Identifying a Reordering of Rows and Columns for Multiple Proximity Matrices Using Multiobjective Programming

This paper is concerned with a problem where K (n×n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, as measured by an appropriate index, for each of the K matrices. A multiobjective programming approach for this problem, which seeks to optimize a weighted function of the K indices, is proposed, and illustrative examples are provided using a set of proximity matrices from the psychological literature. These examples show that, by solving the multiobjective programming model under different weighting schemes, the quantitative analyst can uncover information about the relationships among the matrices and often identify one or more permutations that provide good to excellent index values for all matrices.