R2-Based Hypervolume Contribution Approximation
In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a...
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| Published in: | IEEE transactions on evolutionary computation Vol. 24; no. 1; pp. 185 - 192 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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New York
IEEE
01.02.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-778X, 1941-0026 |
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| Abstract | In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method, and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use. |
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| AbstractList | In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method, and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use. |
| Author | Ni, Xizi Shang, Ke Ishibuchi, Hisao |
| Author_xml | – sequence: 1 givenname: Ke orcidid: 0000-0003-2363-9504 surname: Shang fullname: Shang, Ke email: kshang@foxmail.com organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Southern University of Science and Technology, Shenzhen, China – sequence: 2 givenname: Hisao orcidid: 0000-0001-9186-6472 surname: Ishibuchi fullname: Ishibuchi, Hisao email: hisao@sustc.edu.cn organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Southern University of Science and Technology, Shenzhen, China – sequence: 3 givenname: Xizi orcidid: 0000-0002-6257-200X surname: Ni fullname: Ni, Xizi organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Southern University of Science and Technology, Shenzhen, China |
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| SubjectTerms | Approximation Approximation methods Evolutionary multiobjective optimization (EMO) hypervolume contribution Indexes Methods Monte Carlo methods Monte Carlo simulation Nickel Optimization R2 indicator Sociology |
| Title | R2-Based Hypervolume Contribution Approximation |
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