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On the effects of combining objectives in multi-objective optimization

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Listed:
  • Stephan Dempe
  • Gabriele Eichfelder
  • Jörg Fliege

Abstract

In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multi-objective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multi-objective optimization problem. This approach can be used to reduce the dimensionality of the objective space as well as to discard certain unwanted solutions, especially the ‘extreme’ ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Stephan Dempe & Gabriele Eichfelder & Jörg Fliege, 2015. "On the effects of combining objectives in multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 1-18, August.
  • Handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:1-18
    DOI: 10.1007/s00186-015-0501-5
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    References listed on IDEAS

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