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International Conference on Evolutionary Multi-Criterion Optimization

EMO 2019: Evolutionary Multi-Criterion Optimization pp 332–345Cite as

Comparison of Hypervolume, IGD and IGD+ from the Viewpoint of Optimal Distributions of Solutions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11411))

Abstract

Hypervolume (HV) and inverted generational distance (IGD) have been frequently used as performance indicators to evaluate the quality of solution sets obtained by evolutionary multiobjective optimization (EMO) algorithms. They have also been used in indicator-based EMO algorithms. In some studies on many-objective problems, only the IGD indicator was used due to a large computation load of HV calculation. However, the IGD indicator is not Pareto compliant. This means that a better solution set in terms of the Pareto dominance relation can be evaluated as being worse. Recently the IGD plus (IGD+) indicator has been proposed as a weakly Pareto compliant version of IGD. In this paper, we compare these three indicators from the viewpoint of optimal distributions of solutions. More specifically, we visually demonstrate similarities and differences among the three indicators by numerically calculating near-optimal distributions of solutions to optimize each indicator for some test problems. Our numerical analysis shows that IGD+ is more similar to HV than IGD whereas the formulations of IGD and IGD+ are almost the same.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 61876075), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No. 2017ZT07X386), Shenzhen Peacock Plan (Grant No. KQTD2016112514355531), the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284), and the Program for University Key Laboratory of Guangdong Province (Grant No. 2017KSYS008).

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Authors and Affiliations

  1. Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Hisao Ishibuchi

  2. Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531, Japan

    Ryo Imada, Naoki Masuyama & Yusuke Nojima

Authors
  1. Hisao Ishibuchi
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  2. Ryo Imada
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  3. Naoki Masuyama
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  4. Yusuke Nojima
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Corresponding author

Correspondence to Hisao Ishibuchi .

Editor information

Editors and Affiliations

  1. Michigan State University, East Lansing, MI, USA

    Kalyanmoy Deb

  2. Michigan State University, East Lansing, MI, USA

    Erik Goodman

  3. CINVESTAV-IPN, Mexico, Mexico

    Carlos A. Coello Coello

  4. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  5. University of Jyvaskyla, Jyväskylä, Finland

    Kaisa Miettinen

  6. Otto von Guericke University Magdeburg, Magdeburg, Germany

    Sanaz Mostaghim

  7. Cornell University, Ithaca, NY, USA

    Patrick Reed

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Ishibuchi, H., Imada, R., Masuyama, N., Nojima, Y. (2019). Comparison of Hypervolume, IGD and IGD+ from the Viewpoint of Optimal Distributions of Solutions. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_27

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  • DOI: https://doi.org/10.1007/978-3-030-12598-1_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12597-4

  • Online ISBN: 978-3-030-12598-1

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