Hindawi Publishing Corporation Advances in Mechanical Engineering Volume 2013, Article ID 848292, 12 pages http://dx.doi.org/10.1155/2013/848292 Research Article Coordination Optimization of the First and Last Trains’ Departure Time on Urban Rail Transit Network Wenliang Zhou, Lianbo Deng, Meiquan Xie, and Xia Yang School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China Correspondence should be addressed to Meiquan Xie; [email protected] Received 17 August 2013; Revised 11 October 2013; Accepted 6 November 2013 Academic Editor: Wuhong Wang Copyright © 2013 Wenliang Zhou et al. This 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. Coordinating the departure times of different line directions’ of first and the last trains contributes to passengers’ transferring. In this paper, a coordination optimization model (i.e., M1) referring to the first train’s departure time is constructed firstly to minimize passengers’ total originating waiting time and transfer waiting time for the first trains. Meanwhile, the other coordination optimization model (i.e., M2) of the last trains’ departure time is built to reduce passengers’ transfer waiting time for the last trains and inaccessible passenger volume of all origin-destination (OD) and improve passengers’ accessible reliability for the last trains. Secondly, two genetic algorithms, in which a fixed-length binary-encoding string is designed according to the time interval between the first train departure time and the earliest service time of each line direction or between the last train departure time and the latest service time of each line direction, are designed to solve M1 and M2, respectively. Finally, the validity and rationality of M1, M2, and their solving genetic algorithms are verified with numerical analysis, in which the effects of the parameters in M1 and M2 on coordination optimization result are analyzed. 1. Introduction linear programming model to optimize the train timetable for minimizing the total train travel time, subject to overtaking With the rapid development of urban rail transportation, and crossing headway constraints. Higgins and Kozan [2] urban rail transit networks have been formed in Beijing, described the development and use of a model designed to Shanghai, Guangzhou, and many other big cities in China. optimize train schedules on single line rail corridors. Zhou Under the network operation and management of urban and Zhong [3] proposed a generalized resource-constrained rail transportation, passengers’ alternative travel routes are project scheduling formulation to minimize the total train increased substantially because they can choose different sta- travel time of the train timetable on the single-track railway. tions to transfer, which greatly facilitates passengers’ traveling Li et al. [4] present a simulation method for solving the train but also increases the operation and organization difficulties timetabling problem to minimize the total travel time on of urban rail transportation. Coordinating trains of different the single-track railway. Zhou and Zhong [5]proposeda linesisoneofthemainproblemsofnetworkoperationof multimode resource-constrained project scheduling formu- urban rail transportation. The coordination of arrival and lation to consider acceleration and deceleration time losses departure time of trains from different line directions at in double-track train timetabling applications. Carey [6]and transfer time not only can effectively reduce the passenger Carey and Lockwood [7] solved the train timetabling and transfer waiting time, but also can make lines transport pathing problem in a rail network with one-way and two-way capacities match each other better to improve all trains’ tracks. Lee and Chen [8] presented an optimization heuristic operation efficiencies on urban rail transit network. that includes both train pathing and train timetabling. Carey Train schedule optimization was studied extensively, and and Carville [9] devoted to scheduling and platforming trains a series of excellent achievements has been made. The original at busy complex stations. researches aimed more at train schedule optimization of It is very difficult to solve the railway train schedule. Cai only one line. For example, Szpigel [1]firstdevelopeda et al. [10]andCapraraetal.[11] regarded the train scheduling Downloaded from ade.sagepub.com by guest on June 23, 2016 2 Advances in Mechanical Engineering problemtobeNP-hard.Therearenoaccuratealgorithms train schedules of rail transit networks only with transfer time for solving the train schedule of large-scale and complex [20, 21], or both the transfer time and vehicle operating cost rail network within an acceptable time nowadays. In order [20]. Carey and Crawford [21] were devoted to finding and to obtain a satisfactory train schedule within an acceptable resolving the conflicts in draft train schedules on a network time, the heuristic algorithms are usually designed to solve of busy complex stations. Ghoseiri et al. [22]developinga this problem. Greenberg [12], JovanovicandHarker[´ 13], and multiobjective optimization model for the passenger train Higgins et al. [14] developed a branch-and-bound solution scheduling problem on a railroad network. Liu and Kozan framework to find feasible timetables. Kraft15 [ ]presented [15] presented a feasibility satisfaction procedure algorithm a branch-and-bound approach for solving the train conflict to solve the train scheduling problem which is regarded as to minimize a weighted sum of delay. Based on the branch- a blocking parallel-machine job shop scheduling problem. and-bound algorithm, Zhou and Zhong [5]incorporated Burdett and Kozan [19]proposedanovelhybridjobshop effective dominance rules into this algorithm to generate approach to create new train schedules. Based on the TAS pareto solution for train scheduling problem. Zhou and method proposed by Dorfman and Medanic [16], Li et al. [4] Zhong [3] presented to use a Lagrangian relaxation base lower proposed an algorithm based on the global information of the bound rule, an exact lower bound rule, and a tight upper train to obtain an effective travel advance strategy of the train. boundwhichareadaptedinittoreducethesolutionspace. The coordination of the first and last trains’ arrival and The priority rules, which determine the priority of each train departure time at transfer station is particularly prominent on in a conflict, depend on an estimate of the remaining crossing urban rail transit network. Most reviewed researches about and overtaking delay, as well as the current delay used in some the first and last trains only struggled to reduce passenger algorithm can effectively improve the optimal quality of train transfer waiting time; however, besides that, the first train timetable. Carey [6] and Carey and Lockwood [7]devel- departure time influences passengers origin waiting time oped an iterative decomposition approach which contains for the first train, while the last train departure time affects the several node branching, variable fixing, and bounding the inaccessible passenger volume and passengers’ accessible strategies to reduce the search space for solving the train reliability for last train. These passengers travel requirements timetabling and pathing problem. Dorfman and Medanic are worthy of concerns especially when passengers care more [16] incorporated some priority rules into a discrete event about their travel service levels today. After analyzing the simulation framework to solve large-scale real-world train organization requirements of the first and last trains on urban scheduling problem. S¸ahin [17], Higgins et al. [14], and Liu rail transit network this paper aims to coordinate the first and and Kozan [18] extended some priority rules to backtracking last trains’ departure time of each line direction so that first search, look-ahead search, and metaheuristic algorithms for and last trains’ arrival and departure time connect better at train scheduling, respectively. Burdett and Kozan [19]divided each of the transfer stations to meet as far as possible all travel the scheduling process into two levels: global scheduling service requirements of passenger. to establish an initial train diagram without considering The organization of this paper is as follows. Section 2 conflicts and local scheduling to repair conflicts. Dorfman analyzes the coordination optimization goals and constraints and Medanic [16] developed a local feedback based travel of the first and last trains’ departure time of all rail line advance strategy (TAS) by using a discrete event model of the directions. Section 3 describes passengers’ travel route choice train advance along the lines of railway. Li et al. [4], based on problem based on Logit model. Section 4 presents two the TAS method proposed an algorithm based on the global optimization models, respectively, for the first and last trains’ information of the train to obtain an effective travel advance departure time on urban rail transit network. Section 5 strategy of the train. In some literature, the train scheduling deals with the genetic algorithm development, and Section 6 problem is modeled as a blocking parallel-machine job shop reports on our computational experiments. Finally some scheduling problem solved by the alternative graph model conclusions