Journal of Scheduling

, Volume 15, Issue 1, pp 49–61 | Cite as

Design and statistical analysis of a hybrid local search algorithm for course timetabling

Article

Abstract

We propose a hybrid local search algorithm for the solution of the Curriculum-Based Course Timetabling Problem and we undertake a systematic statistical study of the relative influence of the relevant features on the performances of the algorithm. In particular, we apply modern statistical techniques for the design and analysis of experiments, such as nearly orthogonal space-filling Latin hypercubes and response surface methods. As a result of this analysis, our technique, properly tuned, compares favorably with the best known ones for this problem.

Keywords

University timetabling Statistical analysis Tabu search Simulated annealing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adenso-Diaz, B., & Laguna, M. (2006). Fine-tuning of algorithms using fractional experimental designs and local search. Operations Research, 54(1), 99–114. CrossRefGoogle Scholar
  2. Anagnostopoulos, A., Michel, L., Van Hentenryck, P., & Vergados, Y. (2006). A simulated annealing approach to the traveling tournament problem. Journal of Scheduling, 9(2), 177–193. CrossRefGoogle Scholar
  3. Bang-Jensen, J., Chiarandini, M., Goegebeur, Y., & Jørgensen, B. (2007). Mixed models for the analysis of local search components. In T. Stützle, M. Birattari, & H. Hoos (Eds.), Lecture notes in computer science: Vol. 4638. Engineering stochastic local search algorithms (SLS-2007) (pp. 91–105). Berlin: Springer. Google Scholar
  4. Bonutti, A., De Cesco, F., Di Gaspero, L., & Schaerf, A. (2010) Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results. Annals of Operations Research. doi:10.1007/s10479-010-0707-0 Google Scholar
  5. Box, G. E. P., Hunter, J. S., & Hunter, W. G. (2005). Statistics for experimenters: design, innovation, and discovery (2nd ed.). New York: Wiley-Interscience. Google Scholar
  6. 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(1), 177–192. CrossRefGoogle Scholar
  7. Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2008a). Penalising patterns in timetables: Novel integer programming formulations. In S. Nickel & J. Kalcsics (Eds.), Operations research proceedings 2007. Berlin: Springer. Google Scholar
  8. Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2008b). A branch-and-cut procedure for the Udine corse timetabling. In E. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT-2008). Google Scholar
  9. Causmaecker, P. D., Demeester, P., & Vanden Berghe, G. (2009). A decomposed metaheuristic approach for a real-world university timetabling problem. European Journal of Operational Research, 195(1), 307–318. CrossRefGoogle Scholar
  10. Chiarandini, M., Fawcett, C., & Hoos, H. H. (2008). A modular multiphase heuristic solver for post enrolment course timetabling. In E. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT-2008). Google Scholar
  11. Cioppa, T. M., & Lucas, T. W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics, 49(1), 45–55. CrossRefGoogle Scholar
  12. Coy, S. P., Golden, B. L., Runger, G. C., & Wasil, EA (2001). Using experimental design to find effective parameter settings for heuristics. Journal of Heuristics, 7, 77–97. CrossRefGoogle Scholar
  13. Di Gaspero, L., & Schaerf, A. (2006). Neighborhood portfolio approach for local search applied to timetabling problems. Journal of Mathematical Modeling and Algorithms, 5(1), 65–89. CrossRefGoogle Scholar
  14. 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). School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast (UK), ITC-2007 site: http://www.cs.qub.ac.uk/itc2007/.
  15. Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management Science, 40(10), 1276–1290. CrossRefGoogle Scholar
  16. Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic. CrossRefGoogle Scholar
  17. Hoos, H. H., & Stützle, T. (2005). Stochastic local search—foundations and applications. San Francisco: Morgan Kaufmann. Google Scholar
  18. Hothorn, T., Hornik, K., van de Wiel, M. A., & Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. Journal of Statistical Software, 28(8), 1–23. http://www.jstatsoft.org/v28/i08. Google Scholar
