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An Effective Matheuristic Approach for Robust Bus Driver Rostering with Uncertain Daily Working Hours

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Computational Logistics (ICCL 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14239))

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Abstract

The bus driver rostering problem (BDRP) is a significant problem in public transportation that aims at assigning drivers to bus routes over a given time period while reducing system costs as well as inconveniences. In this work, a mixed-integer linear mathematical model is presented for the problem with the objective of minimizing the total assignment and driver dissatisfaction costs. Uncertainty is considered for the maximum daily working hours of drivers, which appears on the right-hand side of a block of constraints. A set of scenarios regarding the uncertain parameters and robust optimization are considered. A matheuristic approach is proposed consisting of a hybridization of particle swarm optimization (PSO), simulated annealing (SA) and mathematical programming of sub-problems based on the concept of partial optimization metaheuristic under special intensification conditions (POPMUSIC). It is shown that the proposed matheuristic is an effective approach for solving the BDRP by examining its performance on a set of benchmark instances.

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References

  1. Current traffic situation. https://www.der-metronom.de/fahrplan/aktuelle-verkehrslage/. Accessed 20 June 2023

  2. New survey reveals shocking shortage of bus drivers. https://www.unitetheunion.org/news-events/news/2021/november/new-survey-reveals-shocking-shortage-of-bus-drivers/. Accessed 20 June 2023

  3. Barbosa, V., Alvelos, F., Respício, A.: Bus driver rostering by column generation metaheuristics. In: Fonseca, R.J., Weber, G.-W., Telhada, J. (eds.) Computational Management Science. LNEMS, vol. 682, pp. 225–231. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-20430-7_29

    Chapter  Google Scholar 

  4. Ben-Tal, A., Nemirovski, A.: Robust solutions of uncertain linear programs. Oper. Res. Lett. 25(1), 1–13 (1999). https://doi.org/10.1016/s0167-6377(99)00016-4

    Article  Google Scholar 

  5. Bergmann, B., Hommel, G.: Improvements of general multiple test procedures for redundant systems of hypotheses. In: Bauer, P., Hommel, G., Sonnemann, E. (eds.) Multiple Hypothesenprüfung / Multiple Hypotheses Testing, vol. 70, pp. 100–115. Springer, Heidelberg (1988). https://doi.org/10.1007/978-3-642-52307-6_8

    Chapter  Google Scholar 

  6. Blickle, T., Thiele, L.: A comparison of selection schemes used in evolutionary algorithms. Evol. Comput. 4(4), 361–394 (1996). https://doi.org/10.1162/evco.1996.4.4.361

    Article  Google Scholar 

  7. Box, G.E.P., Draper, N.R.: Response Surfaces, Mixtures, and Ridge Analyses, 2nd edn. Wiley, Hoboken (2007)

    Book  Google Scholar 

  8. Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011). https://doi.org/10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

  9. Er-Rbib, S., Desaulniers, G., Elhallaoui, I., Munroe, P.: Preference-based and cyclic bus driver rostering problem with fixed days off. Public Transp. 13(2), 251–286 (2021). https://doi.org/10.1007/s12469-021-00268-y

    Article  Google Scholar 

  10. Ge, L., Kliewer, N., Nourmohammadzadeh, A., Voß, S., Xie, L.: Revisiting the richness of integrated vehicle and crew scheduling. Public Transp. (2022). https://doi.org/10.1007/s12469-022-00292-6

    Article  Google Scholar 

  11. Ge, L., Nourmohammadzadeh, A., Voß, S., Xie, L.: Robust optimization for integrated vehicle and crew scheduling based on uncertainty in the main inputs. In: The Fifth Data Science Meets Optimisation Workshop at IJCAI-22. Vienna (2022). https://sites.google.com/view/ijcai2022dso/. Accessed 30 Apr 2023

  12. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995). https://doi.org/10.1109/ICNN.1995.488968

  13. Kawase, Y., Sumita, H., Fukunaga, T.: Submodular maximization with uncertain knapsack capacity. arxiv (2018). https://arxiv.org/pdf/1803.02565

  14. Ma, J.H., Liu, T., Guan, W.: Solving balanced bus crew rostering problem with genetic algorithm. Appl. Mech. Mater. 361–363, 2070–2074 (2013). https://doi.org/10.4028/www.scientific.net/AMM.361-363.2070

    Article  Google Scholar 

  15. Maniezzo, V., Boschetti, M.A., Stützle, T.: Automatic design for matheuristics. In: Matheuristics. EURO Advanced Tutorials on Operational Research, pp. 35–57. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-70277-9_2

    Chapter  Google Scholar 

  16. Maniezzo, V., Stützle, T., Voß, S. (eds.): Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer, New York (2010). https://doi.org/10.1007/978-1-4419-1306-7

