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Covers and approximations in multiobjective optimization

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Abstract

Due to the growing interest in approximation for multiobjective optimization problems (MOPs), a theoretical framework for defining and classifying sets representing or approximating solution sets for MOPs is developed. The concept of tolerance function is proposed as a tool for modeling representation quality. This notion leads to the extension of the traditional dominance relation to \(t\hbox {-}\)dominance. Two types of sets representing the solution sets are defined: covers and approximations. Their properties are examined in a broader context of multiple solution sets, multiple cones, and multiple quality measures. Applications to complex MOPs are included.

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Authors and Affiliations

  1. LAMSADE, PSL, Université Paris Dauphine, 75775, Paris Cedex 16, France

    Daniel Vanderpooten

  2. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634, USA

    Lakmali Weerasena & Margaret M. Wiecek

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  1. Daniel Vanderpooten
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  2. Lakmali Weerasena
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  3. Margaret M. Wiecek
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Correspondence to Margaret M. Wiecek.

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Vanderpooten, D., Weerasena, L. & Wiecek, M.M. Covers and approximations in multiobjective optimization. J Glob Optim 67, 601–619 (2017). https://doi.org/10.1007/s10898-016-0426-4

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