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.
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.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 11th Workshop on Foundations of genetic algorithms : FOGA '11 |
| Editors | Hans-Georg Beyer, W. B. Langdon |
| Number of pages | 11 |
| Publisher | Association for Computing Machinery |
| Publication date | 2011 |
| Pages | 81-91 |
| ISBN (Print) | 978-1-4503-0633-1 |
| DOIs | |
| Publication status | Published - 2011 |
| Event | Foundations of genetic algorithms - Schwarzenberg, Austria Duration: 5 Jan 2011 → 9 Jan 2011 Conference number: XI |
Conference
| Conference | Foundations of genetic algorithms |
|---|---|
| Number | XI |
| Country/Territory | Austria |
| City | Schwarzenberg |
| Period | 05/01/2011 → 09/01/2011 |