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Evol. Learn. Optim."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Single-objective optimization algorithms search for the single highest quality solution with respect to an objective. Quality diversity (QD) optimization algorithms, such as Covariance Matrix Adaptation MAP-Elites (CMA-ME), search for a collection of solutions that are both high quality with respect to an objective and diverse with respect to specified measure functions. However, CMA-ME suffers from three major limitations highlighted by the QD community: prematurely abandoning the objective in favor of exploration, struggling to explore flat objectives, and having poor performance for low-resolution archives. We propose a new QD algorithm, CMA MAP-Annealing (CMA-MAE), and its differentiable QD variant, CMA-MAE via a Gradient Arborescence (CMA-MAEGA), that address all three limitations. We provide theoretical justifications for the new algorithm with respect to each limitation. 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