Adaptive selection of heuristics for improving exam timetables

Abstract

This paper presents a hyper-heuristic approach which hybridises low-level heuristic moves to improve timetables. Exams which cause a soft-constraint violation in the timetable are ordered and rescheduled to produce a better timetable. It is observed that both the order in which exams are rescheduled and the heuristic moves used to reschedule the exams and improve the timetable affect the quality of the solution produced. After testing different combinations in a hybrid hyper-heuristic approach, the Kempe chain move heuristic and time-slot swapping heuristic proved to be the best heuristic moves to use in a hybridisation. Similarly, it was shown that ordering the exams using Saturation Degree and breaking any ties using Largest Weighted Degree produce the best results. Based on these observations, a methodology is developed to adaptively hybridise the Kempe chain move and timeslot swapping heuristics in two stages. In the first stage, random heuristic sequences are generated and automatically analysed. The heuristics repeated in the best sequences are fixed while the rest are kept empty. In the second stage, sequences are generated by randomly assigning heuristics to the empty positions in an attempt to find the best heuristic sequence. Finally, the generated sequences are applied to the problem. The approach is tested on the Toronto benchmark and the exam timetabling track of the second International Timetabling Competition, to evaluate its generality. The hyper-heuristic with low-level improvement heuristics approach was found to generalise well over the two different datasets and performed comparably to the state of the art approaches.

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References

  1. Abdullah, S., Turabieh, H., & McCollum, B. (2009). A hybridization of electromagnetic-like mechanism and great deluge for examination timetabling problems. In Lecture notes in computer science: Vol. 5818. Proceedings of the 6th international workshop on hybrid metaheuristics, HM2009 (pp. 60–72). Berlin: Springer.

    Google Scholar 

  2. Asmuni, H., Burke, E. K., Garibaldi, J., & McCollum, B. (2004). Fuzzy multiple ordering criteria for examination timetabling. In E. K. Burke & M. Trick (Eds.), Lecture notes in computer science: Vol. 3616. Selected papers from the 5th international conference on the practice and theory of automated timetabling (pp. 334–353). Berlin: Springer.

    Google Scholar 

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

    Article  Google Scholar 

  4. Atsuta, M., Nonobe, K., & Ibaraki, T. (2008). ITC2007 track 1: an approach using general CSP solver. In Practice and theory of automated timetabling, PATAT 2008, August 2008 (pp. 19–22).

    Google Scholar 

  5. Biligan, B., Ozcan, E., & Korkmaz, E. E. (2007). An experimental study on hyper-heuristics and exam timetabling. In E. Burke & H. Rudova (Eds.), Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI: selected papers from the 6th international conference, PATAT 2006 (pp. 394–412).

    Google Scholar 

  6. Burke, E. K., & Bykov, Y. (2008). A late acceptance strategy in hill-climbing for examination timetabling problems. In Practice and theory of automated timetabling, PATAT 2008, August 2008.

    Google Scholar 

  7. Burke, E. K., Kendall, G., Newall, J., Hart, E., Ross, P., & Schulenburg, S. (2003). Hyper-heuristics: an emerging direction in modern search technology. In F. Glover & G. Kochenberger (Eds.), Handbook of meta-heuristics (pp. 457–474). Norwell: Kluwer Academic.

    Google Scholar 

  8. 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.

    Article  Google Scholar 

  9. Burke, E. K., Eckersley, A., McCollum, B., Petrovic, S., & Qu, R. (2010). Hybrid variable neighbourhood approaches to university exam timetabling. European Journal of Operational Research, 206, 46–53.

    Article  Google Scholar 

  10. Burke, E. K., Qu, R., & Soghier, A. (2011). An adaptive tie breaking and hybridisation hyper-heuristic for exam timetabling problems. In D.A. Pelta et al. (Eds.), Nature inspired cooperative strategies for optimization, NICSO 2011 (pp. 205–223)

  11. Caramia, M., Dell Olmo, P., & Italiano, G. F. (2008). Novel local-search-based approaches to university examination timetabling. INFORMS Journal on Computing, 20(1), 86–99.

