Interactive Multiobjective Optimization Using a Set of Additive Value Functions

In this chapter, we present a new interactive procedure for multiobjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second stage, the Decision Maker (DM) is asked to make pairwise comparisons of some solutions from the generated sample. Besides pairwise comparisons, the DM may compare selected pairs from the viewpoint of the intensity of preference, both comprehensively and with respect to a single criterion. This preference information is used to build a preference model composed of all general additive value functions compatible with the obtained information. The set of compatible value functions is then applied on the whole Pareto optimal set, which results in possible and necessary rankings of Pareto optimal solutions. These rankings are used to select a new sample of solutions, which is presented to the DM, and the procedure cycles until a satisfactory solution is selected from the sample or the DM comes to conclusion that there is no satisfactory solution for the current problem setting. Construction of the set of compatible value functions is done using ordinal regression methods called UTAGMS and GRIP. These two methods generalize UTA-like methods and they are competitive to AHP and MACBETH methods. The interactive procedure will be illustrated through an example. Reviewed by: Jerzy Błaszczyński, Poznań University of Technology, Poland Daisuke Sasaki, University of Cambridge, UK Kalyanmoy Deb, Indian Institute of Technology Kanpur, India J. Branke et al. (Eds.): Multiobjective Optimization, LNCS 5252, pp. 97–119, 2008. c © Springer-Verlag Berlin Heidelberg 2008 98 J.R. Figueira et al.