Abstract
In the different stages of the educational system, the demand for efficient planning is increasing. This article treats the \(\mathcal NP \)-hard Consultation Timetabling Problem, a recurrent planning problem for the high schools in Denmark, which has not been described in the literature before. Two versions of the problem are considered, the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Problem (SCTP). It is shown that both problems can be modeled using the same Integer Programming model. Solutions are found using the state-of-the-art MIP solver Gurobi and Adaptive Large Neighborhood Search (ALNS), and computational results are established using 300 real-life datasets. These tests show that the developed ALNS algorithm is significantly outperforming both Gurobi and a currently applied heuristic for the PCTP. For both the PCTP and the SCTP, it is shown that the ALNS algorithm in average provides results within 5 % of optimum. The developed algorithm has been implemented in the commercial product Lectio, and is therefore available for approximately 95 % of the Danish high schools.
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Adenso-Diaz, B., Laguna, M.: Fine-tuning of algorithms using fractional experimental designs and local search. Oper. Res. 54(1), 99–114 (2006)
Azi, N., Gendreau, M., Potvin, J.Y.: An adaptive large neighborhood search for a vehicle routing problem with multiple trips. Technical report, CIRRELT (2010)
Balaprakash, P., Birattari, M., Stützle, T.: Improvement strategies for the f-race algorithm: sampling design and iterative refinement. In: Proceedings of the 4th International Conference on Hybrid Metaheuristics, HM’07, pp. 108–122. Springer, Berlin (2007)
Becker, S., Gottlieb, J., Stützle, T.: Applications of racing algorithms: an industrial perspective. In: Talbi, E.G., Liardet, P., Collet, P., Lutton, E., Schoenauer, M. (eds.) Artificial Evolution. Lecture Notes in Computer Science, vol. 3871, pp. 271–283. Springer, Berlin (2006)
Birattari, M.: The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective, vol. 292: Dissertations in Artificial Intelligence—Infix, 1st edn. Springer, Berlin (2005)
Birbas, T., Daskalaki, S., Housos, E.: School timetabling for quality student and teacher schedules. J. Sched. 12, 177–197 (2009)
Burke, E., Petrovic, S.: Recent research directions in automated timetabling. Eur. J. Oper. Res. 140(2), 266–280 (2002). doi:10.1016/S0377-2217(02)00069-3
Carter, M., Laporte, G.: Recent developments in practical course timetabling. In: Burke, E., Carter, M. (eds.) Practice and Theory of Automated Timetabling II. Lecture Notes in Computer Science, vol. 1408, pp. 3–19. Springer, Berlin (1998)
Chiarandini, M., Birattari, M., Socha, K., Rossi-Doria, O.: An effective hybrid algorithm for university course timetabling. J. Sched. 9, 403–432 (2006)
de Haan, P., Landman, R., Post, G., Ruizenaar, H.: A case study for timetabling in a dutch secondary school. In: Burke, E., Rudova, H. (eds.) Practice and Theory of Automated Timetabling VI. Lecture Notes in Computer Science, vol. 3867, pp. 267–279. Springer, Berlin (2007)
Diao, Y., Eskesen, F., Froehlich, S., Hellerstein, J., Spainhower, L., Surendra, M.: Generic online optimization of multiple configuration parameters with application to a database server. In: Brunner, M., Keller, A. (eds.) Self-Managing Distributed Systems. Lecture Notes in Computer Science, vol. 2867, pp. 79–93. Springer, Berlin (2003)
Erben, W., Keppler, J.: A genetic algorithm solving a weekly course-timetabling problem. In: Burke, E., Ross, P. (eds.) Practice and Theory of Automated Timetabling. Lecture Notes in Computer Science, vol. 1153, pp. 198–211. Springer, Berlin (1996)
Hutter, F., Hoos, H., Leyton-Brown, K., Stützle, T.: Paramils: an automatic algorithm configuration framework. J. Artif. Int. Res. 36, 267–306 (2009)
Kristiansen, S., Stidsen, T.R.: Adaptive large neighborhood search for student sectioning at danish high schools. In: Proceedings of the Ninth International Conference on the Practice and Theory of Automated Timetabling (PATAT, 2012) (2012)
Kristiansen, S., Sørensen, M., Stidsen, T.R.: Elective course planning. Eur. J. Oper. Res. 215(3), 713–720 (2011). doi:10.1016/j.ejor.2011.06.039
