Nesting of Two-Dimensional Irregular Parts Within an Irregular Boundary Using Genetic Algorithm

The present work aims to find an efficient and fast method for the nesting of two-dimensional Irregular or regular parts in an irregular or regular sheet using genetic and heuristic algorithms, with a view to maximizing the utilization of the sheet material. The proposed genetic algorithm gives out the best sequence and orientation of parts, using which the given heuristic generates a nested pattern with bottom left strategy. The heuristic approach makes use of the positioning technique to find out the acceptable position of each part on the sheet. The application of the proposed approach is illustrated by considering both irregular parts and irregular sheets composed of line features. INTRODUCTION In the present day manufacturing scenario, the cutting of two-dimensional parts with the objective of minimizing the wastage of the sheet material is an important activity. This activity is common to many industries such as the shipbuilding, wood, paper, leather, plastic, textile, granite and sheet metal industries, in which regular or irregular shaped parts need to be produced from large sized sheets. In most of these industries, a small amount of saving in material may lead to considerable savings in cost. It is normal practice to generate the best arrangement of the required parts in a sheet, referred to as nesting of two-dimensional parts, before cutting these parts. The nesting process depends on many interrelated parameters such as the cutting process, the shape and variety of parts to be cut, the shape and size of the sheet and subsequent operation required on the parts. Since the nesting problem is specific to the application in a particular industry, the development of nesting software strongly depends on the problem chosen. In the shipbuilding industry where thousands of tons of steel are used, even 15 percent wastage can be substantial. Since the parts are more or less of fixed types and the metal sheet or plate is of standard dimensions, nesting software can make use of this information. Approaches for nesting of regular parts is relatively simple in view of their regular geometry. On the other hand, many engineering components are irregular and may comprise both line and curvilinear features with or without internal features. For nesting of irregular parts whose geometry varies from one part to another, highly complex nesting methods are required. In order to solve the nesting of rectangular and irregular shaped parts in different shaped sheets, different approaches are described in the literature. REVIEW OF EXISTING WORK A simple method of nesting irregular parts is to approximate them into rectangles and nest these rectangles in a sheet. This particular method does not consider the actual geometry of parts during nesting. Jakobs [1] proposed a genetic and heuristic approach for the nesting of polygons, enclosed in rectangular modules, in a rectangular sheet. In this method, a bottom left heuristic algorithm generates a nested pattern for a sequence of rectangular modules obtained by a genetic code. Each irregular part, each feature and each effective region of the sheet is approximated into rectangles. Nee et al [2] addressed the nesting problem using a heuristic method. In a similar way, Han and Na [3] decomposed the irregular parts into rectangles and circles manually and developed a two-stage approach that makes use of both neural networks and simulated annealing algorithms. A self-organization assisted layout learning algorithm based on a neural network generates a reasonably fine pattern of layout and a Associate Professor, Dept. of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, India, SNAME (M). Assistant Ship Surveyor, Indian Register of Shipping, Mumbai, India. Presently Research Assistant, Dept of Mechanical Engineering, Michigan State University, East Lansing, USA. Manuscript received by JSP Committee October 2000 222 NOVEMBER 2000 8756-1417/00/1604-0222500.4710 JOURNAL OF SHIP PRODUCTION simulated annealing algorithm increases the layout efficiency by translating, rotating and swapping the parts. The major limitation of this particular approach is the manual decomposition of different parts into rectangles and circles, which is quite a tedious task. These approaches, which enclose the irregular features of the parts and the sheet in rectangles, may not result in optimal nesting patterns, particularly when the original geometry is quite different from the enclosed geometry. This limitation can be overcome by considering the actual geometry of the sheet and the parts. Towards this, several heuristics have been developed considering the actual part and sheet geometry. Lamousin et al [4] addressed the nesting of irregular parts in an irregular sheet using the No Fit Polygon (NFP) and Internal No Fit Polygon (INFP) concepts. Both NFP and INFP are nothing but the paths traced by a part as it slides in contact with the inner and the outer boundaries of the sheet respectively. For the nesting of parts, each part is placed at the bottom left position of these polygons. Lamousin and Waggenspack [5] studied a different method to nest irregular parts in irregular sheets. This particular method concentrates on a feature-matching algorithm, which joins the convex features of a part with the concave features on the boundary of the sheet material. However, the wastage of the sheet material is found to be more in many cases, when compared to the technique that uses NFP and INFP procedures. Heuristic techniques based on the geometry of the parts and the sheet adopt fixed deterministic rule and sequence dependent procedures for nesting. When the geometry of the parts to be nested changes, a different heuristic may be required to nest them onto the sheet. Thus, heuristic methods for nesting of regular or irregular parts may not give the optimal utilization of sheet material. In view of these limitations with heuristic methods, researchers focused on developing modern heuristic methods such as genetic algorithms, simulated annealing and neural networks for nesting purposes. Ismail and Hon [6] have proposed a genetic approach for the nesting of a multiple variety of parts, with orthogonal edges, in a single rectangular sheet. This particular approach concentrates on moving all parts simultaneously close to horizontal and vertical edges of the sheet. In this, genetic algorithm generates a large number of overlapped patterns before arriving at the final nested pattern. Thus, it requires a larger number of iterations and higher computation time. The overlap checking routines employed in the nesting algorithms are responsible for higher computational time. Moreover, the overlap checking time increases when more line or arc features in an irregular part need to be checked for overlapping with all such features in other parts. The approach presented here proposes a new heuristic and genetic approach for nesting of irregular shaped parts in an irregular sheet. The proposed heuristic is independent of the geometry of the parts and the sheet. It makes use of a new scanning technique for quick identification of a part's acceptable position on the sheet. The approach takes care of an irregular sheet and parts with highly