Hindawi Journal of Control Science and Engineering Volume 2020, Article ID 1868724, 9 pages https://doi.org/10.1155/2020/1868724 Research Article Coordinated Optimization of Departure Time Domains of Multiple Trains at a Station Based on Passenger Satisfaction Zhiqiang Tian,1 Rui Zhang ,1,2 Guofeng Sun,1 and Di Cheng3 1School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China 2School of Economics and Management, Shaanxi Institute of Technology, Xi’an 710300, China 3School of Transportation Engineering, Gansu Forestry Technological College, Tianshui 741000, China Correspondence should be addressed to Rui Zhang; [email protected] Received 19 September 2019; Revised 19 January 2020; Accepted 7 July 2020; Published 1 August 2020 Academic Editor: Manuel Pineda-Sanchez Copyright © 2020 Zhiqiang Tian et al. .is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In order to optimize the passenger train working diagram and improve the passenger satisfaction towards a coordinated op- timization problem of departure time domains of multiple passenger trains at a station, the optimization model is designed to maximize the overall passenger travel satisfaction based on the quantification of the level of passenger travel satisfaction. .e simulated annealing algorithm is then used to solve the model. Finally, 23 pairs of passenger trains from Chengdu Railway Station are selected as examples to verify the feasibility and effectiveness of the algorithm. .e result shows that the model and algorithm proposed in this paper can realize the coordinated optimization of the departure time of multiple trains at a station while considering the passengers’ travel satisfaction, which can provide an effective reference for the compilation of passenger train working diagram. 1. Introduction timetabling problem, respectively. In order to improve the quality of passenger transport service, train service operators .e passenger train-operation plan is designed to solve the have gradually shifted their focus from operation-oriented problem of the layout of the passenger train scheduling line. decision-making to market-oriented decision-making, in- It is mainly to determine the departure time of the passenger cluding the shortest total travel time and the shortest waiting train-operation line after obtaining the reasonable departure time of passengers at the station [3–5], among which the time domains of each passenger train and then to provide a frame and core component of train timetable, departure reasonable framework for the drawing of the passenger train time of departure station determines the operation plan of working diagram. It is also one of the main technical in- passenger train and affects the overall performance of train dicators to measure the strengths and weaknesses of the train service. In the literature, many scholars have studied the working diagram. For Chinese common-speed railway lines departure time domain of trains. Some literature studies the with long running time, the compilation result will directly optimization of train departure time from the perspective of affect the feasibility and compilation quality of the passenger improving passenger travel convenience. Li et al. [6] pro- train working diagram. .erefore, it is particularly impor- posed an improved train scheduling simulation method to tant to determine the departure time of the passenger trains reduce the total train running time and optimize the train on the common-speed railway lines reasonably in the departure time. In order to improve the quality of passenger process of compiling the train working diagram. train service, Vansteenwegen and Oudheusden [7] designed .e optimization of passenger train timetable has a waiting cost function to calculate different types of waiting attracted wide attention in the past decades. Cordeau et al. time and delaying time and then carried out research work to [1] and Caprara et al. [2] have comprehensively reviewed the minimize them. Standard linear programming is used to general train timetabling problem and passenger train optimize the train timetabling. Fu [8] reduced the 2 Journal of Control Science and Engineering quantitative optimization of passenger train timetable to a train at a certain time in the city and is an important in- multiobjective programming problem and proposed an dicator to measure the overall satisfaction of all passengers optimization algorithm to optimize convenient passenger on the train. Due to the fact that a passenger train has travel. Zhou and Zhong [9] studied the passenger train passengers getting on and off at every station passing along scheduling problem with the objective of minimizing the the route, it is necessary to investigate and study the pas- expected waiting time of passenger trains and the total travel senger satisfaction in different travel periods of each station time of trains and solved it by branch and bound algorithm. (city). Ni et al. [10] starting from the aspects of passenger travel Before drawing up the passenger train working dia- convenience and economy, considering the occupancy of the gram, it is impossible to accurately judge the frequency, train’s inbound and outbound tracks and stop tracks, location, and corresponding stop time of the train meeting studied the optimization of passenger train departure time and overtaking along the route. .erefore, it would be domain. impossible to get an accurate travel time for each train. .ere are also some studies on the optimization of train Hence, when calculating the overall satisfaction of pas- departure time from the perspective of railway operation senger trains, it is necessary to use the estimated travel departments. Ni et al. [11] took the optimal time domain of time and the number of passengers getting on and off at trains in and out the station as the objective function and, different stations. with the constraints of the basic capacity of the track in and In order to ensure that the passenger trains departing out of the station in unit time (such as the departure capacity from the station and returning to the station both have and receiving capacity), established an optimization model higher overall satisfaction, the total satisfaction value of of passenger train departure time domain and proposed a paired trains is taken as the main parameter of optimization heuristic priority strategy algorithm for the optimal solution. in this study. .e calculation of the overall satisfaction of Chen et al. [12] set up a model to satisfy the expected arrival/ paired passenger train is made up of the following parts. departure time of passengers with the constraints of arrival and departure capacity of stations, genetic algorithm with 2.1. Passenger Train Travel Time Estimation Based on Existing conflict detection was used to solve the optimal arrival and Train Working Diagram. For common-speed railway lines, departure time of trains, and the Chengdu Station was taken the uncertainties of the passenger train meeting and over- as an example to verify the model and algorithm. taking along the route usually in operation process make the Although there are a lot of in-depth studies on the whole travel time of the train deviate greatly from the pure optimization of the departure time of passenger trains, most running time. .erefore, before calculating the arrival/de- of the literature fails to take into account the long east-west parture time and the overall passenger satisfaction of the direction, large north-south span, and obvious seasonal train, it is necessary to first determine a more reasonable variation characteristics in common-speed railway network train travel time. in China, which makes the departure and arrival time of .rough the analysis of Chinese common-speed railway passenger trains determined by the current time (Beijing network, the main large-scale stations (or hubs) are used as time) reference standard cannot meet the passengers travel the key nodes to divide the network into several smaller need in certain cities very well. For this reason, based on the sections, and the travel time of specific types of trains in each previous studies, this paper takes passenger travel satisfac- section is analyzed, respectively, so as to estimate the travel tion considering time zone deviation as the main evaluation time of all kinds of the trains between any station in the index and puts forward the coordinated optimization of entire network [13]. On this basis, as long as the departure multitrain departure time at a station based on passenger time of the train at the departure station can be obtained, the satisfaction. arrival and departure time of the train at any station along .e rest of the paper will proceed as follows. .e authors the route can be calculated according to the passenger train will first calculate the overall passenger satisfaction of any operational time in each section. pair of passenger trains based on the number of passengers getting on and off the train at each station along the travel route with the estimated travel time. Section 3 establishes an 2.2. Fitting of the Number of Passengers Getting on and off the optimization model of departure time of multiple passenger Trainand Passenger Satisfaction Survey. .e passenger is the trains at a station based on passenger satisfaction. Section 4 main object of passenger train service. .erefore, when