-speed railway,the collaborative optimization of train stopping plan and timetable is studied.The space-time network of train flow and passenger flow of high-speed railway are established.It is found that the optimization of train timetable and stopping plan and passenger assignment are multi-commodity flow problems.The trains(as the users)share the railway capacities(as the resource)in a high-speed railway network,and the passengers(as the users)share the train carrying capacities(as the resource).In addition,we regard train disturbances in different directions as different train headways at cross-line stations to optimize train scheduling practically.Sequentially,a mixed-integer linear programming model with security and coupling constraints is formulated to maximize the loading passengers using an improved train scheduling.The decomposition algorithm based on Lagrange relaxation and ADMM is used to solve the model,and the feasibility of the model and algorithm is verified by taking the railway network of 9 stations and the cross shaped railway network of Taiyuan—Dezhou and Zhengzhou—Beijing high speed railway as examples. |
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