A Cycle Based Optimization Model for the Cyclic Railway Timetabling Problem

Peeters, Leon; Kroon, Leo

doi:10.1007/978-3-642-56423-9_16

Cited by 37 publications

(25 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The integer variables are redefined to count the number of period jumps along cycles of the PESP graph. This reformulation, known as the Cycle Periodicity Formulation (Peeters and Kroon 2001), is more efficient when PESP is solved by MIP solvers, because redundancies in the integer solution space are removed and that better cutting planes can be found.…”

Section: The Periodic Event Scheduling Problemmentioning

confidence: 99%

A multi-level framework for generating train schedules in highly utilised networks

Caimi¹,

Fuchsberger

Laumanns

et al. 2011

Public Transp

View full text Add to dashboard Cite

This paper proposes a comprehensive multi-level framework for railway scheduling, which starts with a high-level commercial description of intended train services and aims to generates a conflict-free detailed schedule as the final outcome. The approach consists of three description levels and corresponding interfaces that enable a structured decomposition of the scheduling problem into sub-problems of manageable size. The starting point is a formal structure for describing the service intention including periodicity information. As typical timetables are neither entirely periodic nor aperiodic, a projection scheme is used to create an augmented periodic problem. This augmented periodic timetabling problem is solved first globally on an aggregated topology and simplified safety model, and subsequently refined locally by considering all details of the infrastructure and train dynamics. In particular, a new model is used that solves the local problem in station areas more efficiently and faster than previous model, which is crucial for the interaction of the different levels. Finally, the generated periodic conflict-free schedule is rolled out over the complete day to create a production plan fulfilling all requirements specified in the service in-4 G. Caimi et al.tention. The presented approach is finally tested and illustrated on a real-world case study for the train services currently in place in the Lucerne region, a highly utilised part of railway network in central Switzerland. There, it is possible to perform the complete procedure in less than 10 minutes. The generated solution is optimal in each step of the multi-level approach and has a comparable quality with the operated schedule.

show abstract

Section: The Periodic Event Scheduling Problemmentioning

confidence: 99%

A multi-level framework for generating train schedules in highly utilised networks

Caimi¹,

Fuchsberger

Laumanns

et al. 2011

Public Transp

View full text Add to dashboard Cite

show abstract

“…Peeters and Kroon [2] presented a mixed-integer nonlinear programming formulation for cyclic railway timetabling, where the integer variables corresponded to cycles in the graph induced by the constraints. Albrecht and Oettich [3] proposed an algorithm for the dynamic modification of train running times to increase the probability of making connections to other means of public transport.…”

Section: Literature Reviewmentioning

confidence: 99%

Last-Train Timetabling under Transfer Demand Uncertainty: Mean-Variance Model and Heuristic Solution

Yang

Gao

et al. 2017

Journal of Advanced Transportation

View full text Add to dashboard Cite

Traditional models of timetable generation for last trains do not account for the fact that decision-maker (DM) often incorporates transfer demand variability within his/her decision-making process. This study aims to develop such a model with particular consideration of the decision-makers' risk preferences in subway systems under uncertainty. First, we formulate an optimization model for last-train timetabling based on mean-variance (MV) theory that explicitly considers two significant factors including the number of successful transfer passengers and the running time of last trains. Then, we add the mean-variance risk measure into the model to generate timetables by adjusting the last trains' departure times and running times for each line. Furthermore, we normalize two heterogeneous terms of the risk measure to provide assistance in getting reasonable results. Due to the complexity of MV model, we design a tabu search (TS) algorithm with specifically designed operators to solve the proposed timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the proposed MV model and the heuristic approach.

show abstract

“…The problem is then solved by branch-and-bound for small size instances by computing bounds through the relaxation of these disjunctive constraints. Jovanovic and Harker [33] [38], and Peeters and Kroon [49] consider the case in which the timetable is identical with a period of one hour (rather than one day as it is the case of the problem considered in the other references), and address the general case of a railway network instead of a single (main) line. The problem is solved through a mixed integer linear programming formulation in which the times are again represented by continuous variables and integer variables are used to impose that the differences between pairs of time variables belong to a certain interval modulo one hour.…”

Section: Introductionmentioning

confidence: 99%

Models and algorithms for combinatorial optimization problems arising in railway applications

Cacchiani

2008

4OR-Q J Oper Res

View full text Add to dashboard Cite

A Cycle Based Optimization Model for the Cyclic Railway Timetabling Problem

Cited by 37 publications

References 3 publications

A multi-level framework for generating train schedules in highly utilised networks

A multi-level framework for generating train schedules in highly utilised networks

Last-Train Timetabling under Transfer Demand Uncertainty: Mean-Variance Model and Heuristic Solution

Models and algorithms for combinatorial optimization problems arising in railway applications

Contact Info

Product

Resources

About