This paper proposes improved local search heuristics based on collision detection for solving volume maximization problems, with a particular focus on single item volume maximization. The objective is to find the biggest item of a predefined shape that can be extracted from a larger container. Both the item and the container are three-dimensional objects and can have irregular shapes. Our goal is to find high-quality solutions for these problems within a reasonable amount of time, even for complex instances where the object and container are represented by thousands of triangles. We consider an approach where the position and orientation of an item are optimized heuristically, while the scale of the item is maximized using a fast inflation procedure. This inflation procedure uses bisection search and collision detection to determine the largest possible scale that satisfies all geometric constraints for a given position and orientation of the item within the container. We introduce improvements to this approach to reduce the required amount of geometric computations required. Finally, we compare our results against a matheuristic method from the literature on an expanded data set, which shows the improved collision detection approach is more than 100 times faster and highlights the impact of our improvements.

中文翻译：

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有效利用碰撞检测来解决体积最大化问题


本文提出了基于碰撞检测的改进的局部搜索启发法来解决体积最大化问题，特别关注单项体积最大化。目标是找到可以从较大容器中提取的预定义形状的最大物品。物品和容器都是三维物体并且可以具有不规则形状。我们的目标是在合理的时间内找到这些问题的高质量解决方案，即使对于对象和容器由数千个三角形表示的复杂实例也是如此。我们考虑一种方法，其中项目的位置和方向被启发式优化，同时使用快速膨胀过程最大化项目的规模。该膨胀过程使用二分搜索和碰撞检测来确定满足容器内物品给定位置和方向的所有几何约束的最大可能比例。我们对此方法进行了改进，以减少所需的几何计算量。最后，我们将我们的结果与扩展数据集文献中的数学方法进行比较，这表明改进的碰撞检测方法速度快了 100 倍以上，并突出了我们改进的影响。