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Combining Local Search into Genetic Algorithm for Bus Schedule Coordination through Small Timetable Modifications

  • Yinghui WuEmail author
Article
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Abstract

Synchronizing bus arrival and departure times at transfer stations could reduce excess transfer times. This paper addresses the planning level of bus schedule coordination problem through small timetable modifications to given an initial timetable. Timetable modifications consist of shifts in initial departure times of vehicles from the depot. Headway-sensitive passenger demand is also considered in this problem. A nonlinear mixed integer-programming model is proposed for the problem to maximize the number of total transferring passengers with smalll excess transfer times. Based on the analysis of the proposed model, a genetic algorithm combining local search (GACLS) is designed to solve this model. Several numerical experiments are performed to show the utility and performance of GACLS. For small case, the proposed GACLS is highly effective, and can obtain the optimal solution with less time than enumeration method. For large real case, the GACLS also has good performances.

Keywords

Bus schedule coordination Nonlinear mixed integer-programming model Local search Genetic algorithm 

Notes

Acknowledgements

This work was jointly supported by grants from the National Natural Science Foundation of China (No. 71601088) and Project funded by China Postdoctoral Science Foundation (No. 2017 M610287).

References

  1. 1.
    Ceder, A.: Public Transit Planning and Operation: Theory, Modeling and Practice [M]. Elsevier, Oxford (2007)CrossRefGoogle Scholar
  2. 2.
    Desaulniers, G., Hickman, M.: Public transit. Handbooks Oper. Res. Manage. Sci. 69–120 (2007)Google Scholar
  3. 3.
    Ibarra-Rojas, O.J., Giesen, R., Rios-Solis, Y.A.: An integrated approach for timetabling and vehicle scheduling problems to analyze the trade-off between level of service and operating costs of transit networks. Transp. Res. B Methodol. 70, 35–46 (2014)CrossRefGoogle Scholar
  4. 4.
    Ibarra-Rojas, O.J., Delgado, F., Giesen, R., Muñoz, J.C.: Planning, operation, and control of bus transport systems: a literature review. Transp. Res. B Methodol. 77, 38–75 (2015)CrossRefGoogle Scholar
  5. 5.
    Petersen, H.L., Larsen, A., Madsen, O.B.G., Petersen, B., Ropke, S.: The simultaneous vehicle scheduling and passenger service problem. Transp. Sci. 47(4), 603–616 (2013)CrossRefGoogle Scholar
  6. 6.
    Ceder, A., Golany, B., Tal, O.: Creating bus timetables with maximal synchronization. Transp. Res. A Policy Pract. 35, 913–928 (2001)CrossRefGoogle Scholar
  7. 7.
    Ibarra-Rojas, O.J., Rios-Solis, Y.A.: Synchronization of bus timetabling. Transp. Res. B Methodol. 46(5), 599–614 (2012)CrossRefGoogle Scholar
  8. 8.
    Shafahi, Y., Khani, A.: A practical model for transfer optimization in a transit network: model formulations and solutions. Transp. Res. A Policy Pract. 44, 377–389 (2010)CrossRefGoogle Scholar
  9. 9.
    Cevallos, F., Zhao, F.: Minimizing transfer times in a public transit network with a genetic algorithm. Transp. Res. Rec. 1971(1), 74–79 (2006)CrossRefGoogle Scholar
  10. 10.
    Mollanejad, M., Aashtiani, H.Z., Rezaeestakhruie, H. (2011). Creating bus timetables with maximum synchronization. In: Proceedings of the 90th Annual Meeting, Transportation Research Board, Paper No. 11–4187, Washington, DCGoogle Scholar
  11. 11.
    Parbo J., Nielsen O.A., Prato C.G.: User perspectives in public transport timetable optimisation. Transportation Research Part C: Emerging Technologies. 48, 269–284 (2014)Google Scholar
  12. 12.
    Wu, J.J., Liu, M.H., et al.: Equity-based timetable synchronization optimization in urban subway network. Transport. Res. Part C. 51, 1–18 (2015a)CrossRefGoogle Scholar
  13. 13.
    Wu, Y.H., Tang, J.F., Yu, Y., Pan, Z.D.: A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time. Transport. Res. Part C. 52, 15–31 (2015b)CrossRefGoogle Scholar
  14. 14.
    Wu, Y.H., Yang, H., Tang, J.F., Yu, Y.: Multi-objective re-synchronizing of bus timetable: model, complexity and solution. Transport. Res. Part C. 67, 149–168 (2016a)CrossRefGoogle Scholar
