A generic approach for nesting of 2-D parts in 2-D sheets using genetic and heuristic algorithms

In this paper, a genetic and heuristic approach is proposed for the nesting of multiple two-dimensional (2-D) shaped parts in multiple 2-D shaped sheets with the aim of minimizing the wastage of the sheet material. The paper proposes a new method of representing the sheet and part geometries in discrete form to arrange the parts on the sheet quickly, irrespective of the complexity in the geometry of the sheets and parts. The proposed heuristic approach considers the sheets and parts in a sequential manner and arranges the parts on the sheets using the bottom-left strategy. The genetic algorithm generates the best sequence of the sheets and parts for nesting the parts on multiple sheets, utilizing the sheet material optimally. The effectiveness of the proposed approach is shown by comparing the results obtained with the present approach to those obtained with the approaches proposed by Jakobs (Eur J Oper Res, 88 (1996) 165), Ramesh Babu and Ramesh Babu (Int J Prod Res, 37(7) 1999 1625), and Jain and Chang (Engng Comput, 14 (1998) 206). The generic nature of the present approach is illustrated by considering a variety of parts, ranging from a simple rectangular shape to a highly irregular shape, in different combinations with or without grain orientation constraint, apart from nesting of multiple irregular shaped parts in multiple sheets of complex geometry. (C) 2001 Elsevier Science Ltd. All rights reserved.