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A parallelized matheuristic for the International Timetabling Competition 2019

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  • Rasmus Ø. Mikkelsen

    (Technical University of Denmark, DTU Management)

  • Dennis S. Holm

    (Technical University of Denmark, DTU Management)

Abstract

The International Timetabling Competition 2019 (ITC 2019) presents a novel and generalized university timetabling problem composed of traditional class time and room assignment and student sectioning. In this paper, we present a parallelized matheuristic tailored to the ITC 2019 problem. The matheuristic is composed of multiple methods using the graph-based mixed-integer programming (MIP) model defined for the ITC 2019 problem by Holm et al. (A graph-based MIP formulation of the International Timetabling Competition 2019. J Sched, 2022. https://doi.org/10.1007/s10951-022-00724-y ). We detail all methods included in the parallelized matheuristic and the collaboration between them. The parallelized matheuristic includes two methods for producing initial solutions and uses a fix-and-optimize matheuristic to improve solutions. Additionally, the method uses the full MIP model to calculate lower bounds. We describe how the methods perform collaboratively through solution sharing, and a diversification scheme invoked when the search stagnates. Furthermore, we explain how we decompose the problem for instances with a large number of students. We evaluate components of the parallelized matheuristic using the 30 benchmark instances of the ITC 2019. The complete parallelized matheuristic performs well, even solving some instances to proven optimality. The presented method is the winning algorithm of the competition, further demonstrating its quality.

Suggested Citation

  • Rasmus Ø. Mikkelsen & Dennis S. Holm, 2022. "A parallelized matheuristic for the International Timetabling Competition 2019," Journal of Scheduling, Springer, vol. 25(4), pages 429-452, August.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:4:d:10.1007_s10951-022-00728-8
    DOI: 10.1007/s10951-022-00728-8
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    References listed on IDEAS

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    1. 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.
    2. Gerald Lach & Marco Lübbecke, 2012. "Curriculum based course timetabling: new solutions to Udine benchmark instances," Annals of Operations Research, Springer, vol. 194(1), pages 255-272, April.
    3. Andrea Bettinelli & Valentina Cacchiani & Roberto Roberti & Paolo Toth, 2015. "Rejoinder on: 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 366-368, July.
    4. Lang, Jan Christian & Shen, Zuo-Jun Max, 2011. "Fix-and-optimize heuristics for capacitated lot-sizing with sequence-dependent setups and substitutions," European Journal of Operational Research, Elsevier, vol. 214(3), pages 595-605, November.
    5. Saviniec, Landir & Santos, Maristela O. & Costa, Alysson M., 2018. "Parallel local search algorithms for high school timetabling problems," European Journal of Operational Research, Elsevier, vol. 265(1), pages 81-98.
    6. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    7. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    8. 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.
    9. 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.
    10. Edmund Burke & Jakub Mareček & Andrew Parkes & Hana Rudová, 2012. "A branch-and-cut procedure for the Udine Course Timetabling problem," Annals of Operations Research, Springer, vol. 194(1), pages 71-87, April.
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    Cited by:

    1. Ceschia, Sara & Di Gaspero, Luca & Schaerf, Andrea, 2023. "Educational timetabling: Problems, benchmarks, and state-of-the-art results," European Journal of Operational Research, Elsevier, vol. 308(1), pages 1-18.
    2. Fabian Dunke & Stefan Nickel, 2023. "A matheuristic for customized multi-level multi-criteria university timetabling," Annals of Operations Research, Springer, vol. 328(2), pages 1313-1348, September.

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