Optimization of Multiperiod Mixed Train Schedule on High-Speed Railway

Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2015, Article ID 107048, 14 pages http://dx.doi.org/10.1155/2015/107048 Research Article Optimization of Multiperiod Mixed Train Schedule on High-Speed Railway Wenliang Zhou,1 Junli Tian,1 Jin Qin,1 Lianbo Deng,1 and TangJian Wei1,2 1 School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China School of Railway Tracks and Transportation, East China Jiaotong University, Nanchang 330013, China 2 Correspondence should be addressed to Wenliang Zhou; zwl Received 6 February 2015; Accepted 24 March 2015 Academic Editor: Carmen Coll Copyright © 2015 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. For providing passengers with periodic operation trains and making trains’ time distribution better fit that of passengers, the multiperiod mixed train schedule is first proposed in this paper. It makes each type of train having same origin, destination, route, and stop stations operate based on a periodic basis and allows different types of train to have various operation periods. Then a model of optimizing multiperiod mixed train schedule is built to minimize passengers generalized travel costs with the constraints of trains of same type operating periodically, safe interval requirements of trains’ departure, and arrival times, and so forth. And its heuristic algorithm is designed to optimize the multiperiod mixed train schedule beginning with generating an initial solution by scheduling all types of train type by type and then repeatedly improving their periodic schedules until the objective value cannot be reduced or the iteration number reaches its maximum. Finally, example results illustrate that the proposed model and algorithm can effectively gain a better multiperiod mixed train schedule. However, its passengers deferred times and advanced times are a little higher than these of an aperiodic train schedule. 1. Introduction Train schedule which determines all trains’ arrival times, departures times, and dwell times at stations is the cornerstone of trains organization and operation for rail enterprise. Generally, it is formulated based on a predesigned train plan which has stipulated all trains origin and destination stations, routes, stop stations, and operation frequencies. However, there are still very few studies such as Michaelis and Schöbel [1], Kaspi and Raviv [2], and Zhou et al. [3] trying to optimize train plan and train schedule integrally in recent years. Obviously, a high-quality train schedule not only contributes to providing passengers with less in-vehicle times and waiting times at origins, but also can bring railway enterprise great convenience in trains organization and operation, which can effectively improve the competitiveness of rail transit in passenger public transportation market. Moreover, train schedule is also the basis of designing the usage plan of railway Electric Multiple Units or locomotives and crew schedule. Surely a better train schedule can effectively reduce the usage count of Electric Multiple Units and crews, which means that more investment and operation costs will be saved for rail enterprise. According to train organization mode, train schedule can be divided into two types, namely, periodic train schedule and aperiodic train schedule. Periodic train schedule makes trains operate on a periodic basis, for example, 1 hour, and has the obvious advantage of regularity of train operation, which is convenient for passengers to be familiar with. Thus, it has been widely adopted in not only high-speed railway but also urban railway system in the world, especially in Japan and European countries. Regarding the optimizing approach of periodic train schedule, trains of peak hour in one day are generally scheduled firstly and then they are copied to other nonpeak hours, and some trains of nonpeak hours are deleted for fitting the decrease of passenger demand. Periodic train scheduling for railway is usually modeled by the Periodic Event Scheduling Problem (PESP) which was first proposed by Willem and Peeters [4]. The main advantage of this model is easily to describe many requirements that 2 practitioners impose on periodic train schedule. Moreover, Liebchen [5] further integrated symmetry into it, and Caimi et al. [6] extended it to propose the Flexible Periodic Event Scheduling Problem (FPESP), which can generate flexible time slots for the departure and arrival times instead of exact times. Besides the PESP model, Serafini and Ukovich [7] proposed a mathematical model for scheduling periodic events with particular time constraints and designed an algorithm of implicit enumeration type for it. Odijk [8] used a mathematical model consisting of periodic time window constraints to construct periodic train schedule. Lindner and Zimmermann [9] developed a mixed integer linear programming model of periodic train schedule with the aim of minimizing operational cost and then decomposed it for being solved by an algorithm integrating cutting plane and branch-and-bound method. For more studies about periodic train schedule, refer to Nachtigall [10], Liebchen [11], and Liebchen and Möhring [12]. Compared with periodic train schedule, aperiodic train schedule has not the periodic regularity of train operation and is optimized integrally based on the time-distance distribution of passenger demand in one day. As aperiodic train scheduling need not consider train periodic operation restriction, and it has more flexibility to arrange trains arrival and departure times. Thus, it can make trains’ time distribution fit that of passenger demand better, which contributes not only to reducing passengers deferred times or advanced times at origin stations, but also improving rail enterprise operation efficiency. Since now, many studies have strived to optimize the aperiodic train schedule with different objectives such as minimizing train travel time and maximizing passenger travel cost using many approaches including mathematics programming method, simulation method, and artificial intelligence method. For example, Szpigel [13] first developed a linear programming model to optimize the aperiodic train schedule for minimizing trains total travel time. Higgins et al. [14] developed a branchand-bound solution framework to optimize aperiodic train schedule. And Zhou and Zhong [15] further applied a lagrangian-relaxation-based lower bound rule, an exact lower bound rule, and a tight upper bound rule into it to improve the optimizing quality and efficiency. Carey and Lockwood [16, 17] developed an iterative decomposition approach which contains several node branches, variable fixing, and bounding strategies to solve the train scheduling and pathing problems. (...truncated)