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Integrating Approximation and Interactive Decision Making in Multicriteria Optimization

Institute of Applied Mathematics, University of Erlangen-Nuremberg, D-91058 Erlangen, Germany
Department of Mathematical Information Technology, FI-40014 University of Jyvaskyla, Finland, and Helsinki School of Economics, FI-00101 Helsinki, Finland
klamroth{at}am.uni-erlangen.de
kaisa.miettinen{at}jyu.fi

We present a new interactive hybrid approach for solving multicriteria optimization problems where features of approximation methods and interactive approaches are incorporated. We produce rough approximations of the nondominated set and let the decision maker indicate with the help of reference points where to refine the approximation. In this way, (s)he iteratively directs the search toward the best nondominated solution. After the decision maker has identified the most interesting region of the nondominated set, the final solution can be fine-tuned with existing interactive methods. We suggest different ways of updating the reference point as well as discuss visualizations that can be used in comparing different nondominated solutions. The new method is computationally relatively inexpensive and easy to use for the decision maker.

Subject classifications: programming; multiple criteria; nonlinear; interactive methods; reference point.
History: Received September 2005; revision received December 2006; accepted March 2007.