A note on the estimation of the Pareto efficient set for multiobjective matrix permutation problems

作者:Brusco Michael J*; Steinley Douglas
来源:BRITISH JOURNAL OF MATHEMATICAL %26 STATISTICAL PSYCHOLOGY, 2012, 65(1): 145-162.
DOI:10.1111/j.2044-8317.2011.02021.x

摘要

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 x 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.

  • 出版日期2012-2

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