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Covers and approximations in multiobjective optimization

Vanderpooten, Daniel; Weerasena, L.; Wiecek, M.M. (2017), Covers and approximations in multiobjective optimization, Journal of Global Optimization, 67, 3, p. 601-619. 10.1007/s10898-016-0426-4

Type
Article accepté pour publication ou publié
Date
2017
Nom de la revue
Journal of Global Optimization
Volume
67
Numéro
3
Éditeur
Springer
Pages
601-619
Identifiant publication
Métadonnées
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Auteur(s)
Vanderpooten, Daniel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Weerasena, L.

Wiecek, M.M.
Résumé (EN)
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-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.
Mots-clés
Multiobjective optimization; Nondominated set; Pareto set; Approximation; Cones; Tolerance function
JEL
C44 - Operations Research; Statistical Decision Theory