  Evolution has produced an astonishing diversity of species, each filling a
different niche. Algorithms like MAP-Elites mimic this divergent evolutionary
process to find a set of behaviorally diverse but high-performing solutions,
called the elites. Our key insight is that species in nature often share a
surprisingly large part of their genome, in spite of occupying very different
niches; similarly, the elites are likely to be concentrated in a specific
"elite hypervolume" whose shape is defined by their common features. In this
paper, we first introduce the elite hypervolume concept and propose two metrics
to characterize it: the genotypic spread and the genotypic similarity. We then
introduce a new variation operator, called "directional variation", that
exploits interspecies (or inter-elites) correlations to accelerate the
MAP-Elites algorithm. We demonstrate the effectiveness of this operator in
three problems (a toy function, a redundant robotic arm, and a hexapod robot).
