Skip to main content
Log in

An improved multi-staged algorithmic process for the solution of the examination timetabling problem

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The efficient creation of examination timetables is a recurring and important problem for universities worldwide. Good timetables typically are characterized by balanced distances between consecutive exams for all students. In this contribution an approach for the examination timetabling problem as defined in the second International Timetabling Competition (http://www.cs.qub.ac.uk/itc2007/) is presented. The solution approach is managed on the top level by GRASP (Greedy Randomized Adaptive Search Procedure) and it involves several optimization algorithms, heuristics and metaheuristics. A construction phase is executed first producing a relatively high quality feasible solution and an improvement phase follows that further ameliorates the produced timetable. Each phase consists of stages that are consumed in a circular fashion. The procedure produces feasible solutions for each dataset provided under the runtime limit imposed by the rules of the ITC07 competition. Results are presented and analyzed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Asmuni, H., Burke, E., Garibaldi, J., & McCollum, B. (2009). An investigation of fuzzy multiple heuristic orderings in the construction of university examination timetables. Computers and Operations Research, 36(4), 981–1001.

    Article  Google Scholar 

  • Balakrishnan, N., Lucena, A., & Wong, R. T. (1992). Scheduling examinations to reduce second order conflicts. Computers and Operations Research, 19, 353–361.

    Article  Google Scholar 

  • Brelaz, D. (1979). New methods to color the vertices of a graph. Communication of the ACM, 22(4), 251–256.

    Article  Google Scholar 

  • Broder, S. (1964). Final examination scheduling. Communications of the ACM, 7(8), 494–498.

    Article  Google Scholar 

  • Burke, E. K., & Newall, J. P. (2004). Solving examination timetabling problems through adaptation of heuristic orderings. Annals of Operations Research, 129, 107–134.

    Article  Google Scholar 

  • Burke, E. K., & Petrovic, S. (2002). Recent research directions in automated timetabling. European Journal of Operational Research, 140, 266–280.

    Article  Google Scholar 

  • Burke, E. K., Newall, J. P., & Weare, R. F. (1996). A memetic algorithm for university exam timetabling. In Lecture notes in computer science : Vol. 1153. Practice and theory of automated timetabling (pp. 241–250). Berlin: Springer. doi:10.1007/3-540-61794-9_63.

    Google Scholar 

  • Burke, E. K., Kingston, J. H., & de Werra, D. (2004). Applications to timetabling. In J. Gross & J. Yellen (Eds.), The handbook of graph theory (pp. 445–474). London, Boca Raton: Chapman Hall/CRC Press.

    Google Scholar 

  • Burke, E. K., Kendal, G., McCollum, B., & McMullan, P. (2007). Constructive versus improvement heuristics: an investigation of examination timetabling. In 3rd Multidisciplinary international scheduling conference: theory and applications, 28–31 August 2007, Paris.

  • Carter, M. W., Laporte, G., & Chinneck, J. W. (1994). A general examination scheduling system. Interfaces, 24, 109–120.

    Article  Google Scholar 

  • Carter, M. W., Laporte, G., & Lee, S.Y. (1996). Examination timetabling: algorithmic strategies and applications. Journal of Operational Research Society, 47, 373–383.

    Google Scholar 

  • Casey, S., & Thompson, J. (2003). GRASPing the examination scheduling problem. In Lecture notes in computer science : Vol. 2740. Practice and theory of automated timetabling (pp. 232–244). Berlin, Heidelberg: Springer.

    Chapter  Google Scholar 

  • David, P. (1998). A constraint-based approach for examination timetabling using local repair techniques. In E. K. Burke & M. W. Carter (Eds.), Lecture notes in computer science : Vol. 1408. Practice and theory of automated timetabling: selected papers from the 2nd international conference (pp. 169–186). Berlin, Heidelberg: Springer.

    Chapter  Google Scholar 

  • Di Caspero, L. (2002). Recolour, Shake and Kick: a recipe for the examination timetabling problem. In E. K. Burke & P. De Causmaecker (Eds.), Proceedings of the 4th international conference on practice and theory of automated timetabling, KaHo St.-Lieven, Gent, Belgium (pp. 404–407). Berlin: Springer.

    Google Scholar 

  • Dowsland, K. A. (1993). Simulated annealing. Modern heuristic techniques for combinatorial problems by C. Reeves. New York: Wiley. ISBN 0-470-22079-1.

    Google Scholar 

  • Eley, M. (2006). Ant algorithms for the exam timetabling problem. In Practice and theory of automated timetabling (pp. 167–180). Berlin: Springer. ISBN 80-210-3726-1.

    Google Scholar 

  • Ersoy, E., Ozcan, E., & Sima Uyar, A. (2007). Memetic algorithms and hyperhill-climbers. In Proceedings of the 3nd multidisciplinary international conference on scheduling: theory and applications, MISTA07 (pp. 159–166).

  • Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133.

    Article  Google Scholar 

  • Gamma, E., Helm, R., Johnson, R., & Vlissides, J. (1994). Design patterns: elements of reusable object-oriented software. Addison-Wesley Professional Computing Series. Reading: Addison-Wesley. ISBN-13: 978-0201633610.

    Google Scholar 

  • Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic. ISBN 0-7923-9965-X.

