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.

GFPack++ 是一个基于注意力机制梯度场学习方法，可以有效地进行 2D 不规则装箱优化，获得更高的空间利用率，支持连续旋转，并拥有较快的运算速度和对任意边界的良好泛化能力。