Skip to main content

Hybrid Graph Heuristics within a Hyper-Heuristic Approach to Exam Timetabling Problems

  • Conference paper
The Next Wave in Computing, Optimization, and Decision Technologies

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 29))

Abstract

This paper is concerned with the hybridization of two graph coloring heuristics (Saturation Degree and Largest Degree), and their application within a hyper-heuristic for exam timetabling problems. Hyper-heuristics can be seen as algorithms which intelligently select appropriate algorithms/heuristics for solving a problem. We developed a Tabu Search based hyper-heuristic to search for heuristic lists (of graph heuristics) for solving problems and investigated the heuristic lists found by employing knowledge discovery techniques. Two hybrid approaches (involving Saturation Degree and Largest Degree) including one which employs Case Based Reasoning are presented and discussed. Both the Tabu Search based hyper-heuristic and the hybrid approaches are tested on random and real-world exam timetabling problems. Experimental results are comparable with the best state-of-the-art approaches (as measured against established benchmark problems). The results also demonstrate an increased level of generality in our approach.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. Bardadym. Computer-Aided School and University Timetabling: The New Wave. In: P. Ross eds. Selected Papers from the 1st International Conference on the Practice and Theory of Automated Timetabling, LNCS 1153, Springer-Verlag, 1996). 2, pp. 22–45. (1995).

    Google Scholar 

  2. E. Burke and P. Ross eds. Selected Papers from the 1st International Conference on the Practice and Theory of Automated Timetabling, LNCS 1153, Springer-Verlag, 1996).

    Google Scholar 

  3. E. Burke and M. Carter eds. Selected Papers from the 2nd International Conference on the Practice and Theory of Automated Timetabling, LNCS 1408. (Springer-Verlag, 1998).

    Google Scholar 

  4. E. Burke and W. Erben, W. eds. Selected Papers from the 3rd International Conference on the Practice and Theory of Automated Timetabling, LNCS 2079, (Springer-Verlag, 2001).

    Google Scholar 

  5. E. Burke, K. Jackson, J Kingston and R. Weare. Automated Timetabling: The State of the Art. The Computer Journal, 40(9): 565–571, (1997).

    Article  Google Scholar 

  6. E. Burke and P. Causmaecker, eds. Selected Papers from the 4th International Conference on the Practice and Theory of Automated Timetabling, LNCS 2740. (Springer-Verlag, 2003).

    Google Scholar 

  7. M. Carter and G. Laporte. Recent Developments in Practical Examination Timetabling. In: P. Ross eds. Selected Papers from the 1st International Conference on the Practice and Theory of Automated Timetabling, LNCS 1153, Springer-Verlag, 1996). 2, pp. 3–21. (1995).

    Google Scholar 

  8. M. Carter and G. Laporte. Recent Developments in Practical Course Timetabling. In: M. Carter eds. Selected Papers from the 2nd International Conference on the Practice and Theory of Automated Timetabling, LNCS 1408. (Springer-Verlag, 1998). 3, pp. 3–19.

    Google Scholar 

  9. A. Schaerf. A Survey of Automated Timetabling. Artificial Intelligence Review. 13(2): 87–127. (1999).

    Article  Google Scholar 

  10. E. Burke and S. Petrovic, Recent Research Directions in Automated Timetabling. EJOR, 140(2): 266–280. (2002).

    Article  MATH  Google Scholar 

  11. D. Brelaz, New Methods to Color the Vertices of a Graph. Communications of the ACM, 22(4): 251–256. (1979).

    Article  MATH  MathSciNet  Google Scholar 

  12. de Werra, Graphs, Hypergraphs and Timetabling. Methods of Operations Research. 49: 201–213. (1985).

    MATH  Google Scholar 

  13. E. Burke, J. Kingston and D. de Werra, Applications to Timetabling, Handbook of Graph Theory, (J. Gross and J. Yellen eds.), pp. 445–474, (Chapman Hall/CRC Press, 2003).

    Google Scholar 

  14. M. Carter, A Lagrangian Relaxation Approach to the Classroom Assignment Problem. IFOR 27(2): 230–246. (1986).

    MathSciNet  Google Scholar 

  15. B. Deris, S. Omatu, H. Ohta and D. Samat. University Timetabling by Constraint-based Reasoning: A Case Study. JORS. 48(12): 1178–1190. (1997).

    Article  MATH  Google Scholar 

  16. K. Nonobe and T. Ibaraki. A Tabu Search Approach to the Constraint Satisfaction Problem as a General Problem Solver. EJOR. 106: 599–623. (1998).

    Article  MATH  Google Scholar 

  17. D. Banks, P. Beel and A. Meisles. A Heuristic Incremental Modelling Approach to Course Timetabling. Proceedings of the Canadian Conference on Artificial Intelligence, pp. 16–29. (1998).

    Google Scholar 

  18. F. Glover, and G. Kochenberger, Handbook of Metaheuristics, Kluwer. 2003.

    Google Scholar 

  19. D. Costa. A Tabu Search for Computing an Operational Timetable. EJOR. 76: 98–110. (1994).

    Article  MATH  Google Scholar 

  20. L. Di Gaspero and A. Schaerf, Tabu Search Techniques for Examination Timetabling, In: W. Erben eds. Selected Papers from the 3rd International Conference on the Practice and Theory of Automated Timetabling, LNCS 2079, (Springer-Verlag, 2001). 4, pp. 104–117. (2000).

