Skip to main content

A parallelized matheuristic for the International Timetabling Competition 2019

Abstract

The International Timetabling Competition 2019 (ITC 2019) presents a novel and generalized university timetabling problem composed of traditional class time and room assignment and student sectioning. In this paper, we present a parallelized matheuristic tailored to the ITC 2019 problem. The matheuristic is composed of multiple methods using the graph-based mixed-integer programming (MIP) model defined for the ITC 2019 problem by Holm et al. (A graph-based MIP formulation of the International Timetabling Competition 2019. J Sched, 2022. https://doi.org/10.1007/s10951-022-00724-y). We detail all methods included in the parallelized matheuristic and the collaboration between them. The parallelized matheuristic includes two methods for producing initial solutions and uses a fix-and-optimize matheuristic to improve solutions. Additionally, the method uses the full MIP model to calculate lower bounds. We describe how the methods perform collaboratively through solution sharing, and a diversification scheme invoked when the search stagnates. Furthermore, we explain how we decompose the problem for instances with a large number of students. We evaluate components of the parallelized matheuristic using the 30 benchmark instances of the ITC 2019. The complete parallelized matheuristic performs well, even solving some instances to proven optimality. The presented method is the winning algorithm of the competition, further demonstrating its quality.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

  1. An updated table is available at https://dsumsoftware.com/itc2019/.

References

  • Bettinelli, A., Cacchiani, V., Roberti, R., & Toth, P. (2015). An overview of curriculum-based course timetabling. Top, 23(2), 313–349. https://doi.org/10.1007/s11750-015-0363-2

    Article  Google Scholar 

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2010). Decomposition, reformulation, and diving in university course timetabling. Computers & Operations Research, 37(3), 582–597. https://doi.org/10.1016/j.cor.2009.02.023 Hybrid Metaheuristics.

    Article  Google Scholar 

  • Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2012). A branch-and-cut procedure for the Udine Course Timetabling problem. Annals of Operations Research, 194(1), 71–87. https://doi.org/10.1007/s10479-010-0828-5

    Article  Google Scholar 

  • Di Gaspero, L., Mccollum, B., & Schaerf, A. (2007). The second International Timetabling Competition (ITC-2007): Curriculum-based course timetabling (Track 3). Technical report. Technical Report QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0, Queen’s University, Belfast.

  • Dorneles, Á. P., de Araújo, O. C., & Buriol, L. S. (2014). A fix-and-optimize heuristic for the high school timetabling problem. Computers & Operations Research, 52, 29–38.

    Article  Google Scholar 

  • Fonseca, G. H., Santos, H. G., & Carrano, E. G. (2016). Integrating matheuristics and metaheuristics for timetabling. Computers & Operations Research, 74, 108–117. https://doi.org/10.1016/j.cor.2016.04.016

    Article  Google Scholar 

  • Glover, F., Laguna, M., & Martí, R. (2000). Fundamentals of scatter search and path relinking. Control and Cybernetics, 29(3), 653–684.

    Google Scholar 

  • Helber, S., & Sahling, F. (2010). A fix-and-optimize approach for the multi-level capacitated lot sizing problem. International Journal of Production Economics, 123(2), 247–256.

    Article  Google Scholar 

  • Holm, D., Mikkelsen, R., Sørensen, M., & Stidsen, T. (2020). A graph-based MIP formulation of the international timetabling competition 2019. Journal of Scheduling. https://doi.org/10.1007/s10951-022-00724-y

  • Kristiansen, S. & Stidsen, T. (2013). A Comprehensive Study of Educational Timetabling—a Survey. Number 8.2013 in DTU Management Engineering Report. DTU Management Engineering.

  • Lach, G., & Lübbecke, M. E. (2012). Curriculum based course timetabling: New solutions to Udine benchmark instances. Annals of Operations Research, 194(1), 255–272. https://doi.org/10.1007/s10479-010-0700-7

    Article  Google Scholar 

  • Lang, J. C., & Shen, Z.-J.M. (2011). Fix-and-optimize heuristics for capacitated lot-sizing with sequence-dependent setups and substitutions. European Journal of Operational Research, 214(3), 595–605.

    Article  Google Scholar 

  • Lewis, R., Paechter, B., & Mccollum, B. (2007). Post enrolment based course timetabling: A description of the problem model used for track two of the second International Timetabling Competition. In Cardiff Working Papers in Accounting and Finance A2007-3, Cardiff Business School, Cardiff University.

