Most existing approaches either fix the container in advance or optimize only a single container dimension through an outer search loop, leaving the remaining dimensions as a manual tuning problem. We present a differentiable packing framework that jointly optimizes all 6N object pose parameters and all three container side lengths inside a single gradient-based loop. The formulation combines six physics-inspired, differentiable loss terms computed directly on triangle meshes through axis-aligned bounding-box proxies. An adaptive squeezing mechanism periodically tightens the container whenever the overlap loss falls below a pair-count-scaled threshold, producing a large initial drop in container volume, followed by small refinements. All pairwise computations are written in tensor-broadcasting form, giving a 3.4 to 54 times speedup over a reference loop-based implementation. The pipeline is implemented in Python and PyTorch, with no physics engine, FFT library, or convex decomposition. On multiple object categories, the method produces containers that are 11 to 32 percent smaller than time-matched DBLF and simulated-annealing baselines at N =100, while running in under 4 minutes per instance on a single consumer GPU.

翻译：现有方法要么预先固定容器尺寸，要么通过外部搜索循环仅优化单一容器维度，其余维度仍需手动调节。本文提出一种可微分装箱框架，通过单梯度循环联合优化全部6N个物体位姿参数与容器三边边长。该框架基于三角形网格，通过轴向包围盒代理计算六个受物理启发的可微损失项。当重叠损失降至阈值（由物体对数缩放决定）时，自适应挤压机制周期性紧缩容器，使容器体积先大幅缩减再精细微调。所有成对运算采用张量广播形式实现，相较基准循环实现获得3.4至54倍加速。管线基于Python和PyTorch实现，无需物理引擎、FFT库或凸分解。在多种物体类别上，当N=100时，该方法生成的容器体积比时间匹配的DBLF和模拟退火基线小11%至32%，且每个实例在单消费级GPU上运行时间不足4分钟。