  17. Mesquita, M., Moz, M., Paias, A., Pato, M.: A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern. Eur. J. Oper. Res. 245(2), 423–437 (2015). https://doi.org/10.1016/j.ejor.2015.03.030

    Article  Google Scholar 

  18. Minoux, M.: On 2-stage robust LP with RHS uncertainty: complexity results and applications. J. Global Optim. 49(3), 521–537 (2011). https://doi.org/10.1007/s10898-010-9645-2

    Article  Google Scholar 

  19. Minoux, M.: Two-stage robust LP with ellipsoidal right-hand side uncertainty is NP-hard. Optim. Lett. 6(7), 1463–1475 (2012). https://doi.org/10.1007/s11590-011-0341-z

    Article  Google Scholar 

  20. Moz, M., Respício, A., Pato, M.V.: Bi-objective evolutionary heuristics for bus driver rostering. Public Transp. 1(3), 189–210 (2009). https://doi.org/10.1007/s12469-009-0013-x

    Article  Google Scholar 

  21. Nurmi, K., Kyngäs, J., Post, G.: Driver rostering for a Finnish bus transportation company. In: IAENG Transactions on Engineering Technologies, vol. 7, pp. 15–35. World Scientific, Singapore and Hackensack NJ (2012). https://doi.org/10.1142/9789814390019_0002

  22. Özaltın, O.Y., Prokopyev, O.A., Schaefer, A.J.: The bilevel knapsack problem with stochastic right-hand sides. Oper. Res. Lett. 38(4), 328–333 (2010). https://doi.org/10.1016/j.orl.2010.04.005

    Article  Google Scholar 

  23. Taillard, É.D., Voß, S.: POPMUSIC – partial optimization metaheuristic under special intensification conditions. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics, vol. 15, pp. 613–629. Springer, Boston (2002). https://doi.org/10.1007/978-1-4615-1507-4_27

    Chapter  Google Scholar 

  24. Xie, L., Suhl, L.: A duty-block network approach for an integrated driver rostering problem in public bus transport. In: Longhurst, J., Brebbia, C.A. (eds.) Urban Transport XVIII, pp. 295–306. WIT Transactions on The Built Environment, WIT Press Southampton, UK (2012). https://doi.org/10.2495/UT120261

  25. Xie, L., Kliewer, N., Suhl, L.: Integrated driver rostering problem in public bus transit. Procedia. Soc. Behav. Sci. 54, 656–665 (2012)

    Article  Google Scholar 

  26. Xie, L., Merschformann, M., Kliewer, N., Suhl, L.: Metaheuristics approach for solving personalized crew rostering problem in public bus transit. J. Heuristics 23(5), 321–347 (2017). https://doi.org/10.1007/s10732-017-9348-7

    Article  Google Scholar 

  27. Xie, L., Suhl, L.: Cyclic and non-cyclic crew rostering problems in public bus transit. OR Spectrum 37(1), 99–136 (2015). https://doi.org/10.1007/s00291-014-0364-9

    Article  Google Scholar 

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Acknowledgements

This research is funded by dtec.bw - Digitalization and Technology Research Center of the Bundeswehr. dtec.bw is funded by the European Union - NextGenerationEU.

The helpful comments of two reviewers are gratefully acknowledged.

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Authors and Affiliations

  1. Institute of Information Systems, University of Hamburg, Hamburg, Germany

    Abtin Nourmohammadzadeh & Stefan Voß

Authors
  1. Abtin Nourmohammadzadeh
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  2. Stefan Voß
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Corresponding author

Correspondence to Abtin Nourmohammadzadeh .

Editor information

Editors and Affiliations

  1. Hochschule für Wirtschaft und Recht Berlin, Berlin, Germany

    Joachim R. Daduna

  2. Deutsches Zentrum für Luft- und Raumfahrt (DLR), Berlin, Germany

    Gernot Liedtke

  3. Deutsches Zentrum für Luft- und Raumfahrt (DLR), Berlin, Germany

    Xiaoning Shi

  4. University of Hamburg, Hamburg, Germany

    Stefan Voß

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Nourmohammadzadeh, A., Voß, S. (2023). An Effective Matheuristic Approach for Robust Bus Driver Rostering with Uncertain Daily Working Hours. In: Daduna, J.R., Liedtke, G., Shi, X., Voß, S. (eds) Computational Logistics. ICCL 2023. Lecture Notes in Computer Science, vol 14239. Springer, Cham. https://doi.org/10.1007/978-3-031-43612-3_23

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  • DOI: https://doi.org/10.1007/978-3-031-43612-3_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43611-6

  • Online ISBN: 978-3-031-43612-3

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