On the use of hypervolume for diversity measurement of Pareto front approximations

Shouyong Jiang; Shengxiang Yang; Miqing Li

doi:10.1109/SSCI.2016.7850225

On the use of hypervolume for diversity measurement of Pareto front approximations

Shouyong Jiang, Shengxiang Yang, Miqing Li

Computing Science

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

11 Citations (Scopus)

Abstract

In multiobjective optimization, a good quality indicator is of great importance to the performance assessment of algorithms. This paper investigates the effectiveness of the widely-used hypervolume indicator, which is the only one found so far to strictly comply with the Pareto dominance. While hypervolume is of undisputed success to assess the quality of an approximation, it is sensitive to misleading cases, particularly for diversity assessment. To address this issue, this paper presents a modified hypervolume indicator based on linear projection for diversity evaluation. In addition to experimental studies to demonstrate the effectiveness of the proposed indicator, the indicator is introduced into the environmental selecction of an indicator-based multiobjective optimization evolutionary algorithm. Experiments show that the proposed indicator yields more evenly-distributed approximations than the original hypervolume indicator.

Original language	English
Title of host publication	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781509042401
DOIs	https://doi.org/10.1109/SSCI.2016.7850225
Publication status	Published - 9 Feb 2017
Event	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016 - Athens, Greece Duration: 6 Dec 2016 → 9 Dec 2016

Publication series

Name	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016

Conference

Conference	2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016
Country/Territory	Greece
City	Athens
Period	6/12/16 → 9/12/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

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10.1109/SSCI.2016.7850225

Cite this

Jiang, S., Yang, S., & Li, M. (2017). On the use of hypervolume for diversity measurement of Pareto front approximations. In 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016 Article 7850225 (2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SSCI.2016.7850225

On the use of hypervolume for diversity measurement of Pareto front approximations. / Jiang, Shouyong; Yang, Shengxiang; Li, Miqing.
2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016. Institute of Electrical and Electronics Engineers Inc., 2017. 7850225 (2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016).

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Jiang, S, Yang, S & Li, M 2017, On the use of hypervolume for diversity measurement of Pareto front approximations. in 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016., 7850225, 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016, Institute of Electrical and Electronics Engineers Inc., 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016, Athens, Greece, 6/12/16. https://doi.org/10.1109/SSCI.2016.7850225

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N2 - In multiobjective optimization, a good quality indicator is of great importance to the performance assessment of algorithms. This paper investigates the effectiveness of the widely-used hypervolume indicator, which is the only one found so far to strictly comply with the Pareto dominance. While hypervolume is of undisputed success to assess the quality of an approximation, it is sensitive to misleading cases, particularly for diversity assessment. To address this issue, this paper presents a modified hypervolume indicator based on linear projection for diversity evaluation. In addition to experimental studies to demonstrate the effectiveness of the proposed indicator, the indicator is introduced into the environmental selecction of an indicator-based multiobjective optimization evolutionary algorithm. Experiments show that the proposed indicator yields more evenly-distributed approximations than the original hypervolume indicator.

AB - In multiobjective optimization, a good quality indicator is of great importance to the performance assessment of algorithms. This paper investigates the effectiveness of the widely-used hypervolume indicator, which is the only one found so far to strictly comply with the Pareto dominance. While hypervolume is of undisputed success to assess the quality of an approximation, it is sensitive to misleading cases, particularly for diversity assessment. To address this issue, this paper presents a modified hypervolume indicator based on linear projection for diversity evaluation. In addition to experimental studies to demonstrate the effectiveness of the proposed indicator, the indicator is introduced into the environmental selecction of an indicator-based multiobjective optimization evolutionary algorithm. Experiments show that the proposed indicator yields more evenly-distributed approximations than the original hypervolume indicator.

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On the use of hypervolume for diversity measurement of Pareto front approximations

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