Advertisement

Soft Computing

, Volume 22, Issue 21, pp 6981–6994 | Cite as

Timetable optimization for single bus line involving fuzzy travel time

  • Xiang Li
  • Hejia Du
  • Hongguang MaEmail author
  • Changjing Shang
Focus
  • 144 Downloads

Abstract

Timetable optimization is an important step for bus operations management, which essentially aims to effectively link up bus carriers and passengers. Generally speaking, bus carriers attempt to minimize the total travel time to reduce its operation cost, while the passengers attempt to minimize their waiting time at stops. In this study, we focus on the timetable optimization problem for a single bus line from both bus carriers’ perspectives and passengers’ perspectives. A bi-objective optimization model is established to minimize the total travel time for all trips along the line and the total waiting time for all passengers at all stops, in which the bus travel times are considered as fuzzy variables due to a variety of disturbances such as weather conditions and traffic conditions. A genetic algorithm with variable-length chromosomes is devised to solve the proposed model. In addition, we present a case study that utilizes real-life bus transit data to illustrate the efficacy of the proposed model and solution algorithm. Compared with the timetable currently being used, the optimal bus timetable produced from this study is able to reduce the total travel time by 26.75% and the total waiting time by 9.96%. The results demonstrate that the established model is effective and useful to seek a practical balance between the bus carriers’ interest and passengers’ interest.

Keywords

Timetable optimization Fuzzy variable Travel time Waiting time Genetic algorithm 

Notes

Funding

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\(\hat{\text {e}}\)r Cymru National Research Network for Low Carbon, Energy and Environment (NRN-LCEE), and partly by a S\(\hat{\text {e}}\)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 or animal participants performed by the author.

