Scheduling fixtures for Basketball New Zealand

This paper describes the problem faced every year by Basketball New Zealand in scheduling the National Basketball League fixtures. This is a combinatorial optimization problem with few constraints but many objectives, which are described in detail. Two features of the problem cause particular difficulty – the requirement that every team plays two matches in at least two rounds during the season and the fact that stadium availability is far from certain at the start of the process and must be negotiated once a draft schedule has been produced, necessitating an iterative process with possibly many drafts before the final schedule is confirmed. A variant of Simulated Annealing is used to solve this problem, producing one or more schedules of high quality. The system will be used in practice for the 2004 season. The paper also reports the results of experiments regarding the use of a potentially useful, but very restrictive, solution structure for the initial solution and possibly beyond. The results of the experiments show that, for this problem at least, it appears best to stick with this restrictive structure for part of the metaheuristic search procedure, but then to remove this restriction for the remainder of the process. This could have interesting implications for other problems.