  15. 15.
    Wu, W., Liu, R., Jin, W.: Designing robust schedule coordination scheme for transit networks with safety control margins. Transp. Res. B Methodol. 93, 495–519 (2016b)CrossRefGoogle Scholar
  16. 16.
    Wong, R.C.W., Yuen, T.W.Y., Fung, K.W., Leung, J.M.Y.: Optimizing timetable synchronization for rail mass transit. Transp. Sci. 42(1), 57–69 (2008)CrossRefGoogle Scholar
  17. 17.
    Niu, H.M., Tian, X.P., Zhou, X.S.: Demand-driven train schedule synchronization for high-speed rail lines. IEEE Trans. Intell. Transp. Syst. 16(5), 2642–2652 (2015)CrossRefGoogle Scholar
  18. 18.
    Wang, Y.H., Tang, T., et al.: Passenger-demands-oriented train scheduling for an urban rail transit network. Transport. Res. Part C. 60, 1–23 (2015)CrossRefGoogle Scholar
  19. 19.
    Kang, L.J., Zhu, X.N.: Strategic timetable scheduling for last trains in urban railway transit networks. Appl. Math. Model. 45, 209–225 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kang, L.J., Wu, J.J., et al.: A case study on the coordination of last trains for the Beijing subway network. Transp. Res. B Methodol. 72, 112–127 (2015a)CrossRefGoogle Scholar
  21. 21.
    Kang, L.J., Wu, J.J., et al.: A practical model for last train rescheduling with train delay in urban railway transit networks. Omega. 50, 29–42 (2015b)CrossRefGoogle Scholar
  22. 22.
    Kang, L.J., Zhu, X.N.: A simulated annealing algorithm for first train transfer problem in urban railway networks. Appl. Math. Model. 40(1), 419–435 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Guo, X., Wu, J.J., et al.: Timetable coordination of first trains in urban railway network: a case study of Beijing. Appl. Math. Model. 40(17-18), 8048–8066 (2016)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Guo, X., Sun, H.J., et al.: Multiperiod-based timetable optimization for metro transit networks. Transp. Res. B Methodol. 96, 46–67 (2017)CrossRefGoogle Scholar
  25. 25.
    Nesheli, M.M., Ceder, A.: A robust, tactic-based, real-time framework for public-transport transfer synchronization. Transp. Res. Part C. 60, 105–123 (2015)CrossRefGoogle Scholar
  26. 26.
    Beasley, D., Bull, D.R., Martin, R.R.: An overview of genetic algorithms: part 1, fundamentals. Univ. Comput. 15, 58–69 (1993)Google Scholar
  27. 27.
    Reeves, C.R.: Genetic algorithms for the operation researcher. INFORMS J. Comput. 9, 231–250 (1997)Google Scholar
  28. 28.
    Yu, Y., Tang, J.F., Sun, W., et al.: Combining local search into non-dominated sorting for multi-objective line-cell conversion problem. Int. J. Comput. Integr. Manuf. 26(4), 316–326 (2013)CrossRefGoogle Scholar
  29. 29.
    HaKLI, H., UGUZ, H.: A novel approach for automated land partitioning using genetic algorithm. Expert Syst. Appl. 82, 10–18 (2017)CrossRefGoogle Scholar
  30. 30.
    Chakroborty, P., Deb, K., Subrahmanyam, P.S.: Optimal scheduling of urban transit systems using genetic algorithms. J. Transp. Eng. 121(6), 544–553 (1995)CrossRefGoogle Scholar
  31. 31.
    Chakroborty, P., Deb, K., Porwal, H.: A genetic algorithm based procedure for optimal transit systems scheduling. In: Proceedings of the Fifth International Conference on Computers in Urban Planning and Urban Management, pp. 330–341. Mumbai, India (1997)Google Scholar
  32. 32.
    Chakroborty, P., Deb, K., Sharma, R.K.: Optimal fleet size distribution and scheduling of urban transit systems using genetic algorithms. Transp. Plan. Technol. 24(3), 209–226 (2001)CrossRefGoogle Scholar
  33. 33.
    Chakroborty, P.: Genetic algorithms for optimal urban transit network design. Comput. Aided Civ. Inf. Eng. 18(3), 184–200 (2003)CrossRefGoogle Scholar
  34. 34.
    Nayeem, M.A., Rahman, M.K., Rahman, M.S.: Transit network design by genetic algorithm with elitism. Transport. Res. Part C. 46, 30–45 (2014)CrossRefGoogle Scholar
  35. 35.
    Yu, Y., Tang, J.F., Gong, J., et al.: Mathematical analysis and solutions for multi-objective line-cell conversion problem. Eur. J. Oper. Res. 236(2), 774–786 (2014)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Economics and ManagementJiangsu University of Science and TechnologyZhenjiangChina
  2. 2.School of Economics and ManagementSoutheast UniversityNanjingChina

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