Annals of Operations Research

, Volume 194, Issue 1, pp 291–315

A new model for automated examination timetabling

  • Barry McCollum
  • Paul McMullan
  • Andrew J. Parkes
  • Edmund K. Burke
  • Rong Qu
Article

Abstract

Automated examination timetabling has been addressed by a wide variety of methodologies and techniques over the last ten years or so. Many of the methods in this broad range of approaches have been evaluated on a collection of benchmark instances provided at the University of Toronto in 1996. Whilst the existence of these datasets has provided an invaluable resource for research into examination timetabling, the instances have significant limitations in terms of their relevance to real-world examination timetabling in modern universities. This paper presents a detailed model which draws upon experiences of implementing examination timetabling systems in universities in Europe, Australasia and America.

This model represents the problem that was presented in the 2nd International Timetabling Competition (ITC2007). In presenting this detailed new model, this paper describes the examination timetabling track introduced as part of the competition. In addition to the model, the datasets used in the competition are also based on current real-world instances introduced by EventMAP Limited. It is hoped that the interest generated as part of the competition will lead to the development, investigation and application of a host of novel and exciting techniques to address this important real-world search domain. Moreover, the motivating goal of this paper is to close the currently existing gap between theory and practice in examination timetabling by presenting the research community with a rigorous model which represents the complexity of the real-world situation. In this paper we describe the model and its motivations, followed by a full formal definition.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahmadi, S., Barone, R., Cheng, P., Cowling, P., & McCollum, B. (2003). Perturbation based variable neighbourhood search in heuristic space for examination timetabling problem. In Proceedings of multidisciplinary international scheduling: theory and applications (MISTA 2003) (pp. 155–171). Nottingham, August 13–16. ISBN: 0-9545821-2-8. Google Scholar
  2. Al-Yakoob, S., Sherali, H., & Al-Jazzaf, M. (2010). A mixed-integer mathematical modeling approach to exam timetabling. Computational Management Science, 7, 19–46. doi:10.1007/s10287-007-0066-8. CrossRefGoogle Scholar
  3. Asmuni, H., Burke, E. K., Garibaldi, J. M., & McCollum, B. (2006). A novel fuzzy approach to evaluate the quality of examination timetabling. In Proceedings of the 6th international conference on the practice and theory of automated timetabling (PATAT 2006) (pp. 82–102). Brno, Czech Republic, August 30th–September 1st 2006. Google Scholar
  4. Atsuta, M., Nonobe, K., & Ibaraki, T. (2008). ITC-2007 track2: an approach using general CSP solver. Available from the ITC-2007 website. http://www.cs.qub.ac.uk/itc2007/winner/bestcoursesolutions/Atsuta_et_al.pdf.
  5. Azimi, Z. N. (2005). Hybrid heuristics for examination timetabling problem. Applied Mathematics and Computation, 163(2), 705–733. CrossRefGoogle Scholar
  6. Borning, A., Duisberg, R., Freeman-Benson, B., Kramer, A., & Woolf, M. (1987). Constraint hierarchies. In N. Meyrowitz (Ed.), Proceedings of the conference on object-oriented programming systems, languages, and applications (OOPSLA) (Vol. 22, pp. 48–60). New York: ACM. CrossRefGoogle Scholar
  7. Borning, A., Freeman-Benson, B., & Wilson, M. (1992). Constraint hierarchies. LISP and Symbolic Computation, 5, 223–270. CrossRefGoogle Scholar
  8. Burke, E. K., & Newall, J. (2004). Solving examination timetabling problems through adaptation of heuristic orderings. Annals of Operations Research, 129, 107–134. CrossRefGoogle Scholar
  9. Burke, E. K., Newall, J., & Weare, R. F. (1996). A memetic algorithm for university exam timetabling. In E. K. Burke & P. Ross (Eds.), Lecture notes in computer science: Vol. 1153. The practice and theory of automated timetabling (pp. 241–250). Berlin: Springer. Google Scholar
  10. Burke, E. K., Petrovic, S., & Qu, R. (2002). Case-based heuristic selection for examination timetabling. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning (SEAL 2002) (pp. 277–281). Singapore, Nov 18–22 2002. Google Scholar
  11. Burke, E. K., Hart, E., Kendall, G., Newall, J., Ross, P., & Schulenburg, S. (2003). Hyper-heuristics: an emerging direction in modern search technology. In Handbook of meta-heuristics (pp. 457–474). Dordrecht: Kluwer Academic. Google Scholar
