Optimizing Student Course Preferences in School Timetabling
- 348 Downloads
School timetabling is a complex problem in combinatorial optimization, requiring the best possible assignment of course sections to teachers, timeslots, and classrooms. There exist standard techniques for generating a school timetable, especially in cohort-based programs where students take the same set of required courses, along with several electives. However, in small interdisciplinary institutions where there are only one or two sections of each course, and there is much diversity in course preferences among individual students, it is very difficult to create an optimal timetable that enables each student to take their desired set of courses while satisfying all of the required constraints.
In this paper, we present a two-part school timetabling algorithm that was applied to generate the optimal Master Timetable for a Canadian all-girls high school, enrolling students in 100% of their core courses and 94% of their most desired electives. We conclude the paper by explaining how this algorithm, combining graph coloring with integer linear programming, can benefit other institutions that need to consider student course preferences in their timetabling.
KeywordsSchool timetabling Post Enrollment Course Timetabling Problem Integer Programming Graph coloring Optimization
The authors thank the reviewers for their insightful comments that significantly improved the final version of this paper. We are grateful to Darlene DeMerchant and Megan Hedderick at St. Margaret’s School for making this collaboration possible. Finally, we acknowledge that the student author’s research was sponsored by a Student Project Grant awarded by the Research and Scholarly Works Committee at Quest University Canada.
- 5.Chiarandini, M., Fawcett, C., Hoos, H.H.: A modular multiphase heuristic solver for post enrolment course timetabling. In: PATAT (2008)Google Scholar
- 8.Fonseca, G.H., Santos, H.G., Carrano, E.G., Stidsen, T.J.: Modelling and solving university course timetabling problems through XHSTT. In: PATAT, vol. 16, pp. 127–138 (2016)Google Scholar
- 9.Google OR-Tools: Fast and portable software for combinatorial optimization. https://developers.google.com/optimization. Accessed 17 Feb 2020
- 10.Gotlieb, C.C.: The construction of class-teacher timetables. In: IFIP Congress, Amsterdam, vol. 62, pp. 73–77 (1963)Google Scholar
- 11.GrinPy: A NetworkX extension for calculating graph invariants. https://pypi.org/project/grinpy/. Accessed 17 Feb 2020
- 12.Hébrard, E., Katsirelos, G.: A hybrid approach for exact coloring of massive graphs. In: Rousseau, L.-M., Stergiou, K. (eds.) CPAIOR 2019. LNCS, vol. 11494, pp. 374–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19212-9_25
- 17.Lewis, R., Paechter, R., McCollum, B.: Post enrolment based course timetabling: a description of the problem model used for track two of the second international timetabling competition (2007)Google Scholar
- 18.Liu, Y., Zhang, D., Leung, S.C.: A simulated annealing algorithm with a new neighborhood structure for the timetabling problem. In: Proceedings of the First ACM/SIGEVO Summit on Genetic and Evolutionary Computation, pp. 381–386 (2009)Google Scholar
- 20.Minh, K.N.T.T., Thanh, N.D.T., Trang, K.T., Hue, N.T.T.: Using Tabu search for solving a high school timetabling problem. In: Nguyen, N.T., Katarzyniak, R., Chen, S.M. (eds.) Advances in Intelligent Information and Database Systems. SCI, vol. 283, pp. 305–313. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12090-9_26CrossRefGoogle Scholar
- 21.NetworkX: Software for complex networks. https://networkx.github.io/. Accessed 17 Feb 2020
- 26.Raghavjee, R., Pillay, N.: An application of genetic algorithms to the school timetabling problem. In: Proceedings of the 2008 Annual Research Conference of the South African Institute of Computer Scientists and Information Technologists on IT Research in Developing Countries: Riding the Wave of Technology, pp. 193–199 (2008)Google Scholar
- 28.St. Margaret’s Boarding School Viewbook. https://www.stmarg.ca/wp-content/uploads/SMS-Boarding-Viewbook.pdf. Accessed 17 Feb 2020