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Covers and approximations in multiobjective optimization

Author

Listed:
  • Daniel Vanderpooten

    (PSL, Université Paris Dauphine)

  • Lakmali Weerasena

    (Clemson University)

  • Margaret M. Wiecek

    (Clemson University)

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 $$t\hbox {-}$$ t - 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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0426-4
    DOI: 10.1007/s10898-016-0426-4
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    Cited by:

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    2. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.

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