Robust Optimization Model And Algorithm For Passenger Flow Control Strategies Of Urban Rail Transit Line And Network For Uncertain Scenarios

As the urban road traffic in our country is increasingly congested,many cities have planned and constructed urban rail transit systems.The urban rail transit is seen as the backbone of urban public transportation due to the advantages of large traffic volume and fast speed.The organization and operation of urban rail transit shift from single-line operation to network operation with the increasing number of rail transit lines in major cities.With the rapid growth of travel demands in the cities,more and more urban rail transit lines are stuck in an oversaturated situation during peak hours.Numerous passengers cannot get on the next train successfully and be detained on the platforms.It would enhance the complexity of scheduling problems in the urban rail transit system,lead to severe platform aggregation,and influence operation security.In addition,if the rail transit system network lacks a large amount of historical passenger flow data for a sufficient period when forecasting passenger flow,the results tend to fail to meet the prediction accuracy requirements.Even if the passenger flow characteristics of the rail transit line are apparent and robust,the actual passenger flow often deviates from the predicted one based on historical passenger flow data because of the emergencies in the rail transit system.Due to the influences of various factors in the actual operation,the passenger demands of urban rail transit are usually uncertain.Based on the above,considering the time-dependent and uncertain passenger demands,this paper deeply analyzed the passenger flow characteristics of urban rail transit lines and networks.The passenger flow control strategy under the operation of lines and networks is studied to provide essential theories and methods for urban rail transit operation and management.The main contributions of this paper are shown as follows:(1)Based on the passenger demands of urban rail transit lines,the dynamic evolution process of passenger flow among stations and trains is described to analyze the matching relationship between transportation capacity and passenger demands in the urban rail transit system.Considering the scenarios with uncertain passenger demands,the robust optimization model is constructed to cooperatively optimize timetable scheduling,passenger flow control strategy,and skip-stop pattern with the constraints of safe headways and train loading restrictions.The purpose of the model is to minimize the number of passengers restricted from the stations,the number of passengers detained on the platforms,total passenger waiting time,and total train trip time.Furthermore,the robust optimization model based on the scenario set is transformed into a deterministic model with linear constraints,which is easy to solve.The numerical experiments are conducted based on the Beijing subway Changping line.The results show that the optimized timetable with skip-stop patterns and passenger flow control strategies can alleviate the station congestion situation,enhance the security of the urban rail transit system and reduce operating costs to a certain extent.Moreover,decision-makers can choose an appropriate number of scenarios and weighting coefficients to balance solution robustness and model robustness.(2)To further ensure passenger travel safety and improve the transportation efficiency of stations,an optimization method of passenger flow control strategy is proposed under the operation condition of the urban rail transit network.The robust optimization model based on scenarios with uncertain passenger demands is proposed based on the dynamic evolution of passenger flow outside stations,on platforms,and in trains of the urban rail transit network and passenger transfer behaviors.The model considers multiple constraints,such as train loading limitation,platforms’ maximum capacity,and transferring and uncertain passenger demands.The model aims to minimize the number of passengers restricted outside the stations,the number of passengers gathered on the platforms,and the number of conducting passenger flow control strategies.Passenger flow control strategies under the large-scale urban rail transit network can be generated to obtain the optimal system and meet the passenger demands.Due to the complexity of solving large-scale network problems,a decomposition algorithm based on Lagrangian relaxation is proposed to decompose the original large-scale network problem into subproblems for each line and solve them separately.The lower bound of the solution to the original problem can be obtained.The heuristic algorithm is applied to quickly achieve the upper bound of the solution to the original problem.The sub-gradient method is used to update the Lagrange multiplier.The upper and lower bounds are continuously approached to improve the computation efficiency effectively.Finally,the numerical experiments are conducted based on the Beijing subway network operation data.The results show that the developed algorithm can quickly solve the problem and obtain a solution with more minor errors.Compared with the case without passenger flow control,the proposed passenger flow control method can effectively alleviate platform congestion.Compared with each passenger demand scenario’s optimal objective function value,the objective function values based on the robust passenger flow control strategy in each scenario have relatively small errors.It indicates that the robust passenger flow control strategies have positive performance in each scenario and can effectively reduce the system’s sensitivity to the disturbance of passenger demands.