Clustering algorithms to increase fairness in collegiate wrestling

In NCAA Division III Wrestling, the question arose how to assign schools to regions in a way that optimizes fairness for individual wrestlers aspiring to the national tournament. The problem fell within cluster analysis but no known clustering algorithms supported its complex and interrelated set of needs. We created several bespoke clustering algorithms based on various heuristics (balanced optimization, weighted spatial clustering, and weighted optimization rectangles) for finding an optimal assignment, and tested each against the generic technique of genetic algorithms. While each of our algorithms had different strengths, the genetic algorithm achieved the highest value on our objective function, including when comparing it to the region assignments that preceded our work. This paper therefore demonstrates a technique that can be used to solve a broad category of clustering problems that arise in athletics, particularly any sport in which athletes compete individually but are assigned to regions as a team.