Research On Optimization Of Division Of Labor Scheme In High-Speed Railway Hub Considering Track Allocation In Passenger Stations

With the continuous development of high-speed railway,an "eight vertical and eight horizontal" high-speed railway network has been built in China,which links the metropolises and covers the main urban areas.As the intersection of the network,the form of the high-speed railway hub has gradually changed from single-station to multi-station with the introduction of new lines.Since the multi-station hub has multiple independent stations,how to make use of station resources becomes the key to improve the overall transportation capacity of high-speed railway hub.From the perspective of overall utilization of resources,considering the line distribution and layout of various facilities in the hub,this paper adopts the method of mathematical model to optimize the train routes,stop patterns,track allocation and arrival and departure times in the hub,and then obtains the division of labor scheme for the high-speed railway hub passenger stations,which takes into account the railway transportation operation cost and the travel demand of urban residents.The main contents are as follows:(1)The division of labor optimization method for passenger stations in the high-speed railway hub considering track allocation is proposed.Firstly,according to the distribution of lines and layout of stations,the high-speed railway hub network is constructed.Then,based on the hub network and taking a single train as the basic research unit,referring to the modeling method of multi-commodity network flow and point-arc model,an optimization model for the division of labor for passenger stations considering track allocation is constructed.Its objective function is to minimize the operation cost of trains in the hub and the travel cost of urban residents,and the constraints include the line capacity and the track capacity.The optimization scheme includes the optimized train routes and track allocation.Finally,an example is designed and the GUROBI optimization software is used to solve the model to obtain the optimized division of labor scheme,which is compared with the commonly used division of labor scheme with fixed connecting directions to verify the effectiveness of the model.(2)The division of labor optimization method for passenger stations in the high-speed railway hub considering the capacity of the Electric Multiple Units(EMUs)depot is proposed.This part is the spatial expansion of the previous part.According to the characteristics of the high-speed railway hub,considering the influence of the storage capacity and maintenance capacity of the EMUs depot on the division of labor scheme,an optimization model for the division of labor of the high-speed railway hub is constructed to optimize the train routes,stop patterns,and track allocation in the EMUs depot.Then,according to the structure and characteristics of the model,a solution algorithm based on Lagrangian relaxation is designed.The capacity constraints and coupling constraints in the relaxation model are incorporated into the objective function.The relaxation model is decomposed into the train shortest path problem with stop constraints.A shortest path solution based on Floyd algorithm is designed to calculate the lower bound,and a heuristic algorithm based on train priority is used to obtain the upper bound,The Lagrange multipliers are updated by sub-gradient method and the relaxation model is solved iteratively.Finally,an example is designed to verify the effectiveness of the model and algorithm.(3)The collaborative optimization method of the division of labor and train timetabling is proposed.This part is the temporal expansion of the first part,which further refines the scheme to the level of train timetabling by adding time dimension.Firstly,the layout of block zone and throat zone is detailed in the physical network,then the physical network is expanded into a space-time network,and a collaborative optimization model is constructed based on the incompatible arc sets.Secondly,in view of the high complexity of constructing the incompatible arc sets,the cumulative flow variable is introduced to represent the occupation of space-time resources by trains,and a collaborative optimization model based on cumulative flow variable is constructed.Then,based on the structure of the model,considering that the Lagrange relaxation algorithm may fall into the symmetry issues,an algorithm based on alternating direction method of multipliers(ADMM)is designed.On the basis of Lagrange multipliers,quadratic term multipliers are added to transfer the relaxed constraints to the objective function.The symmetry issues are broken by differentiating the occupation cost of different trains in the same iteration,so as to improve the solution quality and efficiency.Finally,small-scale and large-scale examples are designed,and the results of ADMM algorithm and Lagrange relaxation algorithm are compared to verify the effectiveness of the models and algorithms.(4)A case study based on a realistic high-speed railway hub in China is demonstrated.The proposed model and algorithms are substituted into the actual high-speed railway hub network to verify the applicability.Specifically,the optimization scheme obtained by the model and algorithm is compared with the practical fixed division scheme,and the differences between the two schemes are analyzed from the aspects of train operation cost,passenger travel cost,line capacity utilization and station track capacity utilization.The results show that the optimization scheme can effectively reduce the train operation cost and passenger travel cost,and the capacity utilization of various facilities is more balanced.The proposed methods can provide theoretical and method basis for the railway transportation department to formulate a scientific and reasonable division of labor scheme for passenger stations in the multi-station high-speed railway hub.