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Measuring the complexity of university timetabling instances

Author

Listed:
  • Felipe Rosa-Rivera

    (Universidad Autónoma de San Luis Potosí)

  • Jose I. Nunez-Varela

    (Universidad Autónoma de San Luis Potosí)

  • Cesar A. Puente-Montejano

    (Universidad Autónoma de San Luis Potosí)

  • Sandra E. Nava-Muñoz

    (Universidad Autónoma de San Luis Potosí)

Abstract

University timetabling is a real-world problem frequently encountered in higher education institutions. It has been studied by many researchers who have proposed a wide variety of solutions. Measuring the variation of the performance of solution approaches across instance spaces is a critical factor for algorithm selection and algorithm configuration, but because of the diverse conditions that define the problem within different educational contexts, measurement has not been formally addressed within the university timetabling context. In this paper, we propose a set of metrics to predict the performance of combinatorial optimization algorithms that generate initial solutions for university timetabling instances. These metrics, derived from the fields of enumerative combinatorics and graph coloring, include size-related instance properties, counting functions, feature ratios and constraint indexes evaluated through a feature selection methodology that, based on regression algorithms, characterizes the empirical hardness of a subspace of synthetically generated instances. The results obtained with this methodology show the current need not only to develop solution strategies for particular cases of the problem, but also to produce a formal description of the conditions that make instance spaces hard to solve, in order to improve and integrate the available solution approaches.

Suggested Citation

  • Felipe Rosa-Rivera & Jose I. Nunez-Varela & Cesar A. Puente-Montejano & Sandra E. Nava-Muñoz, 2021. "Measuring the complexity of university timetabling instances," Journal of Scheduling, Springer, vol. 24(1), pages 103-121, February.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:1:d:10.1007_s10951-020-00641-y
    DOI: 10.1007/s10951-020-00641-y
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    References listed on IDEAS

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    1. Gerhard Post & Jeffrey Kingston & Samad Ahmadi & Sophia Daskalaki & Christos Gogos & Jari Kyngas & Cimmo Nurmi & Nysret Musliu & Nelishia Pillay & Haroldo Santos & Andrea Schaerf, 2014. "XHSTT: an XML archive for high school timetabling problems in different countries," Annals of Operations Research, Springer, vol. 218(1), pages 295-301, July.
    2. 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.
    3. Fonseca, George H.G. & Santos, Haroldo G. & Carrano, Eduardo G. & Stidsen, Thomas J.R., 2017. "Integer programming techniques for educational timetabling," European Journal of Operational Research, Elsevier, vol. 262(1), pages 28-39.
    4. Alex Bonutti & Fabio Cesco & Luca Gaspero & Andrea Schaerf, 2012. "Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results," Annals of Operations Research, Springer, vol. 194(1), pages 59-70, April.
    5. Nelishia Pillay, 2014. "A survey of school timetabling research," Annals of Operations Research, Springer, vol. 218(1), pages 261-293, July.
    6. Soria-Alcaraz, Jorge A. & Ochoa, Gabriela & Swan, Jerry & Carpio, Martin & Puga, Hector & Burke, Edmund K., 2014. "Effective learning hyper-heuristics for the course timetabling problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 77-86.
    7. Messelis, Tommy & De Causmaecker, Patrick, 2014. "An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 233(3), pages 511-528.
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