Efficient use of collision detection for volume maximization problems

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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.