    Article  Google Scholar 

  12. 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 

  13. De Smet, G. (2008). ITC2007—examination track. In Practice and theory of automated timetabling, PATAT 2008, August 2008 (pp. 19–22).

    Google Scholar 

  14. Ersoy, E., Ozcan, E., & Uyar, S. (2007). Memetic algorithms and hill-climbers. In P. Baptiste, G. Kendall, A. M. Kordon, & F. Sourd (Eds.), Proceedings of the 3rd multidisciplinary international conference on scheduling: theory and applications conference, MISTA 2007 (pp. 159–166).

    Google Scholar 

  15. Gogos, C., Alefragis, P., & Housos, E. (2008). A multi-staged algorithmic process for the solution of the examination timetabling problem. In Practice and theory of automated timetabling, PATAT 2008 (pp. 19–22).

    Google Scholar 

  16. Kendall, G., & Mohd Hussin, N. (2005). An investigation of a tabu search based hyper-heuristic for examination timetabling. In G. Kendall, E. Burke, S. Petrovic, & M. Gendreau (Eds.), Selected papers from MISTA 2005 (pp. 309–328). Berlin: Springer.

    Google Scholar 

  17. McCollum, B., McMullan, P., Parkes, A. J., Burke, E. K., & Abdullah, S. (2009). An extended great deluge approach to the examination timetabling problem. In Proceedings of the 4th multidisciplinary international scheduling: theory and applications 2009, MISTA 2009, Dublin, Ireland, 10–12 August (pp. 424–434).

    Google Scholar 

  18. McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Di Gaspero, L., Parkes, A. J., Qu, R., & Burke, E. K. (2010). Setting the research agenda in automated timetabling: the second international timetabling competition. INFORMS Journal of Computing, 22(1), 120–130.

    Article  Google Scholar 

  19. Muller, T. (2008). Itc 2007 solver description: a hybrid approach. In Practice and theory of automated timetabling, PATAT 2008, August 2008 (pp. 19–22).

    Google Scholar 

  20. Pillay, N. (2008). A developmental approach to the examination timetabling problem. In Practice and theory of automated timetabling, PATAT 2008, August 2008 (pp. 19–22).

    Google Scholar 

  21. Pillay, N. (2010). Evolving hyper-heuristics for a highly constrained examination timetabling problem. In Practice and theory of automated timetabling, PATAT’10 (pp. 336–346).

    Google Scholar 

  22. Pillay, N., & Banzhaf, W. (2007). A genetic programming approach to the generation of hyper-heuristic systems for the uncapacitated examination timetabling problem. In J. Neves, et al. (Eds.), Lecture notes in artificial intelligence: Vol. 4874. Progress in artificial intelligence (pp. 223–234).

    Google Scholar 

  23. Pillay, N., & Banzhaf, W. (2009). A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem. European Journal of Operational Research, 197, 482–491.

    Article  Google Scholar 

  24. Qu, R., & Burke, E. K. (2009). Hybridisations within a graph-based hyper-heuristic framework for university timetabling problems. Journal of the Operational Research Society, 60, 1273–1285.

    Article  Google Scholar 

  25. Qu, R., Burke, E. K., & McCollum, B. (2009a). Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems. European Journal of Operational Research, 198(2), 392–404.

    Article  Google Scholar 

  26. Qu, R., Burke, E. K., McCollum, B., Merlot, L. T. G., & Lee, S. Y. (2009b). A survey of search methodologies and automated approaches for examination timetabling. Journal of Scheduling, 12(1), 55–89.

    Article  Google Scholar 

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

    Article  Google Scholar 

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Correspondence to Amr Soghier.

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Burke, E.K., Qu, R. & Soghier, A. Adaptive selection of heuristics for improving exam timetables. Ann Oper Res 218, 129–145 (2014). https://doi.org/10.1007/s10479-012-1140-3

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Keywords

  • Variable Neighbourhood Search
  • Soft Constraint
  • Hard Constraint
  • Saturation Degree
  • Good Quality Solution