A graph coloring constructive hyper-heuristic for examination timetabling problems | Applied Intelligence
Skip to main content
Springer Nature Link
Log in

A graph coloring constructive hyper-heuristic for examination timetabling problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this work we investigate a new graph coloring constructive hyper-heuristic for solving examination timetabling problems. We utilize the hierarchical hybridizations of four low level graph coloring heuristics, these being largest degree, saturation degree, largest colored degree and largest enrollment. These are hybridized to produce four ordered lists. For each list, the difficulty index of scheduling the first exam is calculated by considering its order in all lists to obtain a combined evaluation of its difficulty. The most difficult exam to be scheduled is scheduled first (i.e. the one with the minimum difficulty index). To improve the effectiveness of timeslot selection, a roulette wheel selection mechanism is included in the algorithm to probabilistically select an appropriate timeslot for the chosen exam. We test our proposed approach on the most widely used un-capacitated Carter benchmarks and also on the recently introduced examination timetable dataset from the 2007 International Timetabling Competition. Compared against other methodologies, our results demonstrate that the graph coloring constructive hyper-heuristic produces good results and outperforms other approaches on some of the benchmark instances.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Chapter  Google Scholar 

  2. Asmuni H, Burke EK, Garibaldi J, McCollum B (2005) Fuzzy multiple ordering criteria for examination timetabling. In: Burke EK, Trick M (eds) Practice and theory of automated timetabling V: selected papers from the 5th international conference. Lecture notes in computer science, vol 3616. Springer, Berlin, pp 334–353

    Chapter  Google Scholar 

  3. Atsuta M, Nonobe K, Ibaraki T (2007) ITC2007 Track 1: an approach using general CSP solver. www.cs.qub.ac.uk/itc2007

  4. Ayob M, Malik AMA, Abdullah S, Hamdan AR, Kendall G, Qu R (2007) Solving a practical examination timetabling problem: a case study. In: Gervasi O, Gavrilova M (eds) ICCSA 2007, Part III. LNCS, vol 4707. Springer, Heidelberg, pp 611–624

    Google Scholar 

  5. Burke EK, Dror M, Petrovic S, Qu R (2005) Hybrid graph heuristics in hyper-heuristics applied to exam timetabling problems. In: Golden BL, Raghavan S, Wasil EA (eds) The next wave in computing, optimisation, and decision technologies. Springer, Maryland, pp 79–91

    Chapter  Google Scholar 

  6. Burke EK, Eckersley AJ, McCollum B, Petrovic S, Qu R (2010) Hybrid variable neighbourhood approaches to university exam timetabling. Eur J Oper Res 206:46–53

    Article  MathSciNet  MATH  Google Scholar 

  7. Burke EK, McCollum B, Meisels A, Petrovic S, Qu R (2007) A graph based hyper-heuristic for exam timetabling problems. Eur J Oper Res 176:177–192

    Article  MathSciNet  MATH  Google Scholar 

  8. Burke EK, Petrovic S, Qu R (2006) Case-based heuristic selection for timetabling problems. J Sched 9:115–132

    Article  MATH  Google Scholar 

  9. Burke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Woodward J (2009a) A classification of hyper-heuristics approaches. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics, international series in operations research & management science. Springer, Berlin

    Google Scholar 

  10. Burke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Woodward J (2009b) Exploring hyper-heuristic methodologies with genetic programming, computational intelligence: collaboration, fusion and emergence. In: Mumford C, Jain L (eds) Intelligent systems reference library. Springer, Berlin, pp 177–201

    Google Scholar 

  11. Burke E, Hart E, Kendall G, Newall J, Ross P, Schulenburg S (2003) Hyperheuristics: an emerging direction in modern research technology. In: Handbook of metaheuristics. Kluwer Academic, Dordrecht, pp 457–474 (Chap 16)

    Google Scholar 

  12. Burke EK, Bykov Y, Newall JP, Petrovic S (2004) A time-predefined local search approach to exam timetabling problems. IIE Trans Oper Eng 36(6):509–528

    Article  Google Scholar 

  13. Carter MW, Laporte G, Lee SY (1996) Examination timetabling: algorithmic strategies and applications. J Oper Res Soc 47(3):373–383

    Google Scholar 

  14. De Smet G (2008) ITC2007—examination track, practice and theory of automated timetabling (PATAT 2008), Montreal, 19–22 August 2008

  15. Eley M (2007) Ant algorithms for the exam timetabling problem. In: Burke EK, Rudova H (eds) PATAT 2007. LNCS, vol 3867. Springer, Heidelberg, pp 364–382

    Google Scholar 

  16. Ersoy E, Özcan E, Etaner AS (2007) Memetic algorithms and hyperhill-climbers. In: Proceedings of the 3rd multidisciplinary international conference on scheduling: theory and applications, Paris, France, August 2007, pp 159–166

    Google Scholar 

  17. Gogos C, Alefragis P, Housos E (2010) An improved multi-staged algorithmic process for the solution of the examination timetabling problem. Ann Oper Res. doi:10.1007/s10479-010-0712-3

    Google Scholar 

  18. Gogos C, Alefragis P, Housos E (2008) A multi-staged algorithmic process for the solution of the examination timetabling problem, practice and theory of automated timetabling (PATAT 2008), Montreal, 19–22 August 2008

  19. Kendall G, Hussin NM (2005a) An investigation of a tabu search based hyper-heuristic for examination timetabling. In: Kendall G, Burke E, Petrovic S (eds) Selected papers from multidisciplinary scheduling; theory and applications, pp 309–328

