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In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An…

Data Structures and Algorithms · Computer Science 2021-03-02 Bernardo Martin-Iradi , Stefan Ropke

Periodic timetables are widely adopted in passenger railway operations due to their regular service patterns and well-coordinated train connections. However, fluctuations in passenger demand require varying train services across different…

Optimization and Control · Mathematics 2025-11-14 Zhiyuan Yao , Anita Schöbel , Lei Nie , Sven Jäger

Because of the long planning periods and their long life cycle, railway infrastructure has to be outlined long ahead. At the present, the infrastructure is designed while only little about the intended operation is known. Hence, the…

Computational Complexity · Computer Science 2023-08-02 Nadine Friesen , Tim Sander , Karl Nachtigall , Nils Nießen

A seemingly simple, yet widely applicable subroutine in automated train scheduling is the insertion of a new train path to a timetable in a railway network. We believe it to be the first step towards a new train-rerouting framework in case…

Data Structures and Algorithms · Computer Science 2024-10-29 David Dekker , Carl Henrik Häll , Anders Peterson , Christiane Schmidt

Train scheduling is one of the significant issues in the railway industry in recent years since it has an important role in efficacy of railway infrastructure. In this paper, the timetabling problem of a multiple tracked railway network is…

Optimization and Control · Mathematics 2016-12-13 Afshin Oroojlooy Jadid , Kourosh Eshghi

In this paper we present a framework of key algorithms and data-structures for efficiently generating timetables for any number of AGVs from any given positioning on any given graph to accomplish any given demands as long as a few easily…

Computational Engineering, Finance, and Science · Computer Science 2023-10-19 James Forster

Train timetabling is a difficult and very tightly constrained combinatorial problem that deals with the construction of train schedules. We focus on the particular problem of local reconstruction of the schedule following a small…

Artificial Intelligence · Computer Science 2007-05-23 Marc Schoenauer , Yann Semet

The railway timetables are designed in an optimal manner to maximize the capacity usage of the infrastructure concerning different objectives besides avoiding conflicts. The real-time railway traffic management problem occurs when the…

Optimization and Control · Mathematics 2024-10-28 László Lindenmaier , István Ferenc Lövétei , Szilárd Aradi

Regenerating braking energy is one major pathway to make rail traffic energy-efficient. It is therefore desirable to design timetables that exploit this feature. However, timetables that allow to regenerate energy are often bad for the…

Optimization and Control · Mathematics 2026-05-05 Sarah Roth , Sven Jäger , Niels Lindner , Anita Schöbel

Train timetable rescheduling (TTR) aims to promptly restore the original operation of trains after unexpected disturbances or disruptions. Currently, this work is still done manually by train dispatchers, which is challenging to maintain…

Machine Learning · Computer Science 2024-01-17 Peng Yue , Yaochu Jin , Xuewu Dai , Zhenhua Feng , Dongliang Cui

Using strategic timetables as input for railway network design has become increasingly popular among western European railway infrastructure operators. Although both railway timetabling and railway network design on their own are well…

Optimization and Control · Mathematics 2023-08-02 Tim Sander , Nadine Friesen , Karl Nachtigall , Nils Nießen

This paper defines and solves a mathematical model for finding robust periodic timetables by proposing an extension of the Periodic Event Scheduling Problem (PESP). In order to model delayed and not nominal travel times already in the…

Optimization and Control · Mathematics 2019-07-11 Julius Pätzold

Periodic messages transfer data from sensors to actuators in cars, planes, and complex production machines. When considering a given routing, the unicast message starts at its source and goes over several dedicated resources to reach its…

Networking and Internet Architecture · Computer Science 2025-06-18 Josef Grus , Claire Hanen , Zdeněk Hanzálek

Disruptions in the operational flow of rail traffic can lead to conflicts between train movements, such that a scheduled timetable can no longer be realised. This is where dispatching is applied, existing conflicts are resolved and a…

Optimization and Control · Mathematics 2025-02-26 Maik Schälicke , Karl Nachtigall

Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further…

Optimization and Control · Mathematics 2025-10-15 Stephanie Riedmüller , Niels Lindner

The train timetabling problem in liberalized railway markets represents a challenge to the coordination between infrastructure managers and railway undertakings. Efficient scheduling is critical to maximizing infrastructure capacity and…

Railway scheduling and timetabling are common stages in the classical hierarchical railway planning process and they perhaps represent the step with major influence on user's perception about quality of service. This aspect, in conjunction…

Optimization and Control · Mathematics 2017-01-24 David Canca , Eva Barrena , Encarnación Algaba , Alejandro Zarzo

The local reconstruction of a railway schedule following a small perturbation of the traffic, seeking minimization of the total accumulated delay, is a very difficult and tightly constrained combinatorial problem. Notoriously enough, the…

Artificial Intelligence · Computer Science 2007-05-23 Yann Semet , Marc Schoenauer

This paper investigates the impact of hybridizing a multi-modal Genetic Algorithm with a Graph Neural Network for timetabling optimization. The Graph Neural Network is designed to encapsulate general domain knowledge to improve schedule…

Neural and Evolutionary Computing · Computer Science 2026-02-10 Laura-Maria Cornei , Mihaela-Elena Breabăn

In many countries, a rail network consists of single lines with sidings where interactions between trains occur (meet, pass). In this paper, we study two issues of these networks: first, the scheduling of freight trains in a single line…

Optimization and Control · Mathematics 2019-12-11 Marie Alaghband , Babak Farhang Moghaddam
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