Covers and approximations in multiobjective optimization

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• 作者：Daniel Vanderpooten ; Lakmali Weerasena…
• 关键词：Multiobjective optimization ; Nondominated set ; Pareto set ; Approximation ; Cones ; Tolerance function
• 刊名：Journal of Global Optimization
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：67
• 期：3
• 页码：601-619
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Optimization; Operation Research/Decision Theory; Real Functions; Computer Science, general;
• 出版者：Springer US
• ISSN：1573-2916
• 卷排序：67

文摘

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.