  Geometric discrepancies are standard measures to quantify the irregularity of
distributions. They are an important notion in numerical integration. One of
the most important discrepancy notions is the so-called \emph{star
discrepancy}. Roughly speaking, a point set of low star discrepancy value
allows for a small approximation error in quasi-Monte Carlo integration. It is
thus the most studied discrepancy notion.
  In this work we present a new algorithm to compute point sets of low star
discrepancy. The two components of the algorithm (for the optimization and the
evaluation, respectively) are based on evolutionary principles. Our algorithm
clearly outperforms existing approaches. To the best of our knowledge, it is
also the first algorithm which can be adapted easily to optimize inverse star
discrepancies.
