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Soft Computing

, Volume 22, Issue 21, pp 6995–7003 | Cite as

A minimum-cost model for bus timetabling problem

  • Haitao Yu
  • Hongguang Ma
  • Changjing Shang
  • Xiang Li
  • Randong Xiao
  • Yong DuEmail author
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Abstract

In urban traffic, a bus’ running speed is greatly influenced by the time-dependent road conditions. Based on historical GPS data, this paper formulates a bus’ running speed between each pair of adjacent stops as a step function. A minimum-cost timetabling model is proposed, in which the total operation cost consists of the cost for a fixed setup and that for variable fuel consumption. Furthermore, a genetic algorithm with self-crossover operation is used to optimize the proposed integer nonlinear programming model. Finally, a real-world case study of Yuntong 128 bus line in Beijing is presented. Comparisons among popular timetabling models are given, involving time-dependent running speed, minimum running speed, maximum running speed and average running speed. The results demonstrate that the consideration of time-dependent running speed is helpful to improve the prediction accuracy of the fuel consumption cost by around 12.7%.

Keywords

Bus timetabling Time-dependent speed Fuel consumption Genetic algorithm 

Notes

Acknowledgements

This work was partly supported by Grants from the National Natural Science Foundation of China (No. 71722007), partly by the Welsh Government and Higher Education Funding Council for Wales through the S\(\hat{e}\)r Cymru National Research Network for Low Carbon, Energy and Environment (NRN-LCEE), and partly by a S\(\hat{e}\)r Cymru II COFUND Fellowship, UK.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest in this research.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Haitao Yu
    • 1
    • 2
  • Hongguang Ma
    • 3
  • Changjing Shang
    • 4
  • Xiang Li
    • 4
    • 5
  • Randong Xiao
    • 2
  • Yong Du
    • 2
    Email author
  1. 1.School of Computer Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Beijing Key Laboratory for Comprehensive Traffic Operation Monitoring and ServiceBeijing Transportation Information CenterBeijingChina
  3. 3.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  4. 4.Department of Computer ScienceAberystwyth UniversityAberystwythUK
  5. 5.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina

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