Covers and approximations in multiobjective optimization

Daniel Vanderpooten (), Lakmali Weerasena () and Margaret M. Wiecek ()
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Daniel Vanderpooten: PSL, Université Paris Dauphine
Lakmali Weerasena: Clemson University
Margaret M. Wiecek: Clemson University

Journal of Global Optimization, 2017, vol. 67, issue 3, No 7, 619 pages

Abstract: 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.

Keywords: Multiobjective optimization; Nondominated set; Pareto set; Approximation; Cones; Tolerance function (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0426-4

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