A good stacking method can increase the packaging utility rate and reduce production costs. Much research has focused on 2D arrangements for rectangular, circular, or irregular shapes and regularly shaped 3D objects such as rectangular boxes. Genetic algorithms, simulated annealing, and other heuristic algorithms have been proposed. Recent research on the stacking of irregular-shaped 3D stone pieces has focused on balancing one stone piece on top of others to form one or more vertical towers, given the geometry of the stone pieces and the number of stone pieces available for the task.

Stacking irregular-shaped 3D objects in a package is common in industry. However, there has been relatively little emphasis on the development of algorithms for stacking irregular-shaped 3D objects in a fixed-size container without prior knowledge of the stone geometries and the number of pieces available, with the goal of packing as many stone pieces as possible while maintaining stability. In this paper, three heuristic algorithms are proposed to solve the problem of nesting irregularly shaped stone pieces in layers within a container. All three algorithms use the following approach: (1) approximate the alignment of irregular shapes to a cluster of straight lines; (2) arrange stones one by one at the approximated angles using a step-by-step process; (3) for stability, consider the weight of the stone pieces based on pixel calculations.

An automated real-time stacking system—including sensors, pneumatic suction cups, webcams, conveyor, robot, and programmable logic controller—was developed to evaluate the proposed algorithms using space utilization, stability, and cycle time as measures of performance. The developed algorithms and an existing stacking algorithm (bottom left most, or BLM) were tested using 25 sequences of 30 randomly ordered stone pieces. Results suggest that the developed algorithms effectively solve the stone piece packing problem. All three were significantly better than the BLM algorithm in terms of space utilization and stability, and there was no difference in cycle time. Algorithm 3 was better than Algorithms 1 and 2.

良好的堆码方式可以提高包装利用率，降低生产成本。许多研究都集中在矩形、圆形或不规则形状的 2D 排列以及规则形状的 3D 对象（例如矩形框）上。已经提出了遗传算法、模拟退火和其他启发式算法。考虑到石块的几何形状和可用于该任务的石块数量，最近对不规则形状 3D 石块堆叠的研究集中在平衡一块石块在其他石块之上以形成一个或多个垂直塔。

在包装中堆叠不规则形状的 3D 物体在工业中很常见。然而，相对较少强调开发在固定大小的容器中堆叠不规则形状的 3D 对象的算法，而无需预先了解石头的几何形状和可用的碎片数量，目标是尽可能多地包装石头碎片。在保持稳定的情况下可能。在本文中，提出了三种启发式算法来解决在容器内分层嵌套不规则形状石块的问题。所有三种算法都使用以下方法：（1）将不规则形状的对齐近似为一簇直线；(2)将石子以近似的角度逐一排列；(3) 为了稳定性，根据像素计算考虑石块的重量。

开发了一个自动实时堆叠系统——包括传感器、气动吸盘、网络摄像头、传送带、机器人和可编程逻辑控制器——以使用空间利用率、稳定性和循环时间作为性能衡量标准来评估所提出的算法。使用 30 个随机排序的石块的 25 个序列测试开发的算法和现有的堆叠算法（最左下角，或 BLM）。结果表明，所开发的算法有效地解决了石块包装问题。三者在空间利用率和稳定性上都明显优于BLM算法，在循环时间上没有差异。算法 3 优于算法 1 和 2。