Which algorithm to select in sports timetabling?

TL;DR

This work addresses selecting the best algorithm for ITC2021 sports timetabling by applying instance-space analysis at the problem-type level. It evaluates eight state-of-the-art solvers across a large and diverse instance set, demonstrating that no single algorithm dominates and that problem-type features can predict strong performers via ML methods (including AutoFolio). The study reveals distinct performance footprints for each solver, highlights the complementary value of a solver portfolio, and offers practical recommendations for practitioners on which algorithm to deploy. The findings advance understanding of algorithm performance in sports timetabling and provide a scalable benchmarking framework for future work.

Abstract

Any sports competition needs a timetable, specifying when and where teams meet each other. The recent International Timetabling Competition (ITC2021) on sports timetabling showed that, although it is possible to develop general algorithms, the performance of each algorithm varies considerably over the problem instances. This paper provides an instance space analysis for sports timetabling, resulting in powerful insights into the strengths and weaknesses of eight state-of-the-art algorithms. Based on machine learning techniques, we propose an algorithm selection system that predicts which algorithm is likely to perform best when given the characteristics of a sports timetabling problem instance. Furthermore, we identify which characteristics are important in making that prediction, providing insights in the performance of the algorithms, and suggestions to further improve them. Finally, we assess the empirical hardness of the instances. Our results are based on large computational experiments involving about 50 years of CPU time on more than 500 newly generated problem instances.

Figures (11)

• Figure 1: Building blocks of the problem type analysis framework and their link with the sections of this paper.
• Figure 2: Projections of the problem instances in the original two-dimensional PCA problem type space. The first and second principal components are denoted by $z_1$ and $z_2$, respectively (see VanBulck2022b for the projection matrix used). Grey and blue circles and blue triangles represent the set of training, validation, and ITC2021 problem instances, respectively.
• Figure 3: Projections of the problem instances in the newly generated problem type space. The first and second principal components are denoted by $z_1$ and $z_2$, respectively (see \ref{['eq:weights']} for the projection matrix used). Grey and blue circles and blue triangles represent the set of training, validation, and ITC2021 problem instances, respectively.
• Figure 4: Normalized feature values across the problem type space as shown by the colorbar on the right of each subfigure.
• Figure 5: Percentage of feasible solutions found (a; numbers on top of the bars denote the absolute number of solutions found), and best performing algorithm for each problem instance (b; ties are broken by the ISA toolkit at random). Reprobate and MODAL never resulted in a (unique) best solution, and thus do not appear in the figure in the right.