GFPack++: Improving 2D Irregular Packing by Learning Gradient Field with Attention

2D irregular packing is a classic combinatorial optimization problem with various applications, such as material utilization and texture atlas generation. This NP-hard problem requires efficient algorithms to optimize space utilization. Conventional numerical methods suffer from slow convergence and high computational cost. Existing learning-based methods, such as the score-based diffusion model, also have limitations, such as no rotation support, frequent collisions, and poor adaptability to arbitrary boundaries, and slow inferring. The difficulty of learning from teacher packing is to capture the complex geometric relationships among packing examples, which include the spatial (position, orientation) relationships of objects, their geometric features, and container boundary conditions. Representing these relationships in latent space is challenging. We propose GFPack++, an attention-based gradient field learning approach that addresses this challenge. It consists of two pivotal strategies: \emph{attention-based geometry encoding} for effective feature encoding and \emph{attention-based relation encoding} for learning complex relationships. We investigate the utilization distribution between the teacher and inference data and design a weighting function to prioritize tighter teacher data during training, enhancing learning effectiveness. Our diffusion model supports continuous rotation and outperforms existing methods on various datasets. We achieve higher space utilization over several widely used baselines, one-order faster than the previous diffusion-based method, and promising generalization for arbitrary boundaries. We plan to release our source code and datasets to support further research in this direction.