Interactive multiobjective optimization using a set of additive value functions

J. Figueira, Salvatore Greco, V. Mousseau, R. Slowinski

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


    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 UTA GMS 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.
    Original languageEnglish
    Title of host publicationMultiobjective Optimization: Interactive and Evolutionary Approaches
    EditorsJ. Branke, K. Deb, K. Miettinen, R. Slowinski
    Place of PublicationBerlin
    Number of pages23
    ISBN (Electronic)9783540889083
    ISBN (Print)9783540889076
    Publication statusPublished - 2008

    Publication series

    NameLecture notes in computer science
    ISSN (Print)0302-9743


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