Solving 2D Rectangle Packing Problem Based on Layer Heuristic and Genetic Algorithm

The packing of rectangles is a NP-Complete problem and possesses widespread applications in the industry, such as the cutting of clothing, metal and composition of news. In this paper, an orthogonal rectangle packing problem with rotation of items and without the guillotine packing constraint is considered. A layer-based heuristic algorithm is presented with the combination of genetic algorithm. This heuristic algorithm is mainly based on heuristic strategies inspired by the wall-building rule of bricklayers in daily life. The computational results on Benchmark problems have shown that this algorithm not only runs in shorter time than known meta-heuristic but also finds shorter height.