  19. Hutter, F., Hoos, H. H., & Stützle, T. (2007). Automatic algorithm configuration based on local search. In R. C. Holte & A. Howe (Eds.), Proceedings of the 22nd AAAI conference on artificial intelligence, July 22–26, 2007, Vancouver, British Columbia, Canada (pp. 1152–1157). Google Scholar
  20. Kirkpatrick, S., Gelatt, C. D. Jr., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680. CrossRefGoogle Scholar
  21. Kleijnen, J. P. C., Sanchez, S. M., Lucas, T. W., & Cioppa, T. M. (2005). A user’s guide to the brave new world of designing simulation experiments. INFORMS Journal on Computing, 17, 263–289. CrossRefGoogle Scholar
  22. Lach, G., & Lübbecke, M. (2008a). Curriculum based course timetabling: Optimal solutions to the Udine benchmark instances. In E. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT-2008). Google Scholar
  23. Lach, G., & Lübbecke, M. E. (2008b). Optimal university course timetables and the partial transversal polytope. In C. C. McGeoch (Ed.), Lecture notes in computer science: Vol. 5038. Experimental algorithms, 7th international workshop, WEA 2008 (pp. 235–248). Berlin: Springer. Google Scholar
  24. Lü, Z., & Hao, J. K. (2010). Adaptive tabu search for course timetabling. European Journal of Operational Research, 200(1), 235–244. CrossRefGoogle Scholar
  25. Lucas, T. W., & Sanchez, S. M. (2005). Nolh designs spreeadsheet. http://diana.cs.nps.navy.mil/SeedLab/, visited on August 11, 2010.
  26. McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Di Gaspero, L., 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
  27. Müller, T. (2008). ITC2007 solver description: A hybrid approach. In E. Burke & M. Gendreau (Eds.), Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT-2008). Google Scholar
  28. Murray, K. S., Müller, T., & Rudová, H. (2007). Modeling and solution of a complex university course timetabling problem. In Lecture notes in computer science: Vol. 3867. Practice and theory of automated timetabling VI (pp. 189–209). Berlin: Springer. CrossRefGoogle Scholar
  29. Myers, R. H. Montgomery, D. C. (2002). Response surface methodology (2nd ed.). New York: Wiley. Google Scholar
  30. Paquete, L., Chiarandini, M., & Basso, D. (Eds.) (2006). Proceedings of the workshop on empirical methods for the analysis of algorithms, EMAA 2006. Reykjavik, Iceland. Google Scholar
  31. Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-plus. Berlin: Springer. CrossRefGoogle Scholar
  32. R Development Core Team (2008). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. http://www.R-project.org. Google Scholar
  33. Ridge, E., & Kudenko, D. (2006). Sequential experiment design for screening and tuning parameters of stochastic heuristics. In L. Paquete, M. Chiarandini, & D. Basso (Eds.), Proceedings of the 1st workshop on empirical methods for the analysis of algorithms at the ninth international conference on parallel problem solving from nature (PPSN), Reykjavik, Iceland (pp. 27–34). Google Scholar
  34. Ridge, E., & Kudenko, D. (2007). Tuning the performance of the mmas heuristic. In T. Stützle et al. (Ed.), Lecture notes in computer science: Vol. 4638. Engineering stochastic local search algorithms. Designing, implementing and analyzing effective heuristics, international workshop, SLS 2007, Proceedings, Brussels, Belgium, September 6–8, 2007 (pp. 46–60). Berlin: Springer. CrossRefGoogle Scholar
  35. Ryan, T. P. (2007). Modern experimental design. New York: Wiley. CrossRefGoogle Scholar
  36. Stützle, T., Birattari, M., & Holger, H. H. (Eds.) (2007). Engineering stochastic local search algorithms. In Lecture notes in computer science: Vol. 4638. Designing, implementing and analyzing effective heuristics, international workshop, SLS 2007, Brussels, Belgium, September 6–8, 2007, Proceedings. Berlin: Springer. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ruggero Bellio
    • 1
  • Luca Di Gaspero
    • 2
  • Andrea Schaerf
    • 2
  1. 1.Dipartimento di Scienze StatisticheUniversità di UdineUdineItaly
  2. 2.Dipartimento di Ingegneria Elettrica, Gestionale e MeccanicaUniversità di UdineUdineItaly

Personalised recommendations