Solution of the least squares method problem of pairwise comparison matrices

Bozóki, Sándor (2008) Solution of the least squares method problem of pairwise comparison matrices. Central European Journal of Operations Research, 16 (4). pp. 345-358. ISSN 1435-246X

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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 example having multiple global and local minima.

Item Type: Article
Uncontrolled Keywords: Pairwise comparison matrix · Least squares approximation · Polynomial system · Homotopy method · Incomplete pairwise comparison matrix
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Research Laboratory on Engineering & Management Intelligence
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:32
Last Modified: 11 Dec 2012 15:32
URI: http://eprints.sztaki.hu/id/eprint/5570

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