    Book  Google Scholar 

  • Gogos, C., Alefragis, P., & Housos, E. (2008). A multi staged algorithmic process for the solution of the examination timetabling problem. In Proceedings of the 7th international conference on practice and theory of automated timetabling. University of Montreal, Canada.

  • Gogos, C., Goulas, G., Alefragis, P., & Housos, E. (2009). Pursuit of better results for the examination timetabling problem using grid resources. In Computational intelligence in scheduling, 2009, CI-Sched09 (pp. 48–53). doi:10.1109/SCIS.2009.4927014.

  • Henderson, D., Jacobson, S., & Johnson, A. (2003). The theory and practice of simulated annealing. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics, Chap. 10. Dordrecht: Kluwer Academic. ISBN 978-1-4020-7263-5.

    Google Scholar 

  • Ibaraki, T. (2008). Problem solving by general purpose solvers. In The 7th international symposium on operations research and its applications (ISORA’08), Lijiang, China, ORSC & APORC (pp. 10–17).

  • Joslin, D., & Clements, D. (1999). Squeaky wheel optimization. Journal of Artificial Intelligence Research, 10, 353–373.

    Google Scholar 

  • Kendall, G., & Hussin, N. M. (2005). An investigation of a tabu search based hyper-heuristic for examination timetabling. In G. Kendall, E. K. Burke, & S. Petrovic (Eds.), Selected papers from multidisciplinary scheduling: theory and applications (pp. 309–328).

  • Kingston, J., & Yin-Sun Lynn, B. (2001). A software architecture for timetable construction. In Lecture notes in computer science : Vol. 2079. PATAT 2000 (pp. 342–350). Berlin: Springer.

    Google Scholar 

  • McCollum, B. (2007). A perspective on bridging the gap between theory and practice in university timetabling. In Lecture notes in computer science : Vol. 3867. PATAT 2006 (pp. 3–23). Berlin: Springer. ISBN 978-3-540-77344-3.

    Chapter  Google Scholar 

  • McCollum, B., & McMullan, M. (2007). The second international timetabling competition: examination timetabling track (Technical report: QUB/IEEE/Tech/ITC2007/Exam/v4.0/17). School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast, UK, August 2007.

  • McCollum, B., McMullan, P., Burke, E., Parkes, A., & Qu, R. (2009a). A new model for automated examination timetabling. Submitted to post PATAT Annals of OR.

  • McCollum, B., McMullan, P., Parkes, A., Burke, E., & Abdullah, S. (2009b). An extended great deluge approach to the examination timetabling problem. In Proceedings of MISTA09. The 4th multidisciplinary international conference on scheduling: theory and applications, Dublin, August 2009 (pp. 424–434).

  • McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A., Di Gaspero, L., Qu, R., & Burke, E. (2009c). Setting the research agenda in automated timetabling: the second international timetabling competition. INFORMS Journal of Computing. doi:10.1287/ijoc.1090.0320.

  • McMullan, P. (2007). An extended implementation of the great deluge algorithm for course timetabling. In Lecture notes in computer science: Vol. 4487 (pp. 538–545). Berlin: Springer.

  • Merlot, L. T. G., Boland, N. Hughes B. D., & Stuckey, P. J. (2003). A hybrid algorithm for the examination timetabling problem. In E. K. Burke & P. De Causmaecker (Eds.), Lecture notes in computer science : Vol. 2740. Practice and theory of automated timetabling: selected papers from the 4th international conference (pp. 207–231). Berlin: Springer.

    Chapter  Google Scholar 

  • Muller, T. (2008). ITC 2007: Solver description. In Proceedings of the 7th international conference on practice and theory of automated timetabling. University of Montreal, Canada.

  • Petrovic, S., & Burke, E. K. (2004). Chap. 45. University timetabling. In J. Leung (Ed.), Handbook of scheduling: algorithms, models, and performance analysis. Boca Raton: CRC Press.

    Google Scholar 

  • Pillay, N., & Banzhaf, W. (2008). A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem. European Journal of Operational Research. doi:10.1016/j.ejor.2008.07.023.

  • Qu, R., & Burke, E. K. (2009). Hybridizations within a graph based hyper-heuristic framework for university timetabling problems. Journal of Operational Research Society. doi:10.1057/jors.2008.102.

  • Qu, R., Burke, E., 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. doi:10.1007/s10951-008-0077-5.

    Article  Google Scholar 

  • Resende, M. G. C., & Ribeiro, C. C. (2003). Greedy randomized adaptive search procedures, Chap. 8. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics. Dordrecht: Kluwer. ISBN: 978-1-4020-7263-5.

    Google Scholar 

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

    Article  Google Scholar 

  • Thompson, J. M., & Dowsland, K. A. (1996). Variants of simulated annealing for the examination timetabling problem. Annals of Operations Research, 63(1), 105–128.

    Article  Google Scholar 

  • Welsh, D. J. A., & Powell, M. B. (1967). An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer Journal, 10, 85–86.

    Article  Google Scholar 

  • White, G. M., & Chan, P. W. (1979). Towards the construction of optimal examination schedules. INFOR, 17, 219–229.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christos Gogos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gogos, C., Alefragis, P. & Housos, E. An improved multi-staged algorithmic process for the solution of the examination timetabling problem. Ann Oper Res 194, 203–221 (2012). https://doi.org/10.1007/s10479-010-0712-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-010-0712-3

Keywords

Navigation