Bus Scheduling Timetable Optimization Based on Hybrid Bus Sizes

  • Haitao Yu
  • Hongguang Ma
  • Hejia Du
  • Xiang Li
  • Randong Xiao
  • Yong DuEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 650)


For bus carriers, it is the most basic and important problem to create the bus scheduling timetable based on bus fleet configuration and passenger flow demand. Considering different technical and economic properties, vehicle capacities and limited available number of heterogeneous buses, as well as the time-space characteristics of passenger flow demand, this paper focuses on creating the bus timetables and sizing the buses simultaneously. A bi-objective optimization model is formulated, in which the first objective is to minimum the total operation cost, and the second objective is to maximum the passenger volume. The proposed model is a nonlinear integer programming, thus a genetic algorithm with self-crossover operation is designed to solve it. Finally, a case study in which the model is applied to a real-world case of a bus line in the city of Beijing, China, is presented.


Bus timetable Hybrid sizes Load factor Fleet configuration 


  1. Yan, S.Y., Chi, C.-J., Tang, C.H.: Inter-city bus routing and timetable setting under stochastic demands. Transp. Res. Part A 40, 572–586 (2006)Google Scholar
  2. Yan, Y.D., Meng, Q., Wang, S.A., Guo, X.C.: Robust optimization model of schedule design for a fixed bus route. Transp. Res. Part C 25, 113–121 (2012)CrossRefGoogle Scholar
  3. Vissat, L.L., Clark, A., Gilmore, S.: Finding optimal timetables for Edinburgh bus routes. Electron. Notes Theoret. Comput. Sci. 310(310), 179–199 (2015)CrossRefGoogle Scholar
  4. Wong, S.C., Tong, C.O.: A stochastic transit assignment model using a dynamic schedule-based network. Transp. Res. Part B 33, 107–121 (1999)CrossRefGoogle Scholar
  5. Ceder, A., Golany, B., Tal, O.: Creating bus timetables with maximal synchronization. Transp. Res. Part A 35, 913–928 (2001)Google Scholar
  6. Yan, S.Y., Chen, H.L.: A scheduling model and a solution algorithm for inter-city bus carriers. Transp. Res. Part A 36, 805–825 (2002)Google Scholar
  7. Wu, Y.H., Yang, H., Tang, J.F., Yu, Y.: Multi-objective re-synchronizing of bus timetable: model, complexity and solution. Transp. Res. Part C 67, 149–168 (2016)CrossRefGoogle Scholar
  8. Ceder, A., Hassold, S., Dunlop, C., Chen, I.: Improving urban public transport service using new timetabling strategies with different vehicle sizes. Int. J. Urban Sci. 17(2), 239–258 (2013)CrossRefGoogle Scholar
  9. Sun, D., Xu, Y., Peng, Z.R.: Timetable optimization for single bus line based on hybrid vehicle size model. J. Traffic Transp. Eng. 2(3), 179–186 (2015)Google Scholar
  10. Hurdle, V.F.: Minimum cost schedules for a public transportation route. Transp. Sci. 7(2), 109–137 (1973)MathSciNetCrossRefGoogle Scholar
  11. Chriqui, C., Robillard, P.: Common bus lines. Transp. Sci. 9(2), 115–121 (1975)CrossRefGoogle Scholar
  12. Niu, H.M., Zhou, X.S.: Optimizing urban rail timetable under time-dependent demand and oversaturated conditions. Transp. Res. Part C 36, 212–230 (2013)CrossRefGoogle Scholar
  13. Nguyen, S., Pallottino, A., Malucelli, F.: A modeling framework for passenger assignment on a transport network with timetables. Transp. Sci. 35(3), 238–249 (2001)CrossRefzbMATHGoogle Scholar
  14. Cominetti, R., Correa, J.: Common-lines and passenger assignment in congested. Transp. Sci. 35(3), 250–267 (2001)CrossRefzbMATHGoogle Scholar
  15. Cepeda, M., Cominetti, R., Florian, M.: A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria. Transp. Res. Part B: Methodol. 40(6), 437–459 (2006)CrossRefGoogle Scholar
  16. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Oxford (1975)zbMATHGoogle Scholar
  17. Whitley, D.: A genetic algorithm tutorial. Stat. Comput. 4(2), 65–85 (1994)CrossRefGoogle Scholar
  18. Jones, G., Willett, P., Glen, R.C., Leach, A.R., Taylor, R.: Development and validation of a genetic algorithm for flexible docking. J. Mol. Biol. 267(3), 727–748 (1997)CrossRefGoogle Scholar
  19. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Haitao Yu
    • 1
    • 2
  • Hongguang Ma
    • 3
  • Hejia Du
    • 4
  • Xiang Li
    • 4
  • Randong Xiao
    • 2
  • Yong Du
    • 2
    Email author
  1. 1.School of Computer Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Beijing Transportation Information CenterBeijingChina
  3. 3.School of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  4. 4.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina

Personalised recommendations