A parallelized matheuristic for the International Timetabling Competition 2019

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.

Appendix A: Our submitted solutions and bounds

Table 11 shows the results submitted during the competition, the 10-day results from Sect. 7.5 (Table 10), and our best-known lower bounds. During the competition, we produced the results for the Late instances using the described parallelized matheuristic with the precise setup detailed in Sect. 6.5. Since the competition organizers published the Late instances 10 days before the deadline, we know that we produced our submitted results in less than that. However, we cannot say anything for sure regarding the time to produce our other results. The competition organizers released the Early and Middle instances earlier during the competition, and we have developed the parallelized matheuristic and its components using those instances. Consequently, we have often used previously found solutions for warm-starting MIP solvers and as initial solutions for fix-and-optimize searches and different parameter settings for our methods, including the number of cores.

Therefore, for comparison, Table 11 also shows the results of the 10-day runs produced for this paper. Here, we use hardware and software slightly different from what we used during the competition. Comparing the 10-day and competition results, we see that the presented parallelized algorithm can produce solutions comparable to those submitted in the competition on all instances.

Finally, the table also reports our best-known lower bounds, some of which we have produced with methods not discussed in this paper. Using these lower bounds, we see that we solved five instances to optimality both during the competition and in the 10-day runs.

Table 11 An overview of the best solution we submitted during the competition, the results of the single 10-day run (Table 10), and our best-known lower bounds