Coordination Optimization Of Last-Train Timetables Under Transfer Demand Uncertainty

Urban rail transit system attracts more and more passengers by its characteristics of large capacity,safety,high efficiency,and energy saving.Passenger transfer between different lines in urban rail transit is becoming increasingly common.The connection problem of last trains in the subway has not attracted sufficient attention,resulting in low service capacity and underutilization of some of the last trains,which in turn has caused great waste of resources.Therefore,it is of practical significance to optimize the schedule design of last trains on the urban rail transit network.In addition,few scholars have proposed a timetable optimization plan under passenger flow uncertainty at present,which obviously cannot be practically applied to the current subway operation situation.Fully considering the stochastic characteristics of changing passenger flow,this paper adopts scenario-based random variables to characterize the uncertain distribution of passenger transfer flow,and a mixed integer linear programming model is then established,with an algorithm designed to obtain reasonable and feasible last train timetable schemes.The main research contents of the paper are as follows:(1)First,we analyze the uncertainty of transfer passenger flow between last trains,before a number of representative passenger flow data are selected as several sets of random samples and different passenger flow scenarios are constructed by them.Then probabilities of random samples are collected as the occurrence ones of corresponding scenarios,the proposed model can effectively represent the random characteristics of subway passenger flow.Unlike other probabilistic data models,this aggregate processing method of stochastic data can fully focus on the uncertain distribution characteristics of last-train passenger flow and contribute to robust optimization schedules for last trains.(2)Applying the trade-off rules between the expected utility and indeterminate risks according to the mean-variance theory,the expectation-variance model of the last-train schedule synchronization is constructed under the uncertain environment with the goal of "maximizing the number of successful passenger transfer" and "minimizing the running time on all segments".The different dimension of the expected value and the variance can lead to low sensitivity of the proposed model.Therefore,the Min-Max standardization method is employed to normalize the original model to ensure that the expected utility and the variance reach the equilibrium according to decision requirements.(3)Besides the expectation utility mentioned above,we also propose a non-expectation optimization criterion.Based on the reliability criterion,the max-min reliability model and the percentile reliability model are established.For convenience of solution,the proposed models are transformed into the mixed integer linear programming ones by introducing the reconfiguration method,aiming for the reliable last-train schedules at a certain level of confidence.(4)In view of the characteristics and the computational complexity of the mean-variance model,the maximum-minimization reliability model and the percentile reliability model,a Tabu search algorithm based on solution generation is designed and analyzed in a small subway network and the Beijing metro network.The results show that the calculation time for the Beijing Metro instance is basically guaranteed within 20 minutes,and both of the optimization goals,ie,the total number of passengers and the total running time of last trains on segments,have been significantly improved.Meanwhile,the validity of the last-train timetable optimization models based on the mean-variance and the reliability criteria is verified,with the proposed algorithm testified efficient.