Solving the two-dimensional irregular objects allocation problems by using a two-stage packing approach

Packing problems are combinatorial optimization problems that concern the allocation of multiple objects in a large containment region without overlap and exist almost everywhere in real world. Irregular objects packing problems are more complex than regular ones. In this study, a methodology that hybridizes a two-stage packing approach based on grid approximation with an integer representation based genetic algorithm (GA) is proposed to obtain an efficient allocation of irregular objects in a stock sheet of infinite length and fixed width without overlap. The effectiveness of the proposed methodology is validated by the experiments in the apparel industry, and the results demonstrate that the proposed method outperforms the commonly used bottom-left (BL) placement strategy in combination with random search (RS).