    Chapter  Google Scholar 

  20. Kendall G, Hussin NM (2005b) A tabu search hyper-heuristic approach to the examination timetabling problem at the MARA University of Technology. In: Burke EK, Trick M (eds) Practice and theory of automated timetabling V: selected papers from the 5th international conference. Lecture notes in computer science, vol 3616. Springer, Berlin, pp 199–218

    Google Scholar 

  21. Li J, Burke EK, Qu R (2011) A pattern recognition based intelligent search method and two assignment problem case studies. Appl Intell. doi:10.1007/s10489-010-0270-z

  22. Mansour N, Isahakian V, Ghalayini I (2011) Scatter search technique for exam timetabling. Appl Intell 34:299–310

    Article  Google Scholar 

  23. McCollum B, McMullan P, Burke EK, Parkes AJ, Qu R (2007) A new model for automated examination timetabling. Submitted post PATAT08 special issue of J. Sched. Available as technical report QUB/IEEE/Tech/ITC2007/Exam/v4.0/17 from http://www.cs.qub.ac.uk/itc2007/examtrack/exam_track_index.htm

  24. McCollum B (2007) A perspective on bridging the gap between research and practice in university timetabling. In: Burke EK, Rudova H (eds) Practice and theory of automated timetabling VI. Lecture note in computer science, vol 3867. Springer, Berlin, pp 3–23

    Chapter  Google Scholar 

  25. McCollum B, McMullan P, Parkes A, Burke E, Abdullah S (2009) 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

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  28. Merlot LTG, Boland N, Hughes BD, Stuckey PJ (2003) A hybrid algorithm for the examination timetabling problem. In: Burke EK, De Causmaecker P (eds) Practice and theory of automated timetabling: selected papers from the 4th international conference. Lecture notes in computer science, vol 2740. Springer, Berlin, pp 207–231

    Chapter  Google Scholar 

  29. Müller T (2009) ITC2007 solver description: a hybrid approach. Ann Oper Res 172(1):429–44

    Article  MATH  Google Scholar 

  30. Pillay A (2007) Developmental approach to the examination timetabling problem. www.cs.qub.ac.uk/itc2007

  31. Pillay N, Banzhaf W (2009) A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem. Eur J Oper Res 197(2):482–491

    Article  MATH  Google Scholar 

  32. Pillay N, Banzhaf W (2007) A genetic programming approach to the generation of hyper-heuristics for the uncapacitated examination timetabling problem. In: Neves A et al (eds) Progress in artificial intelligence. Lecture notes in artificial intelligence, vol 4874. Springer, Berlin, pp 223–234

    Chapter  Google Scholar 

  33. Pillay N (2008) An analysis of representations for hyper-heuristics for the uncapacitated examination timetabling problem in a genetic programming system. In: Proceeding of SAICSIT 2008. ACM Press, New York, pp 188–192

    Chapter  Google Scholar 

  34. Qu R, Burke EK (2009) Hybridisations within a graph based hyper-heuristic framework for university timetabling problems. J Oper Res Soc 60:1273–1285

    Article  MATH  Google Scholar 

  35. Qu R, Burke EK (2005) Hybrid variable neighbourhood hyper-heuristics for exam timetabling problems. In: Proceedings of the MIC2005: the sixth metaheuristics international conference, Vienna, Austria, August 2005

    Google Scholar 

  36. Qu R, Burke EK, McCollum B, Merlot LTG, Lee SY (2009) A survey of search methodologies and automated system development for examination timetabling. J Sched 12(1):55–89

    Article  MathSciNet  MATH  Google Scholar 

  37. Ross P, Hart E, Corne D (1998) Some observations about GA-based exam timetabling. In: Burke EK, Carter MW (eds) Practice and theory of automated timetabling: selected papers from the 2nd international conference. Lecture notes in computer science, vol 1408. Springer, Berlin, pp 115–129

    Chapter  Google Scholar 

  38. Sabar NR, Ayob M, Kendall G (2009b) Tabu exponential Monte-Carlo with counter heuristic for examination timetabling. In: Proceedings of 2009 IEEE symposium on computational intelligence in scheduling (CISched 2009), Nashville, Tennessee, USA, 30 Mar–2 Apr, pp 90–94

    Chapter  Google Scholar 

  39. Sabar NR, Ayob M, Kendall G, Qu R (2009a) Roulette wheel graph colouring for solving examination timetabling problems. In: Proceedings of the 3rd international conference on combinatorial optimization and applications. Lecture notes in computer science, vol 5573. Springer, Berlin, pp 463–470

    Chapter  Google Scholar 

  40. Thompson J, Dowsland K (1998) A robust simulated annealing based examination timetabling system. Comput Oper Res 25:637–648

    Article  MATH  Google Scholar 

  41. Yang Y, Petrovic S (2005) A novel similarity measure for heuristic selection in examination timetabling. In: Burke EK, Trick M (eds) Practice and theory of automated timetabling V: selected papers from the 5th international conference. Lecture notes in computer science, vol 3616. Springer, Berlin, pp 377–396

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Data Mining and Optimisation Research Group (DMO), Centre for Artificial Intelligent (CAIT), Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    Nasser R. Sabar & Masri Ayob

  2. ASAP Research Group, School of Computer Science, The University of Nottingham, Nottingham, NG8 1BB, UK

    Rong Qu & Graham Kendall

  3. University of Nottingham Malaysia Campus, 43500, Semenyih, Selangor, Malaysia

    Graham Kendall

Authors
  1. Nasser R. Sabar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masri Ayob
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rong Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Graham Kendall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nasser R. Sabar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sabar, N.R., Ayob, M., Qu, R. et al. A graph coloring constructive hyper-heuristic for examination timetabling problems. Appl Intell 37, 1–11 (2012). https://doi.org/10.1007/s10489-011-0309-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-011-0309-9

Keywords

Search

Navigation