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。

GFPack++：学习梯度场与注意力提高二维不规则装箱

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

The 3D Bin Packing Problem (3D-BPP) is one of the most demanded yet
challenging problems in industry, where an agent must pack variable size items
delivered in sequence into a finite bin with the aim to maximize the space
utilization. It represents a strongly NP-Hard optimization problem such that no
solution has been offered to date with high performance in space utilization.
In this paper, we present a new reinforcement learning (RL) framework for a
3D-BPP solution for improving performance. First, a buffer is introduced to
allow multi-item action selection. By increasing the degree of freedom in
action selection, a more complex policy that results in better packing
performance can be derived. Second, we propose an agnostic data augmentation
strategy that exploits both bin item symmetries for improving sample
efficiency. Third, we implement a model-based RL method adapted from the
popular algorithm AlphaGo, which has shown superhuman performance in zero-sum
games. Our adaptation is capable of working in single-player and score based
environments. In spite of the fact that AlphaGo versions are known to be
computationally heavy, we manage to train the proposed framework with a single
thread and GPU, while obtaining a solution that outperforms the
state-of-the-art results in space utilization.

本文提出了一种基于强化学习框架的三维装箱问题（3D-BPP）解决方案，其中引入了一个缓冲区以允许多物品动作选择，并提出了一种采用容器物品对称性的数据增强策略，采用类似于 AlphaGo 的模型 RL 方法进行实现，用单线程和 GPU 训练该框架，得出了在空间利用率方面优于现有成果的解决方案。