Skip to main content
SpringerLink
Log in

Exact and metaheuristic methods for a real-world examination timetabling problem

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

We propose a portfolio of exact and metaheuristic methods for the rich examination timetabling problem introduced by Battistutta et al. (in: Hebrard, Musliu (eds) 17th International conference on the integration of constraint programming, artificial intelligence, and operations research (CPAIOR-2020), LNCS, vol 12296. Springer, Berlin, pp 69–81, 2020). The problem includes several real-world features that arise in Italian universities, such as examinations split into two parts, possible requirements of multiple rooms for a single examination, and unavailabilities and preferences for periods and rooms. We developed a CP model encoded in the MiniZinc modeling language and solved it with Gecode, as well as two MIP models solved with Gurobi. The first MIP model is encoded natively and the second one again in MiniZinc. Finally, we extended the metaheuristic method based on simulated annealing of Battistutta et al. by introducing a new neighborhood relation. We compare the different techniques on the real-world instances provided by Battistutta et al., which have been slightly refined by correcting some semantic issues. Finally, we developed a solution checker that is publicly available, together with all instances and solutions, for inspection and future comparisons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Abou Kasm, O., Mohandes, B., Diabat, A., & El Khatib, S. (2019). Exam timetabling with allowable conflicts within a time window. Computers & Industrial Engineering, 127, 263–273.

    Article  Google Scholar 

  • Al-Hawari, F., Al-Ashi, M., Abawi, F., & Alouneh, S. (2020). A practical three-phase ILP approach for solving the examination timetabling problem. International Transactions in Operational Research, 27(2), 924–944.

    Article  Google Scholar 

  • Al-Yakoob, S. M., & Sherali, H. D. (2015). Mathematical models and algorithms for a high school timetabling problem. Computers & Operations Research, 61, 56–68.

    Article  Google Scholar 

  • Al-Yakoob, S. M., Sherali, H. D., & Al-Jazzaf, M. (2010). A mixed-integer mathematical modeling approach to exam timetabling. Computational Management Science, 7(1), 19.

    Article  Google Scholar 

  • Arbaoui, T., Boufflet, J. P., & Moukrim, A. (2015). Preprocessing and an improved MIP model for examination timetabling. Annals of Operations Research, 229(1), 19–40.

    Article  Google Scholar 

  • Arbaoui, T., Boufflet, J. P., & Moukrim, A. (2019). Lower bounds and compact mathematical formulations for spacing soft constraints for university examination timetabling problems. Computers & Operations Research, 106, 133–142.

    Article  Google Scholar 

  • Battistutta, M., Ceschia, S., De Cesco, F., Di Gaspero, L., Schaerf, A., & Topan, E. (2020). Local search and constraint programming for a real-world examination timetabling problem. In E. Hebrard, N. Musliu (Eds.). 17th International conference on the integration of constraint programming, artificial intelligence, and operations research (CPAIOR-2020), LNCS, Vol. 12296 (pp. 69–81). Springer.

  • Battistutta, M., Schaerf, A., & Urli, T. (2017). Feature-based tuning of single-stage simulated annealing for examination timetabling. Annals of Operations Research, 252(2), 239–254.

    Article  Google Scholar 

  • Bellio, R., Ceschia, S., Di Gaspero, L., & Schaerf, A. (2021). Two-stage multi-neighborhood simulated annealing for uncapacitated examination timetabling. Computers and Operations Research, 132, 1–9.

    Article  Google Scholar 

  • Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252.

    Article  Google Scholar 

  • Bilgin, B., Özcan, E., & Korkmaz, E. E. (2006). An experimental study on hyper-heuristics and exam timetabling. In International conference on the practice and theory of automated timetabling (pp. 394–412). Springer.

  • Birattari, M., Yuan, Z., Balaprakash, P., & Stützle, T. (2010). F-race and iterated F-race: An overview. In Experimental methods for the analysis of optimization algorithms (pp. 311–336). Springer.

  • Bonutti, A., De Cesco, F., Di Gaspero, L., & Schaerf, A. (2012). Benchmarking curriculum-based course timetabling: Formulations, data formats, instances, validation, visualization, and results. Annals of Operations Research, 194(1), 59–70.

