Which algorithm to select in sports timetabling?

TL;DR

This paper analyzes the performance variability of sports timetabling algorithms, using machine learning to predict the best algorithm for a given instance and providing insights into their strengths and weaknesses.

Contribution

It introduces an instance space analysis and a machine learning-based algorithm selection system for sports timetabling, enhancing understanding and performance prediction.

Findings

Algorithm performance varies significantly across instances.

The selection system accurately predicts the best algorithm for new instances.

Insights into key characteristics influencing algorithm performance.

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.