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.

中文翻译：

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增加大学摔跤公平性的聚类算法

在 NCAA Division III Wrestling 中，问题出现了如何将学校分配到区域，以优化有志参加全国锦标赛的个人摔跤手的公平性。该问题属于聚类分析，但没有已知的聚类算法支持其复杂且相互关联的一组需求。我们创建了几种基于各种启发式（平衡优化、加权空间聚类和加权优化矩形）的定制聚类算法，以找到最佳分配，并针对遗传算法的通用技术对每种算法进行了测试。虽然我们的每个算法都有不同的优势，但遗传算法在我们的目标函数上实现了最高值，包括将其与我们工作之前的区域分配进行比较时。