Solving Polygon Packing Problems with Rotation Using Hierarchical Optimization

Abstract

The polygon packing problem is a combinatorial optimization problem that requires placing a given set of polygons within a rectangular strip with a fixed height and an arbitrary length. And, we aim to minimize the width. However, each polygon must not overlap. In this paper, we propose a new method for converting into the rectangular packing problem using a hierarchical genetic algorithm, which combines multiple pieces and approximates them into a rectangle. Generating a rectangle is divided into steps to optimize 1) the pieces and angles to be combined, and 2) the margins when the rectangle is viewed as a rectangle. In this way, we only consider rotations of 0 and 90 degrees, which is expected to reduce the computational cost significantly. We conduct experiments using a data set with and without rotation, and compare the final result with existing studies.