    Google Scholar 

  21. K. Dowsland, Off the Peg or Made to Measure”, In: M. Carter eds. Selected Papers from the 2nd International Conference on the Practice and Theory of Automated Timetabling, LNCS 1408. (Springer-Verlag, 1998). 3 37–52. (1998).

    Google Scholar 

  22. S. Casey, J. Thompson, A Hybrid Algorithm for the Examination Timetabling Problem. In: P. Causmaecker eds. Selected Papers from the 4th International Conference on the Practice and Theory of Automated Timetabling, LNCS 2740. (Springer-Verlag, 2003). 6, pp. 205–230. (2002).

    Google Scholar 

  23. E. Burke, J. Newall and R. Weare, R. Initialization Strategies and Diversity in Evolutionary Timetabling. Evolutionary Computation, 6(1): 81–103. (1998).

    Google Scholar 

  24. E. Burke and J. Newall. A Multi-Stage Evolutionary Algorithm for the Timetabling Problem. The IEEE Transactions on Evolutionary Computation. 3(1): 63–74. (1999).

    Article  Google Scholar 

  25. D. Leake ed. Case-based Reasoning: Experiences, Lessons and Future Directions. (AAAI Press, Menlo Park, CA. 1996).

    Google Scholar 

  26. E. Burke, B., MacCarthy, S. Petrovic and R. Qu, Structured Cases in Case-Based Reasoning-Re-using and Adapting Cases for Time-tabling Problems. Knowledge-Based Systems, 13(2–3): 159–165. (2000).

    Article  Google Scholar 

  27. E. Burke, B. MacCarthy, S. Petrovic and R. Qu, Multiple-Retrieval Case-Based Reasoning for Course Timetabling Problems. Technical Report NOTTCS-TR-2004-3, School of CSiT, University of Nottingham, U.K. (accepted by JORS, 2004).

    Google Scholar 

  28. E._ Burke, S. Petrovic and R. Qu, Case Based Heuristic Selection for Examination Timetabling. Technical Report NOTTCS-TR-2004-2, School of CSiT, University of Nottingham, U.K. (To appear in Journal of Scheduling, 2005).

    Google Scholar 

  29. S. Petrovic, G. Beddoe and G. Vandem Berghe, Storing and Adapting Repair Experiences in Employee Rostering. In: P. Causmaecker eds. Selected Papers from the 4th International Conference on the Practice and Theory of Automated Timetabling, LNCS 2740. (Springer-Verlag, 2003). 6, pp. 148–165. (2003).

    Google Scholar 

  30. E. Burke, E. Hart, G. Kendall, J. Newall, P. Ross and S. Schulenburg, Hyper-heuristics: an Emerging Direction in Modern Search Technology. In: F. Glover and G. Kochenberger eds., Handbook of Meta-Heuristics, (Kluwer, 2003), pp. 457–474.

    Google Scholar 

  31. G. Kendall, P. Cowling and E. Soubeiga, Choice Function and Random HyperHeuristics. Proceedings of SEAL’02, pp. 667–671. (2002).

    Google Scholar 

  32. E. Burke, G. Kendall. G and E. Soubeiga, A Tabu Search Hyperheuristic for Timetabling and Rostering. Journal of Heuristics. 9(6). (2003).

    Google Scholar 

  33. L. Han and G. Kendall. Investigation of a Tabu Assisted Hyper-Heuristic Genetic Algorithm. Congress on Evolutionary Computation, Canberra, Australia, 2230–2237. (2003).

    Google Scholar 

  34. H. Asmuni, E. Burke, and J. Garibaldi. Fuzzy Multiple Ordering Criteria For Examination Timetabling. To appear in the 5th International Conference on the Practice and Theory of Automated Timetabling. Pittsburgh, USA. Aug 2004.

    Google Scholar 

  35. E. Burke, Y. Bykov, J. Newall and S. Petrovic. A Time-Predefined Local Search Approach to Exam Timetabling Problems. HE Transactions on Operations Engineering, 36(6), 509–528, (2004).

    Google Scholar 

  36. E. Burke and J. Newall, Enhancing Timetable Solutions with Local Search Methods. In: P. Causmaecker eds. Selected Papers from the 4th International Conference on the Practice and Theory of Automated Timetabling, LNCS 2740. (Springer-Verlag, 2003). 6, pp. 195–206. (2002).

    Google Scholar 

  37. M. Caramia, P. Dell’Olmo and G. Italiano, New Algorithms for Examination Timetabling. In: S. Naher and D. Wagner eds. LNCS 1982, pp. 230–241. (2001).

    Google Scholar 

  38. M. Carter, G. Laporte and S. Lee, Examination Timetabling: Algorithmic Strategies and Applications, JORS, 47: 373–383. (1996).

    Google Scholar 

  39. L. Merlot, N. Boland, B. Hughes and P. Stuckey. A Hybrid Algorithm for the Examination Timetabling Problem. In: E. Burke and P. De Causmaecker (eds.) Proceedings of the 4th International Conference on Practice and Theory of Timetabling, pp. 348–371. (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this paper

Cite this paper

Burke, E., Dror, M., Petrovic, S., Qu, R. (2005). Hybrid Graph Heuristics within a Hyper-Heuristic Approach to Exam Timetabling Problems. In: Golden, B., Raghavan, S., Wasil, E. (eds) The Next Wave in Computing, Optimization, and Decision Technologies. Operations Research/Computer Science Interfaces Series, vol 29. Springer, Boston, MA . https://doi.org/10.1007/0-387-23529-9_6

Download citation

  • DOI: https://doi.org/10.1007/0-387-23529-9_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-23528-8

  • Online ISBN: 978-0-387-23529-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics