Applying Heuristic Methods to Schedule Sports Competitions on Multiple Venues

Scheduling sports competitions is a difficult task because it is often very difficult to construct schedules that are considered fair by all competitors. In addition, the schedules should also satisfy a considerably large number of additional requirements and constraints. Most of the sports scheduling problems that have been tackled in the literature refer to competitions in which a venue is associated to each competitor. In these cases, selecting the venue in which each tie will be played is not an issue because this is defined by the status, home or away, of the competitors. Scheduling problems in most sports leagues (football, baseball, rugby, cricket, etc.) fall into this category because each team has its own venue. However, many other sports competitions take place on a set of venues that are neutral to all competitors. This is the case in some international competitions (such as the football world cup, and the Wimbledon tennis tournament) and in recreation leagues using a set of drill stations. In these cases, choosing the venue to play each tie is part of the scheduling process and this often makes the problem more difficulty to solve. Here, we propose the application of heuristic methods for constructing schedules for this type of sports competitions and also the use of metaheuristics for improving the quality of a given schedule. 1 Problem Description In the last three decades or so, the automated construction, using computer techniques, of sports competition schedules has received considerable attention. Among the approaches that have been proposed there are exact algorithms (including methods based on combinatorial design theory) (e.g. [1, 2]) and heuristics (e.g. [4, 5, 8]). We are interested in the problem in which a set of N teams must compete on a set of S neutral venues over T timeslots. A feasible competition schedule should be constructed so that the assignment of venues to the matches is as balanced and fair as possible. A feasible schedule must satisfy the hard constraints: only one match can take place on a given venue at a given timeslot, and each team can compete in exactly one venue at a given timeslot. A particular case is when the problem is balanced. That is, the number of competitors N equals the number of timeslots T and it is twice the number of venues S, i.e. N = T = 2S. Then, each team competes N times and therefore, each team competes against one of the other teams exactly twice (this can be called the repeated match). In each of the T schedule timeslots, all teams in the league must be competing simultaneously. There are three soft constraints that should be satisfied. First, each team must play against each of the other teams at least once. Second, each team must compete in each venue exactly twice. Finally, any pair of teams should not compete against each other more than one time on the same venue. Then, the problem is to find whether a feasible schedule that satisfies all the soft constraints exists.