Annals of Operations Research

, Volume 252, Issue 2, pp 255–282 | Cite as

Adaptive large neighborhood search for the curriculum-based course timetabling problem

  • Alexander Kiefer
  • Richard F. Hartl
  • Alexander Schnell
S.I. : PATAT 2014


In curriculum-based course timetabling, lectures have to be assigned to periods and rooms, while avoiding overlaps between courses of the same curriculum. Taking into account the inherent complexity of the problem, a metaheuristic solution approach is proposed, more precisely an adaptive large neighborhood search, which is based on repetitively destroying and subsequently repairing relatively large parts of the solution. Several problem-specific operators are introduced. The proposed algorithm proves to be very effective for the curriculum-based course timetabling problem. In particular, it outperforms the best algorithms of the international timetabling competition in 2007 and finds five new best known solutions for benchmark instances of the competition.


University courses Timetabling Metaheuristics  Adaptive large neighborhood search  



The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development is gratefully acknowledged. The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC). We acknowledge the constructive input by the anonymous reviewers.


  1. Abdullah, S., & Turabieh, H. (2012). On the use of multi neighbourhood structures within a Tabu-based memetic approach to university timetabling problems. Information Sciences, 191, 146–168.CrossRefGoogle Scholar
  2. Abdullah, S., Ahmadi, S., Burke, E., & Dror, M. (2007). Investigating Ahuja–Orlin’s large neighbourhood search approach for examination timetabling. OR Spectrum, 29(2), 351–372.CrossRefGoogle Scholar
  3. Abdullah, S., Turabieh, H., McCollum, B., & McMullan, P. (2012). A hybrid metaheuristic approach to the university course timetabling problem. Journal of Heuristics, 18(1), 1–23.CrossRefGoogle Scholar
  4. Ahuja, K., & Orlin, J. B. (2002). A survey of very large-scale neighborhood search techniques. Discrete Applied Mathematics, 123(1–3), 75–102.CrossRefGoogle Scholar
  5. Bellio, R., Di Gaspero, L., & Schaerf, A. (2012). Design and statistical analysis of a hybrid local search algorithm for course timetabling. Journal of Scheduling, 15(1), 49–61.CrossRefGoogle Scholar
  6. Bellio, R., Ceschia, S., Di Gaspero, L., Schaerf, A., & Urli, T. (2016). Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem. Computers and Operations Research, 65, 83–92.Google Scholar
  7. Bettinelli, A., Cacchiani, V., Roberti, R., & Toth, P. (2015). An overview of curriculum-based course timetabling. TOP, 23(2), 313–349.CrossRefGoogle Scholar
  8. Bonutti, A., De Cesco, F., Di Gaspero, L., & Schaerf, A. (2012). Benchmarking curriculum-based course timetabling: Formulations, data formats, instances, validation and results. Annals of Operations Research, 194(1), 59–70.CrossRefGoogle Scholar
  9. Brélaz, D. (1979). New methods to color the vertices of a graph. Communications of the ACM, 22(4), 251–256.CrossRefGoogle Scholar
  10. Broder, S. (1964). Final examination scheduling. Communications of the ACM, 7(8), 494–498.CrossRefGoogle Scholar
  11. Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2010). Decomposition, reformulation, and diving in university course timetabling. Computers and Operations Research, 37(3), 582–597.CrossRefGoogle Scholar
  12. Carter, M. W., Laporte, G., & Lee, S. Y. (1996). Examination timetabling: Algorithmic strategies and applications. Journal of the Operational Research Society, 47(3), 373–383.CrossRefGoogle Scholar
  13. Connolly, D. (1992). General purpose simulated annealing. Journal of the Operational Research Society, 43(5), 495–505.CrossRefGoogle Scholar
  14. Cooper, T. B., & Kingston, J. H. (1996). The complexity of timetable construction problems. In E. Burke & P. Ross (Eds.), Practice and theory of automated timetabling. Lecture notes in computer science (Vol. 1153, pp. 281–295). Berlin: Springer.CrossRefGoogle Scholar
  15. De Werra, D. (1985). An introduction to timetabling. European Journal of Operational Research, 19(2), 151–162.CrossRefGoogle Scholar
  16. Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3–18.CrossRefGoogle Scholar
