Hybrid Heuristic-Driven GAT-Transformer Algorithm for Multi-Layer Nesting Under Complex Defects

The nesting and cutting of thin materials are critical processes in industrial manufacturing, often involving multi-layer stacking to optimize production efficiency. However, material defects complicate the process, requiring optimization of both layout and defect avoidance under multi-layer heterogeneous constraints. Moreover, existing methods struggle with large search spaces and high computational complexity, limiting their industrial applicability and affecting material utilization and machining accuracy. To address these challenges, we propose HGATrans-MNCD, an intelligent nesting optimization algorithm that integrates defect avoidance and material waste reduction. Initially, areas with high defect overlap are prioritized using an enhanced No-Fit-Polygons strategy to ensure global defect avoidance. A heuristic approach is then employed to optimize the initial nesting sequence. Subsequently, a Transformer-based module leverages prior knowledge to efficiently perturb and refine the sequence, facilitating global optimization. Experiments on a benchmark dataset of multi-layer defect scenarios demonstrate that HGATrans-MNCD effectively addresses irregular defect patterns, enhancing material utilization by 2–8%. Our algorithm performs especially well in scenarios involving spatially coupled defects, offering a novel solution to complex multi-constraint optimization problems.