References

  1. Arhin S, Noel E, Anderson MF, Williams L, Ribisso A, Stinson R (2016) Optimization of transit total bus stop time models. J Traffic Transp Eng 3(2):146–153Google Scholar
  2. Amin-Naseri MR, Baradaran V (2014) Accurate estimation of average waiting time in public transportation systems. Transp Sci 49(2):213–222CrossRefGoogle Scholar
  3. Ban JX, Liu HX, Yang F, Ran B (2014) A traffic assignment model with fuzzy travel time perceptions. 12th World Congress on Intelligent Transport Systems 6:3385–3396Google Scholar
  4. Bertini RL, El-Geneidy AM (2004) Modeling transit trip time using archived bus dispatch system data. J Transp Eng 130(1):56–67CrossRefGoogle Scholar
  5. Brito J, MartiNez FJ, Moreno JA, Verdegay JL (2010) Fuzzy approach for vehicle routing problems with fuzzy travel time. IEEE Int Conf Fuzzy Syst 23(3):1–8Google Scholar
  6. Ceder A, Golany B, Tal O (2001) Creating bus timetables with maximal synchronization. Transp Res Part A: Policy Pract 35(10):913–928Google Scholar
  7. Chen JX, Liu ZY, Zhu SL, Wang W (2015) Design of limited-stop bus service with capacity constraint and stochastic travel time. Transp Res Part E: Logist Transp Rev 83:1–15CrossRefGoogle Scholar
  8. Ceder A, Philibert L (2014) Transit timetables resulting in even maximum load on individual vehicles. IEEE Trans Intell Transp Syst 15(6):2605–2614CrossRefGoogle Scholar
  9. Djadane M, Goncalves G, Hsu T, Dupas R (2007) Dynamic vehicle routing problems under flexible time windows and fuzzy travel times. Int Conf Serv Syst Serv Manag 2:1519–1524Google Scholar
  10. Guihaire V, Hao JK (2008) Transit network design and scheduling: a global review. Transp Res Part A: Policy Pract 42(10):1251–1273Google Scholar
  11. Hassold S, Ceder A (2014) Public transport vehicle scheduling featuring multiple vehicle types. Transp Res Part B: Methodol 67(9):129–143CrossRefGoogle Scholar
  12. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial Intelligence. University of Michigan Press, OxfordzbMATHGoogle Scholar
  13. Huang YR, Yang LX, Tang T, Cao F, Gao ZY (2016) Saving energy and improving service quality: bicriteria train scheduling in urban rail transit systems. IEEE Trans Intell Transp Syst 17(12):3364–3379CrossRefGoogle Scholar
  14. Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450CrossRefGoogle Scholar
  15. Li X, Liu B (2006) A sufficient and necessary condition for credibility measures. Int J Uncertain Fuzziness Knowl-Based Syst 14(5):527–535MathSciNetCrossRefGoogle Scholar
  16. Liu ZY, Yan YD, Qu XB, Zhang Y (2013) Bus stop-skipping scheme with random travel time. Transp Res Part C: Emerg Technol 35(9):46–56CrossRefGoogle Scholar
  17. Niu HM, Zhou XS (2013) Optimizing urban rail timetable under time-dependent demand and oversaturated conditions. Transp Res Part C: Emerg Technol 36:212–230CrossRefGoogle Scholar
  18. Parbo J, Nielsen OA, Prato CG (2014) User perspectives in public transport timetable optimisation. Transp Res Part C: Emerg Technol 48:269–284CrossRefGoogle Scholar
  19. Pillai AS, Singh K, Saravanan V, Anpalagan A, Woungang I, Barolli L (2018) A genetic algorithm-based method for optimizing the energy consumption and performance of multiprocessor systems. Soft Comput 22(10):3271–3285CrossRefGoogle Scholar
  20. Salicrú M, Fleurent C, Armengol JM (2011) Timetable-based operation in urban transport: run-time optimisation and improvements in the operating process. Transp Res Part A: Policy Pract 45(8):721–740Google Scholar
  21. Sels P, Dewilde T, Cattrysse D, Vansteenwegen P (2016) Reducing the passenger travel time in practice by the automated construction of a robust railway timetable. Transp Res Part B: Methodol 84:124–156CrossRefGoogle Scholar
  22. Sun D, Xu Y, Peng ZR (2015) Timetable optimization for single bus line based on hybrid vehicle size model. J Traffic Transp Eng 2(3):179–186Google Scholar
  23. Tong CO, Wong SC (1999) A stochastic transit assignment model using a dynamic schedule-based network. Transp Res Part B: Methodol 33(2):107–121CrossRefGoogle Scholar
  24. Ting CK, Wang TC, Liaw RT, Hong TP (2017) Genetic algorithm with a structure-based representation for genetic-fuzzy data mining. Soft Comput 21:2871–2885CrossRefGoogle Scholar
  25. Vissat LL, Clark A, Gilmore S (2015) Finding optimal timetables for Edinburgh bus routes. Electron Notes Theor Comput Sci 310:179–199CrossRefGoogle Scholar
  26. Wei M, Sun B (2017) Bi-level programming model for multi-modal regional bus timetable and vehicle dispatch with stochastic travel time. Clust Comput 20(1):1–11MathSciNetCrossRefGoogle Scholar
  27. Wu YH, Tang JF, Yu Y, Pan ZD (2015) A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time. Transp Res Part C: Emerg Technol 52:15–31CrossRefGoogle Scholar
  28. Wu YH, Yang H, Tang JF, Yu Y (2016) Multi-objective re-synchronizing of bus timetable: model, complexity and solution. Transp Res Part C: Emerg Technol 67:149–168CrossRefGoogle Scholar
  29. Wong SC, Tong CO (1999) A stochastic transit assignment model using a dynamic schedule-based network. Transp Res Part B: Methodol 33(2):107–121CrossRefGoogle Scholar
  30. Yan SY, Chen HL (2002) A scheduling model and a solution algorithm for inter-city bus carriers. Transp Res Part A: Policy Pract 36(9):805–825Google Scholar
  31. Yan YD, Meng Q, Wang SA, Guo XC (2012) Robust optimization model of schedule design for a fixed bus route. Transp Res Part C: Emerg Technol 25(8):113–121CrossRefGoogle Scholar
  32. Yan SY, Chi CJ, Tang CH (2006) Inter-city bus routing and timetable setting under stochastic demands. Transp Res Part A: Policy Pract 40(7):572–586Google Scholar
  33. Zhao F, Zeng X (2008) Optimization of transit route network, vehicle headways and timetable for large-scle transit networks. Eur J Oper Res 186(2):841–855CrossRefGoogle Scholar
  34. Zuo XQ, Chen C, Tan W, Zhou MC (2015) Vehicle scheduling of an urban bus line via an improved multiobjective genetic algorithm. IEEE Trans Intell Transp Syst 16(2):1030–1041Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Beijing Advanced Innovation Center for Soft Matter Science and EngineeringBeijing University of Chemical TechnologyBeijingChina
  2. 2.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina
  3. 3.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  4. 4.Department of Computer ScienceAberystwyth UniversityAberystwythUK

Personalised recommendations