The logarithmic hypervolume indicator

9 years 1 months ago
The logarithmic hypervolume indicator
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. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity General Terms Measurement, Hypervolume Indicator Keywords Multiobjective Optimization, Theory, Performance Measures, Selection
Tobias Friedrich, Karl Bringmann, Thomas Voß
Added 28 Aug 2011
Updated 28 Aug 2011
Type Journal
Year 2011
Where FOGA
Authors Tobias Friedrich, Karl Bringmann, Thomas Voß, Christian Igel
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