Robust Optimization Of Train Timetable For Energy-Saving Operations In Urban Rail Transit

Large capacity,low energy consumption,fast speed and convenience are the main advantages of urban rail transit,which plays an important role in alleviating urban traffic congestion and establishing energy-saving travel mode.And it has developed rapidly around the world in recent years.However,with the rapid expansion of network scale and increase of operation mileage,the passenger volume,total energy consumption and operation cost increase rapidly,which has put significant pressure on the operation of urban rail transit.Moreover,the pattern of operating organization is becoming more and more complicated.With frequent occurrence of uncertainties,the trains will deviate from the planned timetable,resulting in the reduction of service quality and operation efficiency.Therefore,it is of great significance to study how to reduce energy consumption and enhance the ability of timetable to resist interference for reducing operation cost and improving service quality.In this paper,the main purpose is to optimize timetable for reducing energy consumption and enhancing robustness of timetable.We analyze the operation process of the train in the section in detail and study the method to reduce operation energy consumption.Considering the uncertainties of operation and the quality of passenger service,we present the model to enhance the robustness of timetable.The main research work of this paper is as follows:(1)Considering the uncertainties of the numbers of arrival passengers and alighting passengers of stations,the robust timetable optimization model is developed.First,the scenario and scheme are used to represent uncertain parameters and headway times,respectively.Then,based on minimum maximum regret value theory,we establish a robust optimization model to minimize the number of stranded passengers under the worst scenario.And the genetic algorithm is designed to solve the model.Finally,the results of Beijing Metro Yizhuang Line show that the proposed robust optimization model could reduce stranded passengers by 53.72%compared with the current timetable.And the relative regret value between the stranded passengers of optimization timetable and minimum stranded passengers is less than 15%,which means the robust timetable could better avoid uncertain risks and is of stronger robustness.(2)An energy-efficient timetable optimization model is proposed from two aspects of reducing tractive energy and increasing the utilization of regenerative energy.First,the running process of a train in a section is divided into six phases:constant force traction,constant power traction,costing,constant power braking,constant force braking and mechanical braking.Considering that the train will not generate regenerative energy during mechanical braking phase,we propose the calculation method of utilization ratio of regenerative energy,which is ratio of utilization time and generation time of regenerative energy.Then,an energy-efficient timetable optimization model is established to minimize the net energy consumption and the genetic algorithm is designed to search the optimal arrival and departure times and headway times.Finally,the results of the example,which is based on Beijing Metro Yizhuang Line,show that the optimization timetable could reduce total energy by 8.27%compared with the current timetable.(3)Based on the above researches,a two-stage robust optimization model for searching energy-efficient timetable of urban rail transit is proposed.In the first stage,we establish a robust model to reduce passenger waiting time and seek the robust headway times;in the second stage,we build an energy-efficient model to minimize net energy consumption and search the optimal arrival and departure times.Then,an internal and external nested genetic algorithm is designed to solve the two-stage model,and the validity of the model and algorithm is verified by an example of Beijing Metro Yizhuang Line.The results show that the optimization timetable could reduce the passenger waiting time by 36.96%and save the energy by 5.94%compared with the current timetable.