An exact global optimization method for deriving weights from pairwise comparison matrices

Abstract

Some multiple-criteria decision making methods rank actions by associating weights to the different criteria or actions, which are pairwise compared via a positive reciprocal matrix A. There is a vast literature on proposals of different mathematical-programming methods to infer weights from such matrix A. However, it is seldom observed that such optimization problems may be multimodal, thus the standard local search resolution techniques suggestedmay be trapped in local optima, yielding a wrong ranking of alternatives. In this note we show that standard tools of global optimization based on interval analysis, lead to globally optimal weights in reasonable time.