Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes
Shunji Umetani, Shohei Murakami
Abstract
We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple procedures of the intersection test without any exceptional handling due to geometric issues, while they often require much memory and computational effort in high-resolution. To reduce the complexity of rasterized shapes, we propose a pair of scanlines representation called the double scanline representation that merges consecutive pixels in each row and column into strips with unit width, respectively. Based on this, we develop coordinate descent heuristics for the raster model that repeat a line search in the horizontal and vertical directions alternately, where we also introduce a corner detection technique used in computer vision to reduce the search space. Computational results for test instances show that the proposed algorithm obtains sufficiently dense layouts of rasterized shapes in high-resolution within a reasonable computation time.