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

• Type: Journal
• Year: 2011
• Where: FOGA
• Authors: Tobias Friedrich, Karl Bringmann, Thomas Voß, Christian Igel
• Keywords: Analysis Of Algorithms, Artificial Intelligence, Evolution Strategy, FOGA 2011, Problem Complexity