Nesting of Irregular Shapes Using Feature Matching and Parallel Genetic Algorithms

Nesting of Irregular Shapes Using Feature Matching and Parallel Genetic Algorithms

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Nesting of Irregular Shapes Using Feature Matching and Parallel Genetic Algorithms Anand Uday Erik D. Goodman Ananda A. Debnath Genetic Algorithms Research and Applications Group (GARAGe) Michigan State University 2857 W. Jolly Road, Okemos, MI 48864 goodman@egr.msu.edu Abstract The problem of finding a dense packing of a set of two-dimensional polygonal shapes within another larger two-dimensional polygon is called nesting. This problem finds wide application in the manufacturing, leather cutting, and textile industries – in short, where material is costly so scrap must be minimized. In this paper, we describe a new approach to solving this problem. It is a hybrid (or memetic) approach, which uses a parallel genetic algorithm and a heuristic based on shape information in the form of feature matching. In our experiments with the parallel GA, we tried various topologies for the communication among subpopulations, and various migration policies. A good choice of communication patterns seems to give subpopulations more time to explore by themselves before they are ”contaminated” by individuals from other subpopulations, while still allowing for useful sharing of building blocks gained. Our test problems show this approach to work well in this type of problem, where the search domain is very large. 1 INTRODUCTION Layout and cutting problems are important in many industries, as they involve the optimal use of valuable raw material. Problems of optimal arrangement of 2-D pieces to be cut from an initial piece of stock material are called nesting problems, and there are many varieties, depending on the shapes of the pieces, constraints on their orientations, etc. The problem to be addressed in this paper can be stated as follows: given a rectangular piece of stock of a specified width and indefinite length, find the optimal arrangement of a given set of polygonal “part” shapes onto that stock such that a) none of the parts overlaps any others, b) all are contained within the boundary of the stock piece, and c) the length of the stock piece used is minimized. In this case, there is no constraint on the orientation of the part shapes, but they may not be “turned over.” Note that there is no constraint, such as convexity, on the shape of the polygonal parts. In recent years, a number of researchers have investigated the problem of nesting of irregular shapes. The heuristic approaches taken to solve this problem can be broadly classified into two categories: rule-based approaches and stochastic algorithms. In a rule-based heuristic, a set of rules is designed to try to take advantage of some characteristics of the shapes of the parts, placing earliest those with certain characteristics, packing together parts with certain matching features, etc. On the other hand, stochastic approaches such as genetic algorithms or simulated annealing, typically use little information about part shapes, instead using only simple “packing” rules and relying on the stochastic algorithm to vary the order in
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Nesting of Irregular Shapes Using Feature Matching and Parallel Genetic Algorithms

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