![]() For numerous artificial and real-life instances, these heuristics generate high-quality timetables using considerably less computational resources compared to integer programming models solved using a state-of-the-art solver.Ī popular format of sports timetables are so-called round-robin tournaments in which teams play each other a fixed number of times. Second, we propose a memetic algorithm that makes use of local search to schedule or reschedule all home games of a team. First, we propose an adaptive large neighborhood method that repeatedly destroys and repairs a timetable. We present two heuristics that can handle these fairness objectives. Naturally, when one also incorporates fairness objectives on top of availability, the problem becomes even more challenging. In this paper, we first establish the computational complexity of time-relaxed timetabling with availability constraints. Besides, it can be important to timetable home and away games alternately. Despite their flexibility, time-relaxed timetables have the drawback that the rest period between teams’ consecutive games can vary considerably, and the difference in the number of games played at any point in the season can become large. This offers time-relaxed timetables additional flexibility to take into account venue availability constraints, stating that a team can only play at home when its venue is available, and player availability constraints stating that a team can only play when its players are available. In contrast to time-constrained sports timetables, time-relaxed timetables utilize (many) more time slots than there are games per team. Sports timetables determine who will play against whom, where, and on which time slot. The repository is publicly available and will be continuously updated as new instances or better solutions become available. For every problem, a short description highlights the most distinguishing characteristics of the problem. The resulting repository provides a (non-exhaustive) overview of most real-life sports timetabling applications published over the last five decades. For this, our repository relies on RobinX, an XML-supported classification framework. The construction of such a repository is not trivial, since there are dozens of constraints that need to be expressed in a standardized format. To mitigate this issue, this article provides a problem instance repository containing over 40 different types of instances covering artificial and real-life problem instances. This is problematic since only a few algorithmic insights are gained. The vast amount and variety of constraints and the lack of generally accepted benchmark problem instances make that timetable algorithms proposed in the literature are often tested on just one or two specific seasons of the competition under consideration. This is a complex matter, since real-life sports timetabling applications are typically highly constrained. The sports timetabling problem is a combinatorial optimization problem that consists of creating a timetable that defines against whom, when and where teams play games. ![]()
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