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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 quality diversity algorithm, Covariance Matrix Adaptation MAP-Annealing (CMA-MAE), and its differentiable quality diversity variant, Covariance Matrix Adaptation MAP-Annealing via a Gradient Arborescence (CMA-MAEGA), that address all three limitations. We provide theoretical justifications for the new algorithm with respect to each limitation. Our theory informs our experiments, which support the theory and show that CMA-MAE achieves state-of-the-art performance and robustness on standard QD benchmark and reinforcement learning domains.

 

In recent years, organic dye molecules as photosensitizers have played a significant role in the field of dye-sensitized solar cells. In this context, two primary dihydroindolocarbazole-based organic dyes (sk201 and sk202), which were synthesized recently by Song et al., and three further designed dyes (DMZ1-3) were theoretically investigated based on density functional theory and time-dependent density functional theory. Molecular geometries, absorption spectra, charge transfer, molecular electrostatic potential and nonlinear optical properties were quantificationally studied and visually presented to reveal the relationships between the molecular structures and performances of dyes. The effects of joining the isolated dyes and TiO2 on the molecular absorption spectra and energy levels were analyzed. Moreover, several parameters, such as efficiency of light-harvesting, driving forces of electron regeneration and injection, excited-state lifetime and vertical dipole moment, were calculated to give the multi-angle demonstrations of the photovoltaic performances for these dyes.