The logarithmic hypervolume indicator
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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The logarithmic hypervolume indicator. / Friedrich, Tobias; Bringmann, Karl; Voß, Thomas; Igel, Christian.
Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11. ed. / Hans-Georg Beyer; W. B. Langdon. Association for Computing Machinery, 2011. p. 81-91.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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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