A fast and scalable deepest-left-bottom-fill algorithm to solve irregular 3D cutting and packing problems using a semi-discrete representation

In this paper, we introduce a fast and scalable algorithm to solve irregular 3D cutting and packing problems. The possibly non-convex pieces and the container are semi-discretised using a grid in two dimensions, resulting in line segments in the third dimension. The semi-discretization algorithm ensures that a non-overlapping placement of the segments, representing two pieces, does not result in any overlap of these pieces. We present a deepest-left-bottom-fill greedy placement algorithm using an optimised ordering of the segment overlap tests to solve the open dimension problem. We also introduce a parallel version of the algorithm with dynamic load balancing. The performance of this placement algorithm is compared with results for some benchmark data sets. Competitive results are obtained within a very short runtime, even when the rotation of pieces is considered. Moreover, our algorithm scales well when the number of pieces and number of allowed rotations increases. We evaluate the performance of the parallel algorithm on a multicore processor using different task sizes. To further improve the solution quality, we implement a hill climbing algorithm based on reordering the pieces on top of the deepest-left-bottom-fill algorithm and we compare its performance with results presented in the literature.