A grid-based heuristic for two-dimensional packing problems

To solve two-dimensional (2D) rectangular packing problems, we introduce a new spatial method based on the discretization of the container into a grid of cells with predefined resolution. Before an item is added, grid cells are checked whether they can accommodate the item. If an appropriate empty cell cluster is found, the item is added and moved towards the bottom-left corner of the container. This placement and sliding method is supplemented by a heuristic that orders the items according to descending size. Order and rotation of items can be improved by hybridizing the heuristic with a genetic algorithm (GA) in which a population of order-rotation chromosomes is evolved. The method is tested on 47 benchmark problems and compared to other methods in the literature. This shows that it is fast and performs very well in finding close to optimal problem solutions. Particularly for large problem sizes, it outperforms some of the currently leading methods, such as heuristic recursive (HR). The hybridization with the GA meta heuristic results in further performance improvements.