title: A note on the estimation of the Pareto efficient set for multiobjective matrix permutation problems.
abstract: There are a number of important problems in quantitative psychology that require the identification of a permutation of the n rows and columns of an n × n proximity matrix. These problems encompass applications such as unidimensional scaling, paired-comparison ranking, and anti-Robinson forms. The importance of simultaneously incorporating multiple objective criteria in matrix permutation applications is well recognized in the literature; however, to date, there has been a reliance on weighted-sum approaches that transform the multiobjective problem into a single-objective optimization problem. Although exact solutions to these single-objective problems produce supported Pareto efficient solutions to the multiobjective problem, many interesting unsupported Pareto efficient solutions may be missed. We illustrate the limitation of the weighted-sum approach with an example from the psychological literature and devise an effective heuristic algorithm for estimating both the supported and unsupported solutions of the Pareto efficient set.
authors.affiliation: Department of Marketing, Florida State University, Florida 32306–1110, USA. mbrusco@cob.fsu.edu
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Brusco
authors.forename: Douglas
authors.initials: D
authors.lastname: Steinley
mesh_terms: D000465:Algorithms; D001307:Auditory Perception; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D015233:Models, Statistical; D011584:Psychology / Q000706:statistics & numerical data*; D014796:Visual Perception