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Solution of the least squares method problem of pairwise comparison matrices

  • Sándor BozókiEmail author
Original Paper

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.

Keywords

Pairwise comparison matrix Least squares approximation Polynomial system Homotopy method Incomplete pairwise comparison matrix 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Laboratory and Department of Operations Research and Decision SystemsComputer and Automation Research Institute, Hungarian Academy of SciencesBudapestHungary

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