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A minimum-cost model for bus timetabling problem

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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%.

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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.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Beihang University, Beijing, 100191, China

    Haitao Yu

  2. Beijing Key Laboratory for Comprehensive Traffic Operation Monitoring and Service, Beijing Transportation Information Center, Beijing, 100161, China

    Haitao Yu, Randong Xiao & Yong Du

  3. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    Hongguang Ma

  4. Department of Computer Science, Aberystwyth University, Aberystwyth, UK

    Changjing Shang & Xiang Li

  5. School of Economics and Management, Beijing University of Chemical Technology, Beijing, 100029, China

    Xiang Li

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  1. Haitao Yu
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  2. Hongguang Ma
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  3. Changjing Shang
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  4. Xiang Li
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  5. Randong Xiao
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  6. Yong Du
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Correspondence to Yong Du.

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Communicated by P. Angelov, F. Chao.

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Yu, H., Ma, H., Shang, C. et al. A minimum-cost model for bus timetabling problem. Soft Comput 22, 6995–7003 (2018). https://doi.org/10.1007/s00500-018-3279-6

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  • DOI: https://doi.org/10.1007/s00500-018-3279-6

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