A Parallel Bucket-Based Bottom-Left-Fill Algorithm for Nesting Problems Using a Semi-Discrete Representation

We discuss the parallelization of the bottom-left-fill algorithm to solve nesting problems on multicore processors. The algorithm uses a semi-discrete representation of both the 2D non-convex pieces and the strip. In case several rotation angles are allowed for each piece, the computation of the tentative placement for each angle is parallelized using OpenMP, limiting the number of threads to the number of rotation angles. The speedup is further limited due to load imbalance. Therefore, we develop a bucket-based bottom-left-fill algorithm, which subdivides the pieces in buckets and places the buckets, while computing an optimal ordering of the pieces in each bucket to improve the solution, i.e., to minimize the length of the strip. The many possible orderings of the pieces in a bucket allow to create many tasks that can be executed concurrently. Dynamic load balancing is used. We evaluate the parallel performance and the solution quality of this new algorithm, using different bucket sizes.