Laporte, G., Musmanno, R., Vocaturo, F.: An adaptive large neighbourhood search heuristic for the capacitated arc-routing problem with stochastic demands. Transp. Sci. 44(1), 125–135 (2010)
Lei, H., Laporte, G., Guo, B.: The capacitated vehicle routing problem with stochastic demands and time windows. Comput. Oper. Res. 38(12), 1775–1783 (2011). doi:10.1016/j.cor.2011.02.007
McCollum, B.: University timetabling: bridging the gap between research and practice. In: Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, pp. 15–35. Springer, Berlin (2006)
Mittelman, H.: Benchmarks for optimization software. http://plato.asu.edu/bench.html (2012)
Montero, E., Riff, M.C., Neveu, B.: An evaluation of off-line calibration techniques for evolutionary algorithms. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO ’10, pp. 299–300. ACM, New York (2010). doi: 10.1145/1830483.1830540
Muller, L.: An adaptive large neighborhood search algorithm for the resource-constrained project scheduling problem. In: MIC 2009: The VIII Metaheuristics International Conference (2009)
Müller, T., Murray, K.: Comprehensive approach to student sectioning. Ann. Oper. Res. 181, 249–269 (2010)
Muller, L.F., Spoorendonk, S.: A hybrid adaptive large neighborhood search algorithm applied to a lot-sizing problem. Tech. Report, DTU Management Engineering (2010)
Muller, L., Spoorendonk, S., Pisinger, D.: A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times. Eur. J. Oper. Res. 218(3), 614–623 (2011)
Pellegrini, P., Birattari, M.: Implementation effort and performance. In: SLS 2007, pp. 31–45. Springer, Berlin (2007)
Pellegrini, P., Stützle, T., Birattari , M.: Off-line vs On-line Tuning: A Study on Max–Min Ant System for the TSP. In: Swarm Intelligence. Lecture Notes in Computer Science, vol. 6234, pp. 239–250. Springer, Berlin (2010)
Pillay, N.: An overview of school timetabling research. In: Proceedings of the International Conference on the Theory and Practice of Automated Timetabling, pp. 321–335, Belfast (2010)
Pisinger, D., Ropke, S.: A general heuristic for vehicle routing problems. Comput. Oper. Res. 34, 2403–2435 (2005)
Pisinger, D., Ropke, S.: Large neighborhood search. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146, pp 399–419. Springer, Berlin (2010)
Potvin, J.Y., Rousseau, J.M.: A parallel route building algorithm for the vehicle routing and scheduling problem with time windows. Eur. J. Oper. Res. 66(3), 331–340 (1993)
Prescott-Gagnon, E., Desaulniers, G., Rousseau, L.M.: A branch-and-price-based large neighborhood search algorithm for the vehicle routing problem with time windows. Networks 54(4), 190–204 (2009). doi:10.1002/net.20332
Ribeiro, G.M., Laporte, G.: An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Comput. Oper. Res. 39(3), 728–735 (2012). doi:10.1016/j.cor.2011.05.005
Ropke, S., Pisinger, D.: An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transp. Sci. 40, 455–472 (2006)
Santos, H., Uchoa, E., Ochi, L., Maculan, N.: Strong bounds with cut and column generation for class-teacher timetabling. Ann. Oper. Res. 194, 399–412 (2010). doi:10.1007/s10479-010-0709-y
Schaerf, A.: A survey of automated timetabling. Artif. Intell. Rev. 13, 87–127 (1999). doi:10.1023/A:1006576209967
Shaw, P.: A new local search algorithm providing high quality solutions to vehicle routing problems. Working Paper, University of Strathclyde, Glasgow (1997)
Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.F. (eds.) Principles and Practice of Constraint Programming-CP98. Lecture Notes in Computer Science, vol. 1520, pp. 417–431. Springer, Berlin (1998)
Sørensen, M., Stidsen, T.R.: High school timetabling: modeling and solving a large number of cases in denmark. In: Proceedings of the Ninth International Conference on the Practice and Theory of Automated Timetabling (PATAT, 2012) (2012)
Tripathy, A.: School timetabling—a case in large binary integer linear programming. Manag. Sci. 30(12), 1473–1489 (1984)
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Kristiansen, S., Sørensen, M., Herold, M.B. et al. The consultation timetabling problem at Danish high schools. J Heuristics 19, 465–495 (2013). https://doi.org/10.1007/s10732-013-9219-9
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DOI: https://doi.org/10.1007/s10732-013-9219-9
Keywords
- High school
- Timetabling
- Metaheuristics
- Integer programming
- Adaptive Large Neighborhood Search
- F-Race tuning