A distance function to support optimized selection decisions

Decision-makers often want to see a diverse collection of good solutions in addition to a solution that is in some mathematical sense an optimal solution to a problem. The purpose of the objective function is to quantify the notion “good”, while the purpose of this paper is to exhibit a suitable function for quantifying the notion “diverse”. We focus on the case where important aspects of the solutions are best represented as matrices or sets of vectors, such as when the solution involves selections. We establish a distance function and its connections with related distance functions used in optimization and psychology. A real-world application illustrates its use for decision support.