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Integer programming for the generalized high school timetabling problem

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Abstract

Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial general-purpose MIP solver. Computational results show that our approach is able to find previously unknown optimal solutions for 2 instances of XHSTT and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best known solutions were found in 9 cases. Furthermore, the approach is compared with the finalists of Round 2 of the International Timetabling Competition 2011 and is shown to be competitive with one of the finalists.

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References

  • Avella, P., D’Auria, B., Salerno, S., & Vasilâev, I. (2007). A computational study of local search algorithms for italian high-school timetabling. Journal of Heuristics, 13, 543–556.

    Article  Google Scholar 

  • Birbas, T., Daskalaki, S., & Housos, E. (2009). School timetabling for quality student and teacher schedules. Journal of Scheduling, 12, 177–197.

    Article  Google Scholar 

  • Bixby, R.E. (2012). Optimization stories, 21st international symposium on mathematical programming Berlin, vol extra, Journal der Deutschen Mathematiker-Vereinigung, chap. A brief history of linear and mixed-integer programming computation (pp. 107–121).

  • ter Braak, M. (2012). A hyperheuristic for generating timetables in the XHSTT format. Master’s thesis, University of Twente.

  • Dorneles, ÁP., de Araújo, O.C., Maria-Brazil, S., & Buriol, L.S. (2012). The impact of compactness requirements on the resolution of high school timetabling problem. In: Congreso Latino-Iberoamericano de Investigación Operativa.

  • da Fonseca, G. H. G., Santos, H. G., Toffolo, T. Â.M., Brito, S. S., & Souza, M. J. F. (2014). GOAL solver: A hybrid local search based solver for high school timetabling. Annals of Operations Research. doi:10.1007/s10479-014-1685-4.

  • Kheiri, A., Özcan, E., & Parkes, A.J. (2012), Hysst: Hyper-heuristic search strategies and timetabling. In: Proceedings of the Ninth International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012) (pp. 497–499).

  • Kingston, J. H. (2013a). 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 Heidelberg: Springer.

    Chapter  Google Scholar 

  • Kingston, J.H. (2013b). High school timetable file format specification: Constraints. Retrieved Dec 8, 2013 from http://sydney.edu.au/engineering/it/~jeff/hseval.cgi?op=spec&part=constraints

  • Kingston, J.H. (2013c). The hseval high school timetable evaluator. Retrieved Dec 8, 2013 from http://sydney.edu.au/engineering/it/~jeff/hseval.cgi

  • Lach, G., & Lübbecke, M. (2012). Curriculum based course timetabling: new solutions to udine benchmark instances. Annals of Operations Research, 194, 255–272.

    Article  Google Scholar 

  • Pimmer, M., & Raidl, G. R. (2013). A timeslot-filling heuristic approach to construct high-school timetables. In L. Di Gaspero, A. Schaerf, & T. Stützle (Eds.), Advances in metaheuristics, operations research/computer science interfaces series (Vol. 53, pp. 143–157). New York: Springer.

    Google Scholar 

  • Post, G. (2013a). Benchmarking project for (high) school timetabling. Retrieved Dec 8, 2013 from http://www.utwente.nl/ctit/hstt/

  • Post, G. (2013b). International Timetabling Competition 2011 results. Retrieved Dec 8, 2013 from http://www.utwente.nl/ctit/hstt/itc2011/results/

  • Post, G., Ahmadi, S., Daskalaki, S., Kingston, J., Kyngas, J., Nurmi, C., et al. (2012a). An xml format for benchmarks in high school timetabling. Annals of Operations Research, 194, 385–397.

    Article  Google Scholar 

  • Post, G., Gaspero, L.D., Kingston, J.H., McCollum, B., & Schaerf, A. (2012b). The third international timetabling competition. In: Proceedings of the 9th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012), Son, Norway.

  • Romrös, J., & Homberger, J. (2012). An evolutionary algorithm for high school timetabling. In: Proceedings of the Ninth International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012) (pp. 485–488). Scandinavia: SINTEF.

  • Santos, H., Uchoa, E., Ochi, L., & Maculan, N. (2012). Strong bounds with cut and column generation for class-teacher timetabling. Annals of Operations Research, 194(1), 399–412.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sørensen, M., & Dahms, F. H. W. (2014). A two-stage decomposition of high school timetabling applied to cases in denmark. Computers & Operations Research, 43, 36–49.

    Article  Google Scholar 

  • Sørensen, M., & Stidsen, T. (2013). Comparing solution approaches for a complete model of high school timetabling. Tech. Rep. 5.2013, DTU Management Engineering, Technical University of Denmark.

  • Sørensen, M., Kristiansen, S., & Stidsen, T.R. (2012). International Timetabling Competition 2011: An adaptive large neighborhood search algorithm. In: Proceedings of the 9th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012) (pp. 489–492). Scandinavia: SINTEF.

  • Valouxis, C., Gogos, C., Alefragis, P., & Housos, E. (2012). Decomposing the high school timetable problem. In: Practice and Theory of Automated Timetabling (PATAT 2012), Son, Norway.

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Authors and Affiliations

  1. Management Science, Department of Management Engineering, Technical University of Denmark, Building 426, Produktionstorvet, 2800, Kgs. Lyngby, Denmark

    Simon Kristiansen, Matias Sørensen & Thomas R. Stidsen

  2. MaCom A/S, Vesterbrogade 48, 1., 1620, Copenhagen V, Denmark

    Simon Kristiansen & Matias Sørensen

Authors
  1. Simon Kristiansen
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  2. Matias Sørensen
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  3. Thomas R. Stidsen
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Correspondence to Matias Sørensen.

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Simon Kristiansen and Matias Sørensen have contributed equally to this work.

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Kristiansen, S., Sørensen, M. & Stidsen, T.R. Integer programming for the generalized high school timetabling problem. J Sched 18, 377–392 (2015). https://doi.org/10.1007/s10951-014-0405-x

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