A Unified Characterization of Multiobjective Robustness via Separation

This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization results for several set order relations, together with the help of image space analysis, some suitable subsets of scalarization image space ar...

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Published in:Journal of optimization theory and applications Vol. 179; no. 1; pp. 86 - 102
Main Authors: Wei, Hong-Zhi, Chen, Chun-Rong, Li, Sheng-Jie
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2018
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Robustness
Theory of Computation
90C31
Uncertain multiobjective optimization
90C30
90C29
Robustness
Linear and nonlinear scalarization
Set order relations
Image space analysis
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Abstract This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization results for several set order relations, together with the help of image space analysis, some suitable subsets of scalarization image space are introduced to make equivalent characterizations for upper set (lower set, set, certainly, respectively) less ordered robustness for uncertain multiobjective optimization problems. In particular, the nonlinear scalarization functional plays a significant role in computing various multiobjective robust solutions. Finally, the corresponding examples are included to show the effectiveness of the results derived in this paper.
AbstractList This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization results for several set order relations, together with the help of image space analysis, some suitable subsets of scalarization image space are introduced to make equivalent characterizations for upper set (lower set, set, certainly, respectively) less ordered robustness for uncertain multiobjective optimization problems. In particular, the nonlinear scalarization functional plays a significant role in computing various multiobjective robust solutions. Finally, the corresponding examples are included to show the effectiveness of the results derived in this paper.
Author Li, Sheng-Jie
Wei, Hong-Zhi
Chen, Chun-Rong
Author_xml – sequence: 1
  givenname: Hong-Zhi
  surname: Wei
  fullname: Wei, Hong-Zhi
  organization: College of Mathematics and Statistics, Chongqing University
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  givenname: Chun-Rong
  orcidid: 0000-0001-8285-7881
  surname: Chen
  fullname: Chen, Chun-Rong
  email: chencr1981@163.com
  organization: College of Mathematics and Statistics, Chongqing University
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  givenname: Sheng-Jie
  surname: Li
  fullname: Li, Sheng-Jie
  organization: College of Mathematics and Statistics, Chongqing University
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Keywords 90C31
Uncertain multiobjective optimization
90C30
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Robustness
Linear and nonlinear scalarization
Set order relations
Image space analysis
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Snippet This paper focuses on a unified approach to characterizing different kinds of multiobjective robustness concepts. Based on linear and nonlinear scalarization...
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SubjectTerms Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Robustness
Theory of Computation
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Title A Unified Characterization of Multiobjective Robustness via Separation
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