Translational placement using simulated annealing and collision free region with parallel processing

The irregular shape packing problem is a combinatorial optimization problem that consists of arranging items on a container in such way that no item overlaps. In this paper we adopt a solution that places the items sequentially, touching the already placed items or the container. To place a new item without overlaps, the collision free region for the new item is robustly computed using non manifold Boolean operations. A simulated annealing algorithm controls the items sequence of placement, the item´s placement and orientation. In this work, the placement occurs at collision free region´s vertices. Several results with benchmark datasets obtained from the literature are reported. Some of them are the best already reported in the literature. To improve the computational cost performance of the algorithm, a parallelization method to determine the collision free region is proposed. We demonstrated two possible algorithms to compute the collision free region, and only one of them can be parallelized. The results showed that the parallelized version is better than the sequential approach only for datasets with very large number of items. The computational cost of the non manifold Boolean operation algorithm is strongly dependent on the number of vertices of the original polygons.