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The Logarithmic Hypervolume Indicator (2011)
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BibTeX
@MISC{Friedrich11thelogarithmic,
author = {Tobias Friedrich and Thomas Voß and et al.},
title = {The Logarithmic Hypervolume Indicator},
year = {2011}
}
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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.
Keyphrases
logarithmic hypervolume indicator good multiplicative approximation pareto front approximation quality new logarithmic hypervolume indicator multi-objective covariance matrix evolution strategy hypervolume indicator close-to-optimal multiplicative approximation ratio classic hypervolume indicator several benchmark function
