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Elective course student sectioning at Danish high schools

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Abstract

The Elective Course Student Sectioning (ECSS) problem is a yearly recurrent planning problem at the Danish high schools. The problem is of assigning students to elective classes given their requests such that as many requests are fulfilled and the violations of the soft constraints are minimized. This paper presents an Adaptive Large Neighborhood Search heuristic for the ESCC. The algorithm is applied to 80 real-life instances from Danish high schools and compared with solutions found by using the state-of-the-art MIP solver Gurobi. The algorithm has been implemented in the commercial product Lectio, and is thereby available for approximately 200 high schools in Denmark.

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References

  • Azi, N., Gendreau, M., & Potvin, J.-Y. (2010). An adaptive large neighborhood search for a vehicle routing problem with multiple trips. CIRRELT.

  • Balaprakash, P., Birattari, M., & Stützle, T. (2007). Improvement strategies for the f-race algorithm: Sampling design and iterative refinement. In Proceedings of the 4th international conference on Hybrid metaheuristics, HM’07. Springer, Berlin, pp. 108–122.

  • Birattari, M. (2005). The problem of tuning metaheuristics as seen from a machine learning perspective (1st ed.). Dissertations in artificial intelligence—Infix (Vol. 292). Springer.

  • Burke, E. K., & Petrovic, S. (2002). Recent research directions in automated timetabling. European Journal of Operational Research, 140(2), 266–280. ISSN 0377–2217.

    Article  Google Scholar 

  • Carter, M. W. (2001). A comprehensive course timetabling and student scheduling system at the university of waterloo. In E. Burke & W. Erben (Eds.), Practice and theory of automated timetabling III. Lecture Notes in Computer Science (Vol. 2079, pp. 64–82) Berlin: Springer. ISBN 978-3-540-42421-5.

  • Carter, M. W., & Laporte, G. (1998). Recent developments in practical course timetabling. In Ed. Burke & M. Carter (Eds.), Practice and theory of automated timetabling II. Lecture Notes in Computer Science (Vol. 1408, pp. 3–19). Berlin: Springer.

  • Chiarandini, M., Birattari, M., Socha, K., & Rossi-Doria, O. (2006). An effective hybrid algorithm for university course timetabling. Journal of Scheduling, 9, 403–432. ISSN 1094–6136.

    Article  Google Scholar 

  • de Haan, P., Landman, R., Post, G., & Ruizenaar, H. (2007). A case study for timetabling in a dutch secondary school. In E. Burke & H. Rudova (Eds.), Practice and theory of automated timetabling VI. Lecture Notes in Computer Science (Vol. 3867, pp. 267–279). Berlin: Springer.

  • Erben, W., & Keppler, J. (1996). A genetic algorithm solving a weekly course-timetabling problem. In E. Burke & P. Ross (Eds.), Practice and theory of automated timetabling. Lecture Notes in Computer Science (Vol. 1153, pp. 198–211). Berlin: Springer.

  • Kristiansen, S., Sørensen, M., & Stidsen, T. R. (2011). Elective course planning. European Journal of Operational Research, 215(3), 713–720. doi:10.1016/j.ejor.2011.06.039. ISSN 0377-2217.

    Article  Google Scholar 

  • Kristiansen, S., Sørensen, M., Herold, M. B., & Stidsen, T. R. (2013). The consultation timetabling problem at danish high schools. Journal of Heuristics, 19(3), 465–495.

    Article  Google Scholar 

  • Laporte, G., Musmanno, R., & Vocaturo, F. (2010). An adaptive large neighbourhood search heuristic for the capacitated arc-routing problem with stochastic demands. Transportation Science, 44(1), 125–135.

    Article  Google Scholar 

  • Lei, H., Laporte, G., & Guo, B. (2011). The capacitated vehicle routing problem with stochastic demands and time windows. Computers & Operations Research, 38(12), 1775–1783. doi:10.1016/j.cor.2011.02.007. ISSN 0305–0548.

