An Optimization to Schedule Train Operations with Phase‐Regular Framework for Intercity Rail Lines

Abstract

The most important operating problem for intercity rail lines, which are characterized with the train operations at rapid speed and high frequency, is to design a service-oriented schedule with the minimum cost. This paper proposes a phase-regular scheduling method which divides a day equally into several time blocks and applies a regular train-departing interval and the same train length for each period under the period-dependent demand conditions. A nonlinear mixed zero-one programming model, which could accurately calculate the passenger waiting time and the in-train crowded cost, is developed in this study. A hybrid genetic algorithm associated with the layered crossover and mutation operation is carefully designed to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is illustrated through the application to Hefei-Wuhan intercity rail line in China.

Optimization of Public Transport Services to Minimize Passengers’ Waiting Times and Maximize Vehicles’ Occupancy Ratios

“…Desired occupancy of each vehicle: 70; • Possible departure time (in minutes) at the first terminal is defined by the time intervals for each service respectively: [16,30], [31,45] [13,24], [25,36], [37,48] [11,20], [21,30], [31,40], [41,50], [51,60]. Table 4 presents the combined results of the proposed method using MOPSO algorithm and the results from the literature.…”

“…A comparison of the presented model against the B&B method and greedy-based heuristic algorithm for using the PRTS simulation algorithm to solve the problem of schedules shows that the given model provides a better indicator for PRTS problem and numerical indicators of optimization functions. The problem of minimizing PWT at the station and the cost of vehicle occupancy is solved using the genetic algorithm in [25]. The models developed for solving the problem of minimizing PWT at the station are defined with preserving the flow of passengers waiting at the station, as shown in [26,27].…”

Optimization Methods in Modern Transportation Systems

“…Phase-regular scheduling (PRS) method that divides the day into a few periods of equal length is shown in [27]. The stations are all marked with 1, 2, …, k, and the trains have the same speeds between stations.…”

“…The occupancy of the vehicle ( ( ) i j Q t ) is the sum of the passengers that remained in the vehicle j, at the station i and passenger entered in the vehicle j at the moment τ. The hybrid genetic algorithm is used for solving the problem on the example of intercity railway line in China consisting of five stations [27].…”

A Branch and Bound Algorithm and Iterative Reordering Strategies for Inserting Additional Trains in Real Time: A Case Study in Germany

“…Based on graph theory he uses integer programming model (IP) formulation and suggests various heuristic solution approaches to solve large-scale real-world instances to optimality. In addition, papers such as [9][10][11][12][13] also present innovative models which are of certain reference value in the field of railway operation optimization. Furthermore, there are indications that some of the previous models and techniques in job shop scheduling could be modified and adapted to solve the TETPI problem.…”