Assessing the quality of the relation between scalarizing function parameters and solutions in multiobjective optimization

Different Multi-Objective Optimization Methods (MOOM) for solving Multi-Objective Optimization Problems (MOOP) have been suggested in the literature. These methods often comprise two stages (not necessarily sequential): i) the search for the Pareto-optimal set and ii) the selection of a single solution from this non-dominated set. Various studies comparing performance of particular aspects of these methods have been carried out. However, a theoretical support that changes on the preferences of a Decision Maker (DM) will be reflected in the same way on the solution of the MOOP given by the MOOM has not been presented. In this work a consistency measure to assess MOOM is proposed. It will used to compare the performance of different methods available in the literature. This study was performed using some benchmark test problems, with two criteria.This work was supported in part by the Portuguese Fundacao para a Ciencia e Tecnologia under grants: PTDC/GES/70168/2006 and SFRH/BD/22808/2005