## The logarithmic hypervolume indicator

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

#### Standard

The logarithmic hypervolume indicator. / Friedrich, Tobias; Bringmann, Karl; Voß, Thomas; Igel, Christian.

Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11. red. / Hans-Georg Beyer; W. B. Langdon. Association for Computing Machinery, 2011. s. 81-91.

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

#### Harvard

Friedrich, T, Bringmann, K, Voß, T & Igel, C 2011, The logarithmic hypervolume indicator. i H-G Beyer & WB Langdon (red), Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11. Association for Computing Machinery, s. 81-91, Foundations of genetic algorithms , Schwarzenberg, Østrig, 05/01/2011. https://doi.org/10.1145/1967654.1967662

#### APA

Friedrich, T., Bringmann, K., Voß, T., & Igel, C. (2011). The logarithmic hypervolume indicator. I H-G. Beyer, & W. B. Langdon (red.), Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11 (s. 81-91). Association for Computing Machinery. https://doi.org/10.1145/1967654.1967662

#### Vancouver

Friedrich T, Bringmann K, Voß T, Igel C. The logarithmic hypervolume indicator. I Beyer H-G, Langdon WB, red., Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11. Association for Computing Machinery. 2011. s. 81-91 https://doi.org/10.1145/1967654.1967662

#### Author

Friedrich, Tobias ; Bringmann, Karl ; Voß, Thomas ; Igel, Christian. / The logarithmic hypervolume indicator. Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11. red. / Hans-Georg Beyer ; W. B. Langdon. Association for Computing Machinery, 2011. s. 81-91

#### Bibtex

title = "The logarithmic hypervolume indicator",
abstract = "It was recently proven that sets of points maximizing the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new “logarithmic hypervolume indicator” and prove that it achieves a close-to-optimal multiplicative approximation ratio. This is experimentally verified on several benchmark functions by comparing the approximation quality of the multi-objective covariance matrix evolution strategy (MO-CMA-ES) with the classic hypervolume indicator and the MO-CMA-ES with the logarithmic hypervolume indicator.",
author = "Tobias Friedrich and Karl Bringmann and Thomas Vo{\ss} and Christian Igel",
year = "2011",
doi = "10.1145/1967654.1967662",
language = "English",
isbn = "978-1-4503-0633-1",
pages = "81--91",
editor = "Hans-Georg Beyer and Langdon, {W. B.}",
booktitle = "Proceedings of the 11th Workshop on Foundations of genetic algorithms",
publisher = "Association for Computing Machinery",
note = "Foundations of genetic algorithms , FOGA 2011 ; Conference date: 05-01-2011 Through 09-01-2011",

}

#### RIS

TY - GEN

T1 - The logarithmic hypervolume indicator

AU - Friedrich, Tobias

AU - Bringmann, Karl

AU - Voß, Thomas

AU - Igel, Christian

N1 - Conference code: XI

PY - 2011

Y1 - 2011

N2 - It was recently proven that sets of points maximizing the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new “logarithmic hypervolume indicator” and prove that it achieves a close-to-optimal multiplicative approximation ratio. This is experimentally verified on several benchmark functions by comparing the approximation quality of the multi-objective covariance matrix evolution strategy (MO-CMA-ES) with the classic hypervolume indicator and the MO-CMA-ES with the logarithmic hypervolume indicator.

AB - It was recently proven that sets of points maximizing the hypervolume indicator do not give a good multiplicative approximation of the Pareto front. We introduce a new “logarithmic hypervolume indicator” and prove that it achieves a close-to-optimal multiplicative approximation ratio. This is experimentally verified on several benchmark functions by comparing the approximation quality of the multi-objective covariance matrix evolution strategy (MO-CMA-ES) with the classic hypervolume indicator and the MO-CMA-ES with the logarithmic hypervolume indicator.

U2 - 10.1145/1967654.1967662

DO - 10.1145/1967654.1967662

M3 - Article in proceedings

SN - 978-1-4503-0633-1

SP - 81

EP - 91

BT - Proceedings of the 11th Workshop on Foundations of genetic algorithms

A2 - Beyer, Hans-Georg

A2 - Langdon, W. B.

PB - Association for Computing Machinery

T2 - Foundations of genetic algorithms

Y2 - 5 January 2011 through 9 January 2011

ER -

ID: 37435609