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.