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Interactive Robust Cone Contraction Method For Multiple Objective Optimization Problems

Author

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  • MIŁOSZ KADZIŃSKI

    (Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland)

  • ROMAN SŁOWIŃSKI

    (Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland;
    Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw, Poland)

Abstract

We introduce a new interactive procedure for multiple objective optimization problems. The identification of the most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he specifies pairwise comparisons of nondominated solutions from a current sample. We represent this preference information by a compatible form of the achievement scalarizing function, i.e., we are searching for weights of objectives which ensure that the reference solutions are compared by the function in the same way as by the DM. Directions of the isoquants of all compatible achievement scalarizing functions create a cone in the evaluation space, with the origin in a reference point. In successive iterations, each new pairwise comparison of solutions contracts the cone which is zooming on a subregion of nondominated points of greatest interest for the DM. The procedure ends when at least one satisfactory solution is selected or when the DM comes to conclusion that there is no such solution for the current problem setting.

Suggested Citation

  • Miłosz Kadziński & Roman Słowiński, 2012. "Interactive Robust Cone Contraction Method For Multiple Objective Optimization Problems," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 327-357.
    • Handle: RePEc:wsi:ijitdm:v:11:y:2012:i:02:n:s0219622012400056
    DOI: 10.1142/S0219622012400056
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    References listed on IDEAS

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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
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