Hierarchical algorithm for large-scale irregular packing problems

• Proposes a novel hierarchical algorithm that classifies parts into three levels based on area and fullness, enabling efficient packing of up to 1400 irregular parts on multiple sheets—a scale beyond prior irregular packing studies. • Introduces an innovative "shape matching" method that uses rotation and translation to achieve contour complementarity, with a shape matching coefficient (SMC) to evaluate match quality. • Integrates box stacking, shape matching, and gravity packing strategies to avoid hooking issues and promote orderly, compact arrangements, yielding higher material utilization than traditional gravity packing. • Maintains computation time suitable for engineering applications, making it practical for shipbuilding, sheet metal processing, and large-scale manufacturing.