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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
twodimensional
polygonal
shapes
within
another larger twodimensional 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 2D 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: rulebased approaches and
stochastic algorithms.
In a rulebased 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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 Fall '11
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