  • Lindahl, M., Sørensen, M., & Stidsen, T. R. (2018). A fix-and-optimize matheuristic for university timetabling. Journal of Heuristics, 24(4), 645-665.

    Article  Google Scholar 

  • McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Di Gaspero, L., Qu, R., & Burke, E. K. (2010). Setting the research agenda in automated timetabling: The second International Timetabling Competition. INFORMS Journal on Computing, 22(1), 120–130. https://doi.org/10.1287/ijoc.1090.0320

    Article  Google Scholar 

  • Müller, T., Rudová, H., & Müllerová, Z. (2018a). University course timetabling and International Timetabling Competition 2019. In Burke, E. K., Di Gaspero, L., McCollum, B., Musliu, N., & Özcan, E., (Eds.), Proceedings of the 12th International Conference of the Practice and Theory of Automated Timetabling (PATAT 2018), Vienna, Austria (pp. 5–31).

  • Müller, T., Rudová, H., & Müllerová, Z. (2018b). University course timetabling and International Timetabling Competition 2019. https://www.unitime.org/present/patat18-slides.pdf. Accessed 12 Apr 2021.

  • Røpke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40(4), 455–472. https://doi.org/10.1287/trsc.1050.0135

    Article  Google Scholar 

  • Saviniec, L., Santos, M. O., & Costa, A. M. (2018). Parallel local search algorithms for high school timetabling problems. European Journal of Operational Research, 265(1), 81–98.

    Article  Google Scholar 

  • Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87–127.

    Article  Google Scholar 

  • Tan, J. S., Goh, S. L., Kendall, G., & Sabar, N. R. (2021). A survey of the state-of-the-art of optimisation methodologies in school timetabling problems. Expert Systems with Applications, 165, 113943.

    Article  Google Scholar 

  • Tripathy, A. (1992). Computerised decision aid for timetabling-a case analysis. Discrete Applied Mathematics, 35(3), 313–323.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rasmus Ø. Mikkelsen.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors have contributed equally to this work. The authors would like to thank Bernd Dammann and Sebastian Borchert for providing valuable support for working with high-performance computing. Dennis S. Holm’s PhD project is part of the Data Science for University Management project (dsumsoftware.com) funded by MaCom A/S and Innovation Fund Denmark (IFD). Rasmus Ø. Mikkelsen’s industrial PhD project is funded by IFD. IFD has supported the work solely financially and has not participated in any research-related activities.

Appendix A: Our submitted solutions and bounds

Appendix A: Our submitted solutions and bounds

Table 11 shows the results submitted during the competition, the 10-day results from Sect. 7.5 (Table 10), and our best-known lower bounds. During the competition, we produced the results for the Late instances using the described parallelized matheuristic with the precise setup detailed in Sect. 6.5. Since the competition organizers published the Late instances 10 days before the deadline, we know that we produced our submitted results in less than that. However, we cannot say anything for sure regarding the time to produce our other results. The competition organizers released the Early and Middle instances earlier during the competition, and we have developed the parallelized matheuristic and its components using those instances. Consequently, we have often used previously found solutions for warm-starting MIP solvers and as initial solutions for fix-and-optimize searches and different parameter settings for our methods, including the number of cores.

Therefore, for comparison, Table 11 also shows the results of the 10-day runs produced for this paper. Here, we use hardware and software slightly different from what we used during the competition. Comparing the 10-day and competition results, we see that the presented parallelized algorithm can produce solutions comparable to those submitted in the competition on all instances.

Finally, the table also reports our best-known lower bounds, some of which we have produced with methods not discussed in this paper. Using these lower bounds, we see that we solved five instances to optimality both during the competition and in the 10-day runs.

Table 11 An overview of the best solution we submitted during the competition, the results of the single 10-day run (Table 10), and our best-known lower bounds

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mikkelsen, R.Ø., Holm, D.S. A parallelized matheuristic for the International Timetabling Competition 2019. J Sched (2022). https://doi.org/10.1007/s10951-022-00728-8

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10951-022-00728-8

Keywords

  • Mixed-integer programming
  • Parallelized matheuristic
  • Fix-and-optimize
  • University timetabling
  • International Timetabling Competition 2019
  • ITC 2019