    Article  Google Scholar 

  • Bron, C., & Kerbosch, J. (1973). Algorithm 457: Finding all cliques of an undirected graph. Communications of the ACM, 16(9), 575–577.

    Article  Google Scholar 

  • Burke, E. K., & Bykov, Y. (2016). An adaptive flex-deluge approach to university exam timetabling. INFORMS Journal on Computing, 28(4), 781–794.

    Article  Google Scholar 

  • Carter, M. W., Laporte, G., & Lee, S. Y. (1996). Examination timetabling: Algorithmic strategies and applications. Journal of the Operational Research Society, 74, 373–383.

    Article  Google Scholar 

  • Cataldo, A., Ferrer, J. C., Miranda, J., Rey, P. A., & Sauré, A. (2017). An integer programming approach to curriculum-based examination timetabling. Annals of Operations Research, 258(2), 369–393.

    Article  Google Scholar 

  • Daskalaki, S., & Birbas, T. (2005). Efficient solutions for a university timetabling problem through integer programming. European Journal of Operational Research, 160(1), 106–120.

    Article  Google Scholar 

  • Dekker, J. J., Björdal, G., Carlsson, M., Flener, P., & Monette, J. (2017). Auto-tabling for subproblem presolving in MiniZinc. Constraints, 22(4), 512–529.

    Article  Google Scholar 

  • Dekker, J.J., de la Banda, M.G., Schutt, A., Stuckey, P.J., & Tack, G. (2018). Solver-independent large neighbourhood search. In J. N. Hooker (Ed.) CP 2018, LNCS, Vol. 11008 (pp. 81–98). Springer.

  • Demeester, P., Bilgin, B., De Causmaecker, P., & Vanden Berghe, G. (2012). A hyperheuristic approach to examination timetabling problems: Benchmarks and a new problem from practice. Journal of Scheduling, 15(1), 83–103.

    Article  Google Scholar 

  • Gecode Team. (2019). Gecode: A generic constraint development environment. The Gecode solver and its MiniZinc backend are available at https://www.gecode.org

  • Genc, B., & O’Sullivan, B. (2020). A two-phase constraint programming model for examination timetabling at University College Cork. In International conference on principles and practice of constraint programming (pp. 724–742). Springer.

  • Güler, M. G., Geçici, E., Köroğlu, T., & Becit, E. (2021). A web-based decision support system for examination timetabling. Expert Systems with Applications, 183, 1–11.

    Article  Google Scholar 

  • Gurobi Optimization, LLC. (2021). Gurobi Optimizer Reference Manual. https://www.gurobi.com

  • Hammersley, J. M., & Handscomb, D. C. (1964). Monte Carlo methods. Chapman and Hall.

  • June, T. L., Obit, J. H., Leau, Y. B., & Bolongkikit, J. (2019). Implementation of constraint programming and simulated annealing for examination timetabling problem. In R. Alfred, Y. Lim, A. Ibrahim, & P. Anthony (Eds.), Computational Science and Technology. Lecture Notes in Electrical Engineering (pp. 175–184). Springer.

  • Kahar, M. M., & Kendall, G. (2010). The examination timetabling problem at Universiti Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution. European Journal of Operational Research, 207(2), 557–565.

    Article  Google Scholar 

  • Kahar, M. M., & Kendall, G. (2015). A great deluge algorithm for a real-world examination timetabling problem. Journal of the Operational Research Society, 66(1), 116–133.

    Article  Google Scholar 

  • Keskin, M. E., Döyen, A., Akyer, H., & Güler, M. G. (2018). Examination timetabling problem with scarce resources: A case study. European Journal of Industrial Engineering, 12(6), 855–874.

    Article  Google Scholar 

  • Kristiansen, S., Sørensen, M., & Stidsen, T. R. (2015). Integer programming for the generalized high school timetabling problem. Journal of Scheduling, 18(4), 377–392.

    Article  Google Scholar 

  • Lach, G., & Lübbecke, M. E. (2008). Optimal university course timetables and the partial transversal polytope. In International workshop on experimental and efficient algorithms (pp. 235–248). Springer.

  • Lach, G., & Lübbecke, M. E. (2012). Curriculum based course timetabling: New solutions to Udine benchmark instances. Annals of Operations Research, 194(1), 255–272.