  12. Burke, E. K., Bykov, Y., Newall, J., & Petrovic, S. (2004). A time-predefined local search approach to exam timetabling problems. IIE Transactions, 36, 509–528. CrossRefGoogle Scholar
  13. Burke, E. K., Dror, M., Petrovic, S., & Qu, R. (2005). Hybrid graph heuristics within a hyper-heuristic approach to exam timetabling problems. In The next wave in computing, optimization, and decision technologies (pp. 79–91). Berlin: Springer. CrossRefGoogle Scholar
  14. Burke, E. K., Petrovic, S., & Qu, R. (2006). Case based heuristic selection for timetabling problems. Journal of Scheduling, 9(2), 115–132. CrossRefGoogle Scholar
  15. Burke, E. K., McCollum, B., Meisels, A., Petrovic, S., & Qu, R. (2007). A graph-based hyper-heuristic for educational timetabling problems. European Journal of Operational Research, 176, 177–192. CrossRefGoogle Scholar
  16. Burke, E. K., McCollum, B., McMullan, P., & Parkes, A. J. (2008). Multi-objective aspects of the examination timetabling competition track. In Proceedings of PATAT 2008. Montreal, Canada, August 2008. Google Scholar
  17. Burke, E. K., Eckersley, A. J., McCollum, B., Petrovic, S., & Qu, R. (2010). Hybrid variable neighbourhood approaches to university exam timetabling. European Journal of Operational Research, 206, 46–53. CrossRefGoogle Scholar
  18. Callennec, B. L., & Boulic, R. (2004). Interactive motion deformation with prioritized constraints. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on computer animation, SCA’04 (pp. 163–171). Aire-la-Ville, Switzerland, Switzerland. Aire-la-Ville: Eurographics Association. CrossRefGoogle Scholar
  19. Carter, M. W., Laporte, G., & Lee, S. Y. (1996). Examination timetabling: algorithmic strategies and applications. The Journal of the Operational Research Society, 47(3), 373–383. Google Scholar
  20. David, P. (1998). A constraint-based approach for examination timetabling using local repair techniques. In E. K. Burke & M. W. Carter (Eds.), Springer lecture notes in computer science: Vol. 1408. Practice and theory of automated timetabling: selected papers from the 2nd international conference (pp. 169–186). CrossRefGoogle Scholar
  21. de Werra, D., Asratian, A. S., & Durand, S. (2002). Complexity of some special types of timetabling problems. Journal of Scheduling, 5, 171–183. CrossRefGoogle Scholar
  22. Di Gaspero, L. (2002). Recolour, shake and kick: a recipe for the examination timetabling problem. In E. K. Burke & P. D. Causmaecker (Eds.), Proceedings of the 4th international conference on the practice and theory of automated timetabling. KaHo St.-Lieven, Gent, Belgium (pp. 404–407). Google Scholar
  23. Di Gaspero, L., & Schaerf, A. (2001). Tabu search techniques for examination timetabling. In E. K. Burke & W. Erben (Eds.), Lecture notes in computer science (LNCS): Vol. 2079. Practice and theory of automated timetabling: selected papers from the 3rd international conference (pp. 104–117). CrossRefGoogle Scholar
  24. Di Gaspero, L., McCollum, B., & Schaerf, A. (2007). The second international timetabling competition (ITC-2007): curriculum-based course timetabling (track 3) (Tech. Rep. QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0/1) August 2007, Queen’s University Belfast. http://www.cs.qub.ac.uk/itc2007/.
  25. Dowsland, K. A., & Thompson, J. (2005). Ant colony optimization for the examination scheduling problem. The Journal of the Operational Research Society, 56(4), 426–438. CrossRefGoogle Scholar
  26. Dubois, D., Fargier, H., & Prade, H. (1996). Possibility theory in constraint satisfaction problems: handling priority, preference and uncertainty. Applied Intelligence, 6, 287–309. CrossRefGoogle Scholar
  27. Duong, T. A., & Lam, K. H. (2004). Combining constraint programming and simulated annealing on university exam timetabling. In Proceedings of the 2nd international conference in computer sciences, research, innovation & vision for the future (RIVF2004) (pp. 205–210). Hanoi, Vietnam, February 2004. Google Scholar
  28. Gogos, C., Alefragis, P., & Housos, E. (2010). An improved multi-staged algorithmic process for the solution of the examination timetabling problem. Annals of Operations Research. doi:10.1007/s10479-010-0712-3
  29. Henz, M., Yap, R. H. C., Lim, Y. F., Lua, S. C., Walser, J. P., & Shi, X. P. (2004). Solving hierarchical constraints over finite domains with local search. Annals of Mathematics and Artificial Intelligence, 40, 283–301. CrossRefGoogle Scholar
  30. 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 (Cardiff Working Papers in Accounting and Finance A2007-3), Cardiff Business School, Cardiff University, August 2007. Google Scholar
