Solution of the least squares method problem of pairwise comparison matrices

Solution of the least squares method problem of pairwise comparison matrices

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Article ID: iaor200910686
Country: Germany
Volume: 16
Issue: 4
Start Page Number: 345
End Page Number: 358
Publication Date: Dec 2008
Journal: Central European Journal of Operations Research
Authors:
Keywords: matrices, programming: nonlinear
Abstract:

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non–convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical examples having multiple global and local minima.

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