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.
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References
Ceder, A.: Public Transit Planning and Operation: Theory, Modeling and Practice [M]. Elsevier, Oxford (2007)
Desaulniers, G., Hickman, M.: Public transit. Handbooks Oper. Res. Manage. Sci. 69–120 (2007)
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)
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)
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)
Ceder, A., Golany, B., Tal, O.: Creating bus timetables with maximal synchronization. Transp. Res. A Policy Pract. 35, 913–928 (2001)
Ibarra-Rojas, O.J., Rios-Solis, Y.A.: Synchronization of bus timetabling. Transp. Res. B Methodol. 46(5), 599–614 (2012)
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)
Cevallos, F., Zhao, F.: Minimizing transfer times in a public transit network with a genetic algorithm. Transp. Res. Rec. 1971(1), 74–79 (2006)
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, DC
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)
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)
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)
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)
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)
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)
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)
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)
Kang, L.J., Zhu, X.N.: Strategic timetable scheduling for last trains in urban railway transit networks. Appl. Math. Model. 45, 209–225 (2017)
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)
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)
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)
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)
Guo, X., Sun, H.J., et al.: Multiperiod-based timetable optimization for metro transit networks. Transp. Res. B Methodol. 96, 46–67 (2017)
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)
Beasley, D., Bull, D.R., Martin, R.R.: An overview of genetic algorithms: part 1, fundamentals. Univ. Comput. 15, 58–69 (1993)
Reeves, C.R.: Genetic algorithms for the operation researcher. INFORMS J. Comput. 9, 231–250 (1997)
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)
HaKLI, H., UGUZ, H.: A novel approach for automated land partitioning using genetic algorithm. Expert Syst. Appl. 82, 10–18 (2017)
Chakroborty, P., Deb, K., Subrahmanyam, P.S.: Optimal scheduling of urban transit systems using genetic algorithms. J. Transp. Eng. 121(6), 544–553 (1995)
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)
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)
Chakroborty, P.: Genetic algorithms for optimal urban transit network design. Comput. Aided Civ. Inf. Eng. 18(3), 184–200 (2003)
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)
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)
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).
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Wu, Y. Combining Local Search into Genetic Algorithm for Bus Schedule Coordination through Small Timetable Modifications. Int. J. ITS Res. 17, 102–113 (2019). https://doi.org/10.1007/s13177-018-0165-7
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DOI: https://doi.org/10.1007/s13177-018-0165-7