A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms.
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| Title: | A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms. |
|---|---|
| Authors: | He, Linjun1 (AUTHOR) this.helj@gmail.com, Ishibuchi, Hisao1 (AUTHOR) hisao@sustech.edu.cn, Trivedi, Anupam2 (AUTHOR) eleatr@nus.edu.sg, Wang, Handing3 (AUTHOR) hdwang@xidian.edu.cn, Nan, Yang1 (AUTHOR) nany@mail.sustech.edu.cn, Srinivasan, Dipti2 (AUTHOR) dipti@nus.edu.sg |
| Source: | IEEE Transactions on Evolutionary Computation. Dec2021, Vol. 25 Issue 6, p1028-1048. 21p. |
| Subjects: | Fix-point estimation, Evolutionary computation, Mathematical optimization |
| Abstract: | A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori, many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range. [ABSTRACT FROM AUTHOR] |
| Copyright of IEEE Transactions on Evolutionary Computation is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 153924826 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22He%2C+Linjun%22">He, Linjun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> this.helj@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Ishibuchi%2C+Hisao%22">Ishibuchi, Hisao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hisao@sustech.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Trivedi%2C+Anupam%22">Trivedi, Anupam</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> eleatr@nus.edu.sg</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Handing%22">Wang, Handing</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> hdwang@xidian.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Nan%2C+Yang%22">Nan, Yang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nany@mail.sustech.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Srinivasan%2C+Dipti%22">Srinivasan, Dipti</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> dipti@nus.edu.sg</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Evolutionary+Computation%22">IEEE Transactions on Evolutionary Computation</searchLink>. Dec2021, Vol. 25 Issue 6, p1028-1048. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fix-point+estimation%22">Fix-point estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Evolutionary+computation%22">Evolutionary computation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori, many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IEEE Transactions on Evolutionary Computation is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1109/TEVC.2021.3076514 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 1028 Subjects: – SubjectFull: Fix-point estimation Type: general – SubjectFull: Evolutionary computation Type: general – SubjectFull: Mathematical optimization Type: general Titles: – TitleFull: A Survey of Normalization Methods in Multiobjective Evolutionary Algorithms. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: He, Linjun – PersonEntity: Name: NameFull: Ishibuchi, Hisao – PersonEntity: Name: NameFull: Trivedi, Anupam – PersonEntity: Name: NameFull: Wang, Handing – PersonEntity: Name: NameFull: Nan, Yang – PersonEntity: Name: NameFull: Srinivasan, Dipti IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 1089778X Numbering: – Type: volume Value: 25 – Type: issue Value: 6 Titles: – TitleFull: IEEE Transactions on Evolutionary Computation Type: main |
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