  31. McCollum, B. (2007). A perspective on bridging the gap between theory and practice in university timetabling. In Lecture notes in computer science (LNCS): Vol. 3867. Revised selected papers of PATAT 2006, Proceedings of the 6th international conference on the practice and theory of automated timetabling (pp. 3–23). Google Scholar
  32. McCollum, B., McMullan, P., Burke, E. K., Parkes, A. J., & Qu, R. (2007). The second international timetabling competition: examination timetabling track (Tech. Rep. QUB/IEEE/Tech/ITC2007/Exam/v4.0/17.2007), Queen’s University Belfast. http://www.cs.qub.ac.uk/itc2007/.
  33. McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Gaspero, L. D., 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. CrossRefGoogle Scholar
  34. Merlot, L. T. G., Boland, N., Hughes, B. D., & Stuckey, P. J. (2003). A hybrid algorithm for the examination timetabling problem. In Springer lecture notes in computer science: Vol. 2740. Practice and theory of automated timetabling: selected papers from the 4th international conference (pp. 207–231). CrossRefGoogle Scholar
  35. Meseguer, P., Bouhmala, N., Bouzoubaa, T., Irgens, M., & Sánchez, M. (2003). Current approaches for solving over-constrained problems. Constraints, 8, 9–39. doi:10.1023/A:1021902812784. CrossRefGoogle Scholar
  36. Metaheuristics Network, International timetable competition 2002 (2003). http://www.idsia.ch/Files/ttcomp2002/. Organised by the metaheuristics network, http://www.metaheuristics.net/ and PATAT 2002 http://www.asap.cs.nott.ac.uk/patat/patat02/patat02.shtml. Accessed April 2008.
  37. Müller, T. (2009). ITC2007 solver description: a hybrid approach. Annals of Operations Research, 172, 429–446. CrossRefGoogle Scholar
  38. Mumford, C. L. (2007). An order based evolutionary approach to dual objective examination timetabling. In Proceedings of the 2007 IEEE symposium on computational intelligence in scheduling (CI-Sched 2007), Honolulu, Hawaii, 1–5th April. Google Scholar
  39. Paquete, L., & Stützle, T. (2002). Empirical analysis of tabu search for the lexicographic optimization of the examination timetabling problem. In E. Burke & P. D. Causmaecker (Eds.), Proceedings of the 4th international conference on practice and theory of automated timetabling. Google Scholar
  40. Parkes, A. J., & Özcan, E. (2010). Properties of Yeditepe examination timetabling benchmark instances. In Proc. of the 8th international conference on the practice and theory of automated timetabling (PATAT 2010). Google Scholar
  41. Pillay, N. (2008). A developmental approach to the examination timetabling problem. http://www.cs.qub.ac.uk/itc2007/winner/bestexamsolutions/pillay.pdf.
  42. 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
  43. Ross, P., Corne, D., & Terashima-Marín, H. (1996). The phase transition niche for evolutionary algorithms in timetabling. In E. K. Burke & M. A. Trick (Eds.), Lecture notes in computer science: Vol. 1153. Selected papers from the first international conference on the theory and practice of automated timetabling (PATAT 95) (pp. 309–324). New York: Springer. Google Scholar
  44. Ross, P., Marin-Blazquez, J., & Hart, E. (2004). Hyper-heuristics applied to class and exam timetabling problems. In Proceedings of the 2004 congress on evolutionary computation (CEC2004) (pp. 1691–1698). Google Scholar
  45. Smet, G. D. (2008). ITC 2007—examination track. Available from the ITC-2007 website. http://www.cs.qub.ac.uk/itc2007/.
  46. Thompson, J., & Dowsland, K. (1998). A robust simulated annealing based examination timetabling system. Computers & Operations Research, 25, 637–648. CrossRefGoogle Scholar
  47. Tsang, E., Mills, P., & Williams, R. (1999). A computer aided constraint programming system. In The 1st international conference on the practical application of constraint technologies and logic programming (PACLP) (pp. 81–93). Google Scholar
  48. van Loon, J. N. M. (1981). Irreducibly inconsistent systems of linear inequalities. European Journal of Operational Research, 8(3), 283–288. CrossRefGoogle Scholar
  49. White, G. M., & Xie, B. S. (2001). Examination timetables and tabu search with longer-term memory. In E. K. Burke & W. Erben (Eds.), Practice and theory of automated timetabling: selected papers from the 3rd international conference. Google Scholar
  50. Wong, T., Cote, P., & Gely, P. (2002). Final exam timetabling: a practical approach. In IEEE Canadian conference on electrical and computer engineering (CCECE 2002) (Vol. 2, pp. 726–731). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Barry McCollum
    • 1
  • Paul McMullan
    • 1
  • Andrew J. Parkes
    • 2
  • Edmund K. Burke
    • 2
  • Rong Qu
    • 2
  1. 1.School of Computer ScienceQueen’s University BelfastBelfastUK
  2. 2.School of Computer ScienceUniversity of NottinghamNottinghamUK

Personalised recommendations