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Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems

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  • Roman Efremov
  • Georgy Kamenev

Abstract

The paper describes new results in the field of multiobjective optimization techniques. The Interactive Decision Maps (IDM) technique is based on approximation of Feasible Criterion Set (FCS) and subsequent visualization of the Pareto frontier of FCS by interactive displaying the bi-criteria slices of FCS. The Estimation Refinement (ER) method is now the main method for approximating convex FCS in the framework of IDM. The properties of the ER method are studied. We prove that the number of facets of the approximation constructed by ER and the number of the support function calculations of an approximated set are asymptotically optimal. These results are important from the point of view of real-life applications of ER. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Roman Efremov & Georgy Kamenev, 2009. "Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems," Annals of Operations Research, Springer, vol. 166(1), pages 271-279, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:271-279:10.1007/s10479-008-0418-y
    DOI: 10.1007/s10479-008-0418-y
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    Cited by:

    1. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    2. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2011. "Constructing a Pareto front approximation for decision making," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 209-234, April.
    3. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.

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