A genetic algorithm approach to periodic railway synchronization

Nachtigall, Karl; Voget, Stefan

doi:10.1016/0305-0548(95)00032-1

Cited by 121 publications

(48 citation statements)

References 7 publications

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“…In 2002, Giesemann [4] utilized numeration to establish a simple mathematical model and get a train timetable suitable for a small station. In 1996, Nachtigall and Voget [5] worked out a train timetable with passengers' minimum latency as the objective. In 2000, based on Serafini and Ukovich's idea, Linder [6] introduced the branch and bound method into train timetable design and rolling stock turnover programming, with the objective of a minimum train fleet.…”

Section: Introductionmentioning

confidence: 99%

Working out an incomplete cyclic train timetable for high-speed railways by computer

Yang

Tan

et al. 2010

WIT Transactions on the Built Environment

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Cyclic train timetables as a popular mode of train operation have been successfully applied for many years in European railways, especially in highspeed railways (hereinafter referred to as 'HSR'). However, in China, most studies on the train timetables of HSR still follow the traditional mode. By analyzing the characteristics of Chinese HSR, this paper proposes an incomplete cyclic timetable mode that will be more suitable for the Chinese situation. The characteristics and process of working out incomplete a cyclic train timetable are discussed. There are four key issues involved in developing this kind of timetable: (1) Adaptability analyzing. This paper analyzes the proportion of trains that can be operated cyclically in terms of the technical condition and passenger flow of each HSR in order to determine the structure of the timetable. (2) Model developing. By analyzing the condition of the Chinese HSR, the existing model is improved to solve the problem more precisely and practically. (3) Non-cyclic train path insertion. According to the travel demand of passengers, the principles and technologies of inserting non-cyclic train paths into cyclic train paths is developed. (4) Seasonal expanding. The seasonal fluctuation of passenger flow makes more non-cyclic train paths. The ways to balance the disaccord in different periods are discussed to keep the operation efficient. Furthermore, a system using VC++ is designed with consideration of the four issues in its functions and working process, based on inputting the solution of the model. Finally, a successful case of the Beijing-Shanghai HSR shows the feasibility of the incomplete cyclic timetable and the practical value of the system.

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Section: Introductionmentioning

confidence: 99%

Working out an incomplete cyclic train timetable for high-speed railways by computer

Yang

Tan

et al. 2010

WIT Transactions on the Built Environment

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“…Martinelli and Teng [11] used the Neural Network to routing in a railway. Nachtigall and Voget [12] applied the Genetic Algorithm to solve train scheduling problems. Gorman [6] used a combination of Genetic algorithm and Tabu Search for addressing the weekly routing and scheduling problem.…”

Section: Introductionmentioning

confidence: 99%

A new idea for train scheduling using ant colony optimization

Ghoseiri¹

2006

WIT Transactions on the Built Environment, Vol 88

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This paper develops a new algorithm to the train scheduling problem using Ant Colony System (ACS) meta-heuristic. At first, a mathematical model for a kind of train scheduling problem is developed and then the algorithm based on the meta-heuristic is presented to solve the problem. The problem is considered as a traveling salesman problem (TSP) wherein cities represent the trains. ACS determines the sequence of trains dispatched on the graph of the TSP. Based on the sequence obtained and removing for collisions incurred, train scheduling is determined. Numerical examples in small and medium sizes are solved by using the algorithm. The solutions are compared to the exact optimum solutions to check for quality and accuracy. Comparison of the solutions shows that the algorithm results in good enough quality and time savings. A case study is presented to illustrate the solution.

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“…This bi-level minimisation problem is extremely difficult to solve mathematically, since the timetable optimisation is a non-linear non-convex mixed integer problem (NP-Hard according to Nachtigall and Voget, 1996;Cevallos and Zhao, 2006), with passenger flows defined by the route choice model, where the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach was developed based on the idea of varying the offset of the bus lines.…”

Section: Heuristic Solution Approachmentioning

confidence: 99%

User perspectives in public transport timetable optimisation

Parbo

Nielsen

Prato

2014

Transportation Research Part C: Emerging Technologies

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a b s t r a c tThe present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line.In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers' route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence.The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD).

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A genetic algorithm approach to periodic railway synchronization

Cited by 121 publications

References 7 publications

Working out an incomplete cyclic train timetable for high-speed railways by computer

Working out an incomplete cyclic train timetable for high-speed railways by computer

A new idea for train scheduling using ant colony optimization

User perspectives in public transport timetable optimisation

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