  Diversity plays a crucial role in evolutionary computation. While diversity
has been mainly used to prevent the population of an evolutionary algorithm
from premature convergence, the use of evolutionary algorithms to obtain a
diverse set of solutions has gained increasing attention in recent years.
Diversity optimization in terms of features on the underlying problem allows to
obtain a better understanding of possible solutions to the problem at hand and
can be used for algorithm selection when dealing with combinatorial
optimization problems such as the Traveling Salesperson Problem. We explore the
use of the star-discrepancy measure to guide the diversity optimization process
of an evolutionary algorithm.
  In our experimental investigations, we consider our discrepancy-based
diversity optimization approaches for evolving diverse sets of images as well
as instances of the Traveling Salesperson problem where a local search is not
able to find near optimal solutions. Our experimental investigations comparing
three diversity optimization approaches show that a discrepancy-based diversity
optimization approach using a tie-breaking rule based on weighted differences
to surrounding feature points provides the best results in terms of the star
discrepancy measure.
