Fast generation of centroids for MAP-Elites

Abstract

The use of MAP-Elites in high-dimensional behavioral spaces requires a scalable method for dividing the space into regions of equal volume. So far, the recommended approach to generate these regions has been the Centroidal Voronoi Tesselation (CVT), but this algorithm has a significant computational cost (typically a few minutes for more than 50 dimensions). In this paper, we investigate alternative approaches to generate regions of equal volumes for MAP-Elites. In particular, we experiment with generating region centroids with low-discrepancy sequences (Sobol, Halton), pseudorandom numbers, and a simple blue noise generator. Our results show that, for spaces with 100 dimensions, most methods perform similarly, including pseudo-random numbers. For spaces with dimensions between 5 and 50, a CVT generates significantly better centroids. In lower dimensions (1--5), a scrambled Sobol sequence generates well-spread centroids in a few milliseconds.