The goal in Circle Optimization Problem is to determine the optimal plan to cut a 2 dimensional sheet
to satisfy a set of customers demands. Circle Optimization problems may involve a variety of
objectives, minimizing trim loss, maximizing profit, and so on. In order to solve the Circle
Optimization Problem we use a cutting pattern optimizer and mathematical programming. In
general, the circle optimization problem is reduce to an integer programming application. Because of
its complexity, solutions to the 2 dimensional cutting stock problem have often been generated using
genetic algorithms. This is due, in part, to the fact that the 2 dimensional circle optimization problem
may also be reduced to a bin-packing problem. The circle optimization problem is to determine how to
cut a number of circles out of a given stock of rectangular sheets. Most variants of the nesting problem
is the problem of packing shapes within some regions without overlap. The cutting stock problem asks
for a minimization of the area of a rectangular region. In the cutting industry a multitude of additional
constraints are very often necessary. The shapes or regions can have different quality zones or
even holes. The nesting problem occurs in a number of industries and it seems to have many names.
In the clothing industry it is called marker making, while the metal industry call it simply nesting. In
a theoretical context the problem is most often called the two-dimensional cutting stock problem.
The 2 dimensional circle optimization problem is a classic combinatorial optimization problem in which
a number of circles of various lengths must be cut from an inventory of 2d material. The two-
dimensional cutting stock problem may be applied in a number of industries, glass, shoe-leather
cutting, furniture, machine-building, etc. The problem is as follows : a set of circles is to be
placed on a given area of a stock material with minimum of trim-loss. The cutting pattern has no
overlaps of the circles and meets all technological requirements. The circle optimization problem has
gained a lot of attention in many industrial sectors. Circle optimization problems are essential in many
industries. These problems are treated in different fields. The reduction of scrap may not only affects
cost of materials used but may also reduce the costs of handling and labor. A great number of problems
are essentially based on the same logical structure of the Cutting and Packing problems. The circle
optimization problem is an example of a large scale optimization problems. This means that this
problem requires a computing effort that increases exponentially with the problem size. Since the
circle optimization problem is an efficient approximation algorithms, namely, algorithms that do not
produce optimal but rather close-to-optimal solution, Cutting and packing problems are encountered
in many industries. The wood-, glass- and paper industry are mainly concerned with the cutting
of regular figures, whereas in the textile and leather industry irregular, arbitrary items are to be packed.
Circle Optimization Problems are concerned with the efficient use of limited resources to meet desired
objectives. Optimization problems are characterized by the large number of solutions that satisfy the
basic conditions of circle optimization. A solution that satisfies both the conditions of the problem and
the given objective is named an optimum solution. An example is the manufacturer who must search
the combination of the available resource to maximize his profit. As the optimization problem has some
objective that guides the selection of the solution to be used, the Circle Optimization Problem aid in
choosing a particular solution as the best solution to a given problem. The optimization process is
divided into 2 distinct computional processes: Process one is concerned with searching a first feasible
solution, while Process two, which starts with this first solution, is concerned with obtaining an optimal
solution. In Process one the selection of a new circle to be introduced into the basis depends only on a
criterion that increases the efficiency. The number of operations required in Process two depend on how
close the first solution is to the maximum. The closer the first solution, the fewer the operations
required. The calculation process repeats the optimization of selecting circles to be eliminated and then
new circles to be introduced into the basis, until an admissible basis to the solution is finded. The total
number of operations can be reduced, if we utilize some of our knowledge about the expected solution.
The selection of a new basis determines a new circle which is a neighbor to the old circle. This process
continue and after a number of steps stop at the maximum value or until an indication is given that no
beter solution exists.
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