  We focus on the challenge of finding a diverse collection of quality
solutions on complex continuous domains. While quality diver-sity (QD)
algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are
designed to generate a diverse range of solutions, these algorithms require a
large number of evaluations for exploration of continuous spaces. Meanwhile,
variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are
among the best-performing derivative-free optimizers in single-objective
continuous domains. This paper proposes a new QD algorithm called Covariance
Matrix Adaptation MAP-Elites (CMA-ME). Our new algorithm combines the
self-adaptation techniques of CMA-ES with archiving and mapping techniques for
maintaining diversity in QD. Results from experiments based on standard
continuous optimization benchmarks show that CMA-ME finds better-quality
solutions than MAP-Elites; similarly, results on the strategic game Hearthstone
show that CMA-ME finds both a higher overall quality and broader diversity of
strategies than both CMA-ES and MAP-Elites. Overall, CMA-ME more than doubles
the performance of MAP-Elites using standard QD performance metrics. These
results suggest that QD algorithms augmented by operators from state-of-the-art
optimization algorithms can yield high-performing methods for simultaneously
exploring and optimizing continuous search spaces, with significant
applications to design, testing, and reinforcement learning among other
domains.
