Grail-AD: Request-Driven Algorithm Evolution for 2D Graphite Material Packing

Growing large single-crystal graphite enables structural-superlubric devices, but converting grown crystals into products requires packing independently rotatable rectangular items into irregular usable regions while maintaining safe distances for laser cutting kerf. The physical crystals are expensive to acquire and their morphology is difficult to control. We release a dataset of large-scale single-crystal graphite flakes and propose Grail-AD, a closed-loop framework that connects a scale-controlled crystal image generator to a population of evolving packing algorithms. The generator combines pretrained feature alignment, scale control, and representation-based retrieval to supply diverse crystal images. The packing evolution employs an LLM-driven heuristic search with a composite objective combining geometrically valid packing count and a spacing reward — with an image-request mechanism through which algorithms query specific morphologies from the generator; cases that promote progress are retained while unsolvable ones are rejected, forming a task-directed data engine. Retrospective evaluation of 45 runs spanning three search frameworks, five image-supply schemes, and three repeats on a frozen independent 100-image test set shows that conditioned requests yield a higher retrospective maximum than matched Fixed runs in 22 of 27 comparisons. OpenEvolve improves in all nine matched comparisons; Real Request averages 34,638 versus 27,094 for Fixed, a 27.8% gain. MLES Request improves in all three matched comparisons, with a 10.7% mean gain. Because the reported score for each run is the retrospective maximum over its candidate pool, these results characterize candidate-discovery capability under a fixed search budget rather than unbiased deployment performance. This approach may extend to the product design and manufacturing of other two-dimensional crystal materials, including transferred heterostructures.