    Article  Google Scholar 

  • Müller, T., & Murray, K. (2010). Comprehensive approach to student sectioning. Annals of Operations Research, 181, 249–269. ISSN 0254–5330.

    Article  Google Scholar 

  • Muller, L. F., & Spoorendonk, S. (2010). A hybrid adaptive large neighborhood search algorithm applied to a lot-sizing problem. DTU Management Engineering: Technical report.

  • Muller, L. F. (2009). An adaptive large neighborhood search algorithm for the resource-constrained project scheduling problem. In MIC 2009: The VIII Metaheuristics International Conference.

  • Pellegrini, P., & Birattari, M. (2007). Implementation effort and performance. pp. 31–45.

  • Pillay, N. (2010). An overview of school timetabling research. In Proceedings of the international conference on the theory and practice of automated timetabling (pp. 321–335). Belfast, United Kingdom.

  • Pisinger, D., & Ropke, S. (2005). A general heuristic for vehicle routing problems. Computers & Operations Research, 34, 2403–2435. ISSN 0305–0548.

    Article  Google Scholar 

  • Pisinger, D., & Ropke, S. (2010). Large neighborhood search. In M. Gendreau & J.-Y. Potvin (Eds.), Handbook of metaheuristics (Vol. 146, pp. 399–419). International Series in Operations Research & Management Science. New York: Springer. ISBN 978-1-4419-1665-5.

  • Post, G., Di Gaspero, L., Kingston, J. H., McCollum, B., & Schaerf, A. (2012). The third international timetabling competition. In Proceedings of the ninth international conference on the practice and theory of automated timetabling (PATAT 2012), Son, Norway.

  • Ribeiro, G. M., & Laporte, G. (2012). An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research, 39(3), 728–735. ISSN 0305-0548.

    Article  Google Scholar 

  • Ropke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40, 455–472. ISSN 1526–5447.

    Article  Google Scholar 

  • Rudova, H., & Murray, K. (2003). University course timetabling with soft constraints. In Practice and theory of automated timetabling IV, pp. 310–328.

  • Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13, 87–127. ISSN 0269–2821.

    Article  Google Scholar 

  • Shaw, P. (1997). A new local search algorithm providing high quality solutions to vehicle routing problems.

  • Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In M. Maher & J.-F. Puget (Eds.), Principles and practice of constraint programming CP98. Lecture Notes in Computer Science (Vol. 1520, pp. 417–431). Berlin: Springer.

  • Sørensen, M., & Stidsen, T. R. (2013). Integer programming and adaptive large neighborhood search for real-world instances of high school timetabling. Annals of Operations Research, PATAT 2012 SI.

  • Sørensen, M., Kristiansen, S., & Stidsen, T. R. (2012). International timetabling competition 2011: An adaptive large neighborhood search algorithm. In Proceedings of the ninth international conference on the practice and theory of automated timetabling (PATAT 2012), pp. 489–492. SINTEF.

  • Steeg, J., & Schröder, M. (2008). A hybrid approach to solve the periodic home health care problem. In J. Kalcsics & S. Nickel (Eds.), Operations research proceedings 2007. Operations Research Proceedings (Vol. 2007, pp. 297–302). Berlin: Springer. ISBN 978-3-540-77903-2.

  • Welsh, D. J. A., & Powell, M. B. (1967). An upper bound for the chromatic number of a graph and its application to timetabling problems. The Computer Journal, 10(1): 85–86. doi:10.1093/comjnl/10.1.85. URL http://comjnl.oxfordjournals.org/content/10/1/85.abstract.

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Acknowledgments

The authors thank Michael Bigom Herold from MaCom A/S for kindly helping determining the problem and setting the weights for the problem, and MaCom A/S for providing all the data.

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Correspondence to Simon Kristiansen.

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Kristiansen, S., Stidsen, T.R. Elective course student sectioning at Danish high schools. Ann Oper Res 239, 99–117 (2016). https://doi.org/10.1007/s10479-014-1593-7

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