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Lower bounds for the ITC-2007 curriculum-based course timetabling problem

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  • Hao, Jin-Kao
  • Benlic, Una

Abstract

This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partition-based approach that is based on the "divide and conquer" principle. The proposed approach uses iterative tabu search to partition the initial problem into sub-problems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches.

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  • Hao, Jin-Kao & Benlic, Una, 2011. "Lower bounds for the ITC-2007 curriculum-based course timetabling problem," European Journal of Operational Research, Elsevier, vol. 212(3), pages 464-472, August.
  • Handle: RePEc:eee:ejores:v:212:y:2011:i:3:p:464-472
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    1. De Causmaecker, Patrick & Demeester, Peter & Vanden Berghe, Greet, 2009. "A decomposed metaheuristic approach for a real-world university timetabling problem," European Journal of Operational Research, Elsevier, vol. 195(1), pages 307-318, May.
    2. Michel Vasquez & Jin-Kao Hao, 2003. "Upper Bounds for the SPOT 5 Daily Photograph Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 7(1), pages 87-103, March.
    3. van den Broek, John & Hurkens, Cor & Woeginger, Gerhard, 2009. "Timetabling problems at the TU Eindhoven," European Journal of Operational Research, Elsevier, vol. 196(3), pages 877-885, August.
    4. Barry McCollum & Andrea Schaerf & Ben Paechter & Paul McMullan & Rhyd Lewis & Andrew J. Parkes & Luca Di Gaspero & Rong Qu & Edmund K. Burke, 2010. "Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 120-130, February.
    5. Lü, Zhipeng & Hao, Jin-Kao, 2010. "Adaptive Tabu Search for course timetabling," European Journal of Operational Research, Elsevier, vol. 200(1), pages 235-244, January.
    6. Al-Yakoob, Salem M. & Sherali, Hanif D., 2007. "A mixed-integer programming approach to a class timetabling problem: A case study with gender policies and traffic considerations," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1028-1044, August.
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    Cited by:

    1. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "An overview of curriculum-based course timetabling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 313-349, July.
    2. Massimiliano Caramia & Stefano Giordani, 2020. "Curriculum-Based Course Timetabling with Student Flow, Soft Constraints, and Smoothing Objectives: an Application to a Real Case Study," SN Operations Research Forum, Springer, vol. 1(2), pages 1-21, June.
    3. Vermuyten, Hendrik & Lemmens, Stef & Marques, Inês & Beliën, Jeroen, 2016. "Developing compact course timetables with optimized student flows," European Journal of Operational Research, Elsevier, vol. 251(2), pages 651-661.
    4. Bagger, Niels-Christian F. & Sørensen, Matias & Stidsen, Thomas R., 2019. "Dantzig–Wolfe decomposition of the daily course pattern formulation for curriculum-based course timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 430-446.
    5. Michael Lindahl & Matias Sørensen & Thomas R. Stidsen, 2018. "A fix-and-optimize matheuristic for university timetabling," Journal of Heuristics, Springer, vol. 24(4), pages 645-665, August.
    6. Niels-Christian Fink Bagger & Guy Desaulniers & Jacques Desrosiers, 2019. "Daily course pattern formulation and valid inequalities for the curriculum-based course timetabling problem," Journal of Scheduling, Springer, vol. 22(2), pages 155-172, April.
    7. Niels-Christian F. Bagger & Simon Kristiansen & Matias Sørensen & Thomas R. Stidsen, 2019. "Flow formulations for curriculum-based course timetabling," Annals of Operations Research, Springer, vol. 280(1), pages 121-150, September.

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