    Article  Google Scholar 

  • Leite, N., Fernandes, C., Melício, F., & Rosa, A. (2018). A cellular memetic algorithm for the examination timetabling problem. Computers and Operations Research, 94, 118–138.

    Article  Google Scholar 

  • Leite, N., Melício, F., & Rosa, A. (2019). A fast simulated annealing algorithm for the examination timetabling problem. Expert Systems with Applications, 122, 137–151.

    Article  Google Scholar 

  • Luby, M., Sinclair, A., & Zuckerman, D. (1993). Optimal speedup of Las Vegas algorithms. Information Processing Letters, 47(4), 173–180.

    Article  Google Scholar 

  • Maniezzo, V., Boschetti, M. A., & Stützle, T. (2021). Matheuristics: Algorithms and implementations. Springer.

  • McCollum, B., McMullan, P., Burke, E. K., Parkes, A. J., & Qu, R. (2007). The second international timetabling competition: Examination timetabling track. Technical Report. QUB/IEEE/Tech/ITC2007/Exam/v4.0/17. Queen’s University.

  • Muklason, A., Parkes, A. J., Özcan, E., McCollum, B., & McMullan, P. (2017). Fairness in examination timetabling: Student preferences and extended formulations. Applied Soft Computing, 55, 302-318.

    Article  Google Scholar 

  • Müller, T. (2016). Real-life examination timetabling. Journal of Scheduling, 19(3), 257–270.

    Article  Google Scholar 

  • Nethercote, N., Stuckey, P. J., Becket, R., Brand, S., Duck, G. J., & Tack, G. (2007). MiniZinc: Towards a standard CP modelling language. In: C. Bessière (Ed). CP 2007, LNCS, Vol .4741 (pp 529–543). Springer, the MiniZinc toolchain is available at https://www.minizinc.org

  • Ohrimenko, O., Stuckey, P. J., & Codish, M. (2009). Propagation via lazy clause generation. Constraints, 14(3), 357–391.

    Article  Google Scholar 

  • Özcan, E., & Ersoy, E. (2005). Final exam scheduler-fes. In 2005 IEEE congress on evolutionary computation, Vol. 2 (pp. 1356–1363). IEEE.

  • Parkes, A. J., & Özcan, E. (2010). Properties of Yeditepe examination timetabling benchmark instances. In Proceedings of the 8th international conference on the practice and theory of automated timetabling (pp 531–534).

  • Qu, R., Burke, E. K., McCollum, B., Merlot, L., & Lee, S. (2009). A survey of search methodologies and automated system development for examination timetabling. Journal of Scheduling, 12(1), 55–89.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In M. Maher, J. F. Puget (Eds.) CP 1998, LNCS, Vol. 1520 (pp. 417–431). Springer.

  • Sørensen, M., & Dahms, F. H. (2014). A two-stage decomposition of high school timetabling applied to cases in Denmark. Computers & Operations Research, 43, 36–49.

    Article  Google Scholar 

  • Stuckey, P. J., et al. (2020). The MiniZinc Handbook, 2nd edn. Monash University. https://www.minizinc.org/

  • Urli, T. (2013). json2run: A tool for experiment design & analysis. arXiv:1305.1112

  • Woumans, G., De Boeck, L., Beliën, J., & Creemers, S. (2016). A column generation approach for solving the examination-timetabling problem. European Journal of Operational Research, 253(1), 178–194.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RISE Research Institutes of Sweden, Uppsala, Sweden

    Mats Carlsson

  2. University of Udine, Udine, Italy

    Sara Ceschia, Luca Di Gaspero & Andrea Schaerf

  3. Technical University of Denmark, Lyngby, Denmark

    Rasmus Ørnstrup Mikkelsen & Thomas Jacob Riis Stidsen

Authors
  1. Mats Carlsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Ceschia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luca Di Gaspero
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rasmus Ørnstrup Mikkelsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrea Schaerf
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Thomas Jacob Riis Stidsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rasmus Ørnstrup Mikkelsen.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carlsson, M., Ceschia, S., Di Gaspero, L. et al. Exact and metaheuristic methods for a real-world examination timetabling problem. J Sched 26, 353–367 (2023). https://doi.org/10.1007/s10951-023-00778-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-023-00778-6

Keywords

Search

Navigation