Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes

TL;DR

This paper introduces coordinate descent heuristics for the irregular strip packing problem with rasterized shapes, utilizing a novel double scanline representation and corner detection to efficiently produce dense layouts in high-resolution settings.

Contribution

It proposes a new double scanline representation and a coordinate descent heuristic with corner detection for efficient packing of rasterized shapes.

Findings

Achieves dense layouts in high-resolution within reasonable time

Reduces complexity of rasterized shapes with the double scanline representation

Effective in handling high-resolution rasterized shape packing

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.