 Application Program Development

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.