  17. Di Gaspero, L., McCollum, B., & Schaerf, A. (2007). The second international timetabling competition (ITC-2007): Curriculum-based course timetabling (track 3). Technical report QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0, Queen’s University, Belfast, UK.Google Scholar
  18. Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management Science, 40(10), 1276–1290.CrossRefGoogle Scholar
  19. Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.CrossRefGoogle Scholar
  20. Kristiansen, S., & Stidsen, T. (2013). A comprehensive study of educational timetabling—A survey. DTU management engineering report, Department of Management Engineering, Technical University of Denmark.Google Scholar
  21. Kristiansen, S., Sørensen, M., Herold, M., & Stidsen, T. (2013). The consultation timetabling problem at danish high schools. Journal of Heuristics, 19(3), 465–495.CrossRefGoogle Scholar
  22. Lach, G., & Lübbecke, M. E. (2012). Curriculum based course timetabling: New solutions to Udine benchmark instances. Annals of Operations Research, 194(1), 255–272.CrossRefGoogle Scholar
  23. Lewis, R. (2008). A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum, 30(1), 167–190.CrossRefGoogle Scholar
  24. Lewis, R., & Thompson, J. (2015). Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem. European Journal of Operational Research, 240(3), 637–648.CrossRefGoogle Scholar
  25. Lü, Z., & Hao, J. K. (2010). Adaptive tabu search for course timetabling. European Journal of Operational Research, 200(1), 235–244.CrossRefGoogle Scholar
  26. McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., et al. (2010). Setting the research agenda in automated timetabling: The second international timetabling competition. INFORMS Journal on Computing, 22(1), 120–130.CrossRefGoogle Scholar
  27. Muller, L. (2009). An adaptive large neighborhood search algorithm for the resource-constrained project scheduling problem. In MIC 2009: The VIII Metaheuristics international conference.Google Scholar
  28. Muller, L. F., Spoorendonk, S., & Pisinger, D. (2012). A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times. European Journal of Operational Research, 218(3), 614–623.CrossRefGoogle Scholar
  29. Müller, T. (2009). ITC-2007 solver description: A hybrid approach. Annals of Operations Research, 172(1), 429–446.CrossRefGoogle Scholar
  30. Petrovic, S., & Burke, E. (2004). University timetabling. In J. Y. T. Leung (Ed.), Handbook of scheduling: Algorithms, models, and performance analysis, chapter 45. Boca Raton: Chapman Hall/CRC Press.Google Scholar
  31. Pisinger, D., & Ropke, S. (2007). A general heuristic for vehicle routing problems. Computers and Operations Research, 34(8), 2403–2435.CrossRefGoogle Scholar
  32. 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.CrossRefGoogle Scholar
  33. Ropke, 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.CrossRefGoogle Scholar
  34. Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87–127.CrossRefGoogle Scholar
  35. Schrimpf, G., Schneider, J., Stamm-Wilbrandt, H., & Dueck, G. (2000). Record breaking optimization results using the ruin and recreate principle. Journal of Computational Physics, 159(2), 139–171.CrossRefGoogle Scholar
  36. Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In M. Maher & J. F. Puget (Eds.), Principles and practice of constraint programming—CP98. Lecture notes in computer science (Vol. 1520, pp. 417–431). Berlin: Springer.Google Scholar
  37. Sørensen, M., & Stidsen, T. (2012). High school timetabling: Modeling and solving a large number of cases in denmark. In Proceedings of the ninth international conference on the practice and theory of automated timetabling (PATAT 2012), pp. 359–364.Google Scholar
  38. Sørensen, M., Kristiansen, S., & Stidsen, T. (2012). International timetabling competition 2011: An adaptive large neighborhood search algorithm. In Proceedings of the ninth international conference on the practice and theory of automated timetabling (PATAT 2012), pp. 489–492.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Alexander Kiefer
    • 1
  • Richard F. Hartl
    • 2
  • Alexander Schnell
    • 2
  1. 1.Christian Doppler Laboratory for Efficient Intermodal Transport Operations, Department of Business AdministrationUniversity of ViennaViennaAustria
  2. 2.Department of Business AdministrationUniversity of ViennaViennaAustria

Personalised recommendations