DNA nanotechnology has introduced the ability to create structures at the molecular scale, which is a promising approach for the implementation of very large swarms. However, the movement of such structures is heavily influenced by their size, prompting shape design optimization. Here, we use a quality-diversity approach to optimize the size of structures assembled from sets of DNA strands. We introduced a surrogate model to accelerate evaluations, with the ground truth provided by oxDNA, a physics-based simulator. We then iterate between optimization rounds using the QD algorithm, direct evaluation of promising and potentially mispredicted sets with oxDNA, and training of the surrogate model. We show that this approach efficiently generates diverse candidate sets at a fraction of simulation costs. Additionally, the surrogate model is reusable, enhancing the overall performance of future optimization tasks.