An Optimization Of Train Scheduling For Urban Rail Transits Under Time-dependent Conditions

With the acceleration of the process of China’s urbanization, there is an increasingdemand for urban transportation travel，and the contradiction between supply and demand isparticularly prominent. Urban rail transits with large capacity and high-speed can effectivelyease traffic congestion, while rail transit scheduling is day-to-day transport organization ofurban rail transit command center, which reflected the level of rail transport operators in orderto achieve security, punctuality, comfortable, efficient operation services.Optimization of train scheduling can improve the operating efficiency of the urban railtransit, however, existing scheduling solution is lack of time-varying characteristics andpassenger trains crowded. In this paper, on the basis of careful analysis of the results ofexisted studies, considering the time-dependent conditions and passenger trains crowdedconditions, we mainly research the optimization of train scheduling scheme, and the contentsare as follows:(i) Passenger demand is the basis of the scheduling of urban rail transit, on summarizedurban rail transit morphological and spatial and temporal distribution characteristics, thispaper gets the conclusion that passenger flow distribution has obvious imbalance variableconditions under time-varying conditions, and analysis relationship between passengerspace-time imbalance and train scheduling scheme. Based on time-varying passenger demand,considering the train crowded conditions and passenger arrival time windows, this paper alsoproposes car congestion degree and the station to punish them as the optimization goals oftrain plan.(ii) With empty train scheduling of single line is optimized. Through analyzing timevarying of traffic demand and requirements of train running, the mathematical model isbuilt which is to optimize train operation scheme under time varying environment, whoseconstraints are requirements of train running and supplied train and the optimizationobjective is to minimize passengers waiting time, the degree of crowd and punished ofpassengers arrived station. Based on the characteristics of the model using geneticalgorithms to solve the example, and further discussion of the parameters in the model, theresults show that optimized scheduling scheme to better meet the interests of bothpassengers and operations.(iii) In transfer conditions, the paper analyzes time varying of two lines，and considerstransit passenger flow influence on train operation scheduling. A collaborative optimizationmathematical model is built which is to optimize train operation scheme. Characteristics ofthe train running and the number of available train each line is the constraints. And theminimum of passengers waiting time, the degree of crowd, punished of passengers arrivedstation and transfer waiting time, as well as the maximization of the total number ofpassengers transfer are objective function. Using Genetic Algorithm to solve the example, the solution is an uneven schedule. The uneven schedule reduces passenger waiting time, transferwaiting time, the station punishment and the degree of congestion compared with equalizationscheme.By optimizing the urban rail train operation scheme, it is great significance to getreasonable departure timetable, enhance passenger travel comfort, and reduce the cost of railoperators.