Skip to main content
SpringerLink
Log in

GOAL solver: a hybrid local search based solver for high school timetabling

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

Abstract

This work presents a local search approach to the High School Timetabling Problem. The addressed timetabling model is the one stated in the Third International Timetabling Competition (ITC 2011), which considered many instances from educational institutions around the world and attracted seventeen competitors. Our team, named GOAL (Group of Optimization and Algorithms), developed a solver built upon the Kingston High School Timetabling Engine. Several neighborhood structures were developed and used in a hybrid metaheuristic based on Simulated Annealing and Iterated Local Search. The developed algorithm was the winner of the competition and produced the best known solutions for almost all instances.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. http://www.utwente.nl/ctit/hstt/, accessed on 30th April, 2013.

  2. http://www.idsia.ch/Files/ttcomp2002/, accessed on 30th April, 2013.

  3. http://www.cs.qub.ac.uk/itc2007/, accessed on 30th April, 2013.

  4. http://www.utwente.nl/ctit/hstt/itc2011/welcome/, accessed on 30th April, 2013.

  5. http://sydney.edu.au/engineering/it/~jeff/hseval.cgi, accessed on April, 2013.

  6. http://www.utwente.nl/ctit/hstt/archives/XHSTT-2012, accessed on April, 2013.

  7. On instances AustraliaSAHS96 and AustraliaTES99, the initial solution generated by KHE was better than the provided solution, so KHE was used in these cases.

  8. http://www.utwente.nl/ctit/hstt/archives/XHSTT-2013/

  9. 100 neighbors were considered in our tests.

  10. Excluding the Brazilian instances, in which we could not compete.

  11. We would like to highlight that for some of these instance there isn’t a known feasible solution yet.

References

  • de Haan, P., Landman, R., Post, G., & Ruizenaar, H. (2007). A case study for timetabling in a dutch secondary school. In: Lecture notes in computer science: VI practice and theory of automated timetabling (Vol. 3867, pp. 267–279). Berlin: Springer.

  • Even, S., Itai, A., & Shamir, A. (1976). On the complexity of timetable and multicommodity flow problems. SIAM Jounal of Computing, 5(4), 691–703.

    Article  Google Scholar 

  • Gendreau, M., & Potvin, J. (Eds.). (2010). Handbook of metaheuristics, international series in operations research and management science, (2nd ed., Vol. 146). Berlin: Springer.

    Google Scholar 

  • Johnson, D.S., Aragon, C.R., McGeoch, L., & Schevon, C. (1991). Optimization by simulated annealing: An experimental evaluation Part II, graph coloring and number partitioning. Operations Research, 39(3):378–406, doi:10.1287/opre.39.3.378, http://pubsonline.informs.org/doi/abs/10.1287/opre.39.3.378

  • Kingston, J. (2013). Educational timetabling. In A. S. Uyar, E. Ozcan, & N. Urquhart (Eds.), Automated scheduling and planning, studies in computational intelligence (Vol. 505, pp. 91–108). Berlin: Springer. doi:10.1007/978-3-642-39304-4_4.

  • Kingston, J.H. (2005). A tiling algorithm for high school timetabling. In: Lecture notes in computer science: V Practice and theory of automated timetabling (Vol. 3616, pp. 208–225). Berlin: Springer.

  • Kingston, J. H. (2006). Hierarchical timetable construction. In Problems, proceedings of the first international conference on the practice and theory of automated timetabling.

  • Kingston, J. H. (2012). A software library for school timetabling. http://sydney.edu.au/engineering/it/~jeff/khe/, Retrieved April 2012.

  • Kirkpatrick, S., Gellat, D. C., & Vecchi, M. P. (1983). Otimization by simulated annealing. Science, 202, 671–680.

    Article  Google Scholar 

  • Kristiansen, S., & Stidsen, T. R. (2013). A comprehensive study of educational timetabling, a survey. Report 8.2013, DTU Management Engineering.

  • Lourenco, H. R., Martin, O. C., & Stutzle, T. (2003). Iterated local search. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics, chap 11. Boston: Kluwer Academic Publishers.

    Google Scholar 

  • Lú, Z., & Hao, J. K. (2010). Adaptive Tabu Search for course timetabling. European Journal of Operational Research, 200(1), 235–244.

    Article  Google Scholar 

  • Muller, T. (2009). ITC2007 solver description: A hybrid approach. Annals of Operations Research, 172(1), 429–446.

  • Nurmi, K., & Kyngas, J. (2007). A framework for school timetabling problem. In Proceedings of the 3rd multidisciplinary international scheduling conference: theory and applications, Paris (pp. 386–393).

  • Pillay, N. (2013). A survey of school timetabling research. Annals of Operations Research. doi:10.1007/s10479-013-1321-8.

  • Post, G., Ahmadi, S., Daskalaki, S., Kingston, J. H., Kyngas, J., Nurmi, C., et al. (2010). An XML format for benchmarks in High School Timetabling. Annals of Operations Research, 3867, 267–279.

    Google Scholar 

  • Post, G., Kingston, J. H., Ahmadi, S., Daskalaki, S., Gogos, C., Kyngas, J., Nurmi, C., Musliu, N., Pillay, N., Santos, H., & Schaerf, A. (2014). XHSTT: An XML archive for high school timetabling problems in different countries. Annals of Operations Research, 218(1), 295–301. doi:10.1007/s10479-011-1012-2.

  • Post, G., Gaspero, L., Kingston, J., McCollum, B., & Schaerf, A. (2013). The third international timetabling competition. Annals of Operations Research, 1–7. doi:10.1007/s10479-013-1340-5.

  • Santos, H. G., Ochi, L. S., & Souza, M. J. F. (2005). A tabu search heuristic with efficient diversification strategies for the class/teacher timetabling problem. ACM Journal of Experimental Algorithmics, 10, 2–9.

    Google Scholar 

  • Santos, H. G., Uchoa, E., Ochi, L., & Maculan, N. (2012). Strong bounds with cut and column generation for class-teacher timetabling. Annals of Operations Research, 194, 399–412.

    Article  Google Scholar 

  • Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87–127.

    Article  Google Scholar 

  • Souza, M., Ochi, L., & Maculan, N. (2003). A GRASP-Tabu Search Algorithm for solving School Timetabling Problems. Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Valourix, C., & Housos, E. (2003). Constraint programming approach for school timetabling. Computers & Operations Research, 30, 1555–1572.

    Article  Google Scholar 

  • Wright, M. (1996). School timetabling using heuristic search. Journal of Operational Research Society, 47, 347–357.

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge FAPEMIG (Grant APQ-04611-10) and CNPq (Grant 552289/2011-6) for supporting the development of this research.

Author information

Authors and Affiliations

  1. Computing and Information Systems Department, Federal University of Ouro Preto, Ouro Preto, Brazil

    George Henrique Godim da Fonseca

  2. Computer Science Department, Federal University of Ouro Preto, Ouro Preto, Brazil

    Haroldo Gambini Santos, Túlio Ângelo Machado Toffolo, Samuel Souza Brito & Marcone Jamilson Freitas Souza

Authors
  1. George Henrique Godim da Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haroldo Gambini Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Túlio Ângelo Machado Toffolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Samuel Souza Brito
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marcone Jamilson Freitas Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Túlio Ângelo Machado Toffolo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

da Fonseca, G.H.G., Santos, H.G., Toffolo, T.Â.M. et al. GOAL solver: a hybrid local search based solver for high school timetabling. Ann Oper Res 239, 77–97 (2016). https://doi.org/10.1007/s10479-014-1685-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-014-1685-4

Keywords

Search

Navigation