Most partitioning methods used in psychological research seek to produce homogeneous groups (i.e., groups with low intra‐group dissimilarity). However, there are also applications where the goal is to provide heterogeneous groups (i.e., groups with high intra‐group dissimilarity). Examples of these anticlustering contexts include construction of stimulus sets, formation of student groups, assignment of employees to project work teams, and assembly of test forms from a bank of items. Unfortunately, most commercial software packages are not equipped to accommodate the objective criteria and constraints that commonly arise for anticlustering problems. Two important objective criteria for anticlustering based on information in a dissimilarity matrix are: a diversity measure based on within‐cluster sums of dissimilarities; and a dispersion measure based on the within‐cluster minimum dissimilarities. In many instances, it is possible to find a partition that provides a large improvement in one of these two criteria with little (or no) sacrifice in the other criterion. For this reason, it is of significant value to explore the trade‐offs that arise between these two criteria. Accordingly, the key contribution of this paper is the formulation of a bicriterion optimization problem for anticlustering based on the diversity and dispersion criteria, along with heuristics to approximate the Pareto efficient set of partitions. A motivating example and computational study are provided within the framework of test assembly.

中文翻译：

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结合反聚类的多样性和分散标准：双标准方法。

心理学研究中使用的大多数划分方法都试图产生同质的群体（即群体内差异性较低的群体）。然而，也有一些应用程序的目标是提供异质组（即具有高组内差异的组）。这些反聚类上下文的示例包括刺激集的构建、学生团体的形成、将员工分配到项目工作团队以及从项目库中组装测试表格。不幸的是，大多数商业软件包都无法适应反聚类问题通常出现的客观标准和约束。基于在相似矩阵信息anticlustering两个重要的客观标准：一个多样性基于类内差异总和的度量；以及基于簇内最小差异的离散度量。在许多情况下，有可能找到一个分区，它在这两个标准中的一个方面提供了很大的改进，而在另一个标准中几乎没有（或没有）牺牲。因此，探索这两个标准之间的权衡具有重要价值。因此，本文的主要贡献是基于多样性和分散标准制定了反聚类的双准则优化问题，以及近似帕累托有效分区集的启发式方法。在测试装配的框架内提供了一个激励示例和计算研究。