Model And Algorithm Of Train Timetabling For Additional Trains On A Urban Rail Network

Because high-speed railway trains are easily disturbed and form different delays,especially in the evening when a large number of high-speed railway trains are delayed,and it has a serious impact on passengers arriving at the terminal station and then transferring to urban rail trains.With the expansion of urban rail network scale,the passenger traffic is increasing,and the uncertainty of the delays of high-speed railway trains have brought great challenges for urban rail transit trains to connect high-speed railway delay trains.At the same time,the high-speed railway trains are delayed,which makes it impossible for passengers to transfer to urban rail train to reach their destinations conveniently and cost-effectively,and increase passengers1 extra travel expenses,and reduce the service quality of urban rail.Therefore,it is necessary to research a scientific and reasonable method,which considers high-speed railway trains’delay into the timetabling of the urban rail train,to improve the service quality of the transition in terminal stations,so that it’s convenient for passengers to choose high-speed railway and urban rail transitThe existed research has proposed a large number of models and algorithms for the timetabling and optimization of urban rail train,and considering passenger transfer,However,most of research is aimed at the transfer demand of multiple origins and multiple destinations,but do not consider the trains’ delay.Further,when connecting high-speed railway trains in the evening and serving passengers from high-speed railways trains(transition demand for single origin and multiple destinations),the uncertainty of high-speed railway trains’ delays has an impact on passengers’ transfer demand.So the existed research on urban rail transit train schedule timetabling or optimization method is no longer applicable for this condition.For this purpose,the following research is carried outThis paper takes the timetabling of urban rail trains’timetable under the condition of passengers’ transfer demand as the research background,and focuses on the integration the uncertainty of the high-speed railway trains’ delay into timetabling,and establishes model of train timetabling for additional trains on a urban rail network considering the evening high-speed railway train delay.Based on the difficulty and characternstics of the bi-objective model,the bi-objective mixed integer programming model is rewritten into double single-objective mixed integer programming models by using the epsilon constraint method to solve the problem.The correctness and effectiveness of the model are verified by examples of different scales.The main research of this paper is as follows:(1)Analyze the timetable optimization and timetabling methods for considering transfer convergence at home and abroad,and summarize its research status and problems,and design the roadmap of this paper.(2)Analyze the delay characteristics of high-speed railway trains and the description method of stochastic delay,the characteristics of the travel demand of high-speed railway passengers during the night;And analyzes the transfer process of high-speed railway passengers at the terminal station and the transfer station during the night,and reconstructe the physical topology of the urban rail transit network to clarify modeling ideas.(3)Establish the model of train timetabling for additional trains on an urban rail network considering delay high-speed railway trains at night.By considering the high-speed railway line and the urban rail as network,mathematical language ion,establishing hypothetical conditions,laying the foundation of the model;this paper analyze the transfer relationship between high-speed railway trains and urban rail transit trains,and build an integer programming model.(4)Based on the bi-objective programming model and the complexity of the solution,epsilon constraint method is cited,and the bi-objective programming model is rewritten as double single-objective programming models.By adjusting the value of epsilon,the corresponding optimal solution is obtained.Finally,a set of Pareto optimal solution combinations(Pareto frontier)is formed.(5)Algorithm design.In order to better deal with the solution pressure of the large-scale problem especially,this paper introduces the double-layer circulation of Simulated-Annealing in crossing and mutation of the traditional Genetic-Algorithm for the model P1,and designs Genetic simulated-annealing algorithm to improve the efficiency of the model.(6)Examples analysis.Firstly,the correctness of the model is verified by a simple network,and then different delay scenes of high-speed railway trains are set up.Further,a large scale containing evening trains of JingHu high-speed railway and Beijing urban rail trains is calculated,all passengers can be transferred to urban rail transit train to reach their destination in any designed delay scenes,the effectiveness of the model are analyzed by CPLEX software.The results show that the model can improve the efficiency and correctness of urban rail trains timetabling,and the timetable compiled by model P1 has strong anti-interference to the uncertainty of high-speed railway trains delay to service high-speed railway passengers.