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About Description Cutting Stock Problem Circle Optimization Problem
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  A triangle is a 3-sided polygon. Every triangle has three sides and three angles, some of which may be
  the same.   All triangles are convex.   Triangles can be classified according to the number of their equal
  sides. A triangle with 3 equal sides is called equilateral, a triangle with 2 equal sides is called isosceles,
  and a triangle  with no equal sides is called scalene.  The portion of the area enclosed by the triangle is
  called   the   triangle interior.    The   sum of angles in a triangle is pi radians or 180 degrees.    If a line is
  drawn   parallel   to   one side of   a   triangle   so that   it intersects the other two sides,   it divides them
  proportionally. The term nesting is used to describe a wide variety of two-dimensional cutting problems.
  They all   involve a   non-overlapping   placement of a set of triangles within some region of 2d area. The
  basic   requirement  is to produce a solution with no overlap between the triangles. This means that the
  items   must be   placed  without   creating   overlap between the triangles.   The generation of a cutting
  pattern depends on   the order of handling the triangles,   and the way of fitting these triangles into the
  sheet with respect to the sheet boundaries. The two-dimensional cutting stock problem may be applied
  in a number of industries, including   clothing industry, shoe-leather cutting, furniture industry, etc. The
  problem is as follows: a set of triangles is to be placed on a given area of a stock-material with minimum
  of trim-loss.   Permissible placement of wanted triangles on stock-material is called cutting pattern. The
  cutting pattern   has no overlaps of the triangles and meets all technological requirements. The quality
  of a cutting pattern   is determined   by the cutting ratio, which is defined as the ratio between the total
  area of   the placed   triangles and the   total   area of the   stock-material.   Nesting software is used to
  generate optimized   layouts and reduced scrap for both   Rectangular and Triangular cutting processes.
  The nesting   technology   is based on algorithms designed to optimize the cutting layouts.   It provides
  high   utilization layouts,   significantly   reducing the waste and maximizing productivity.  In the cutting
  problems   one or more   pieces   of   material   or space   must be   divided   into smaller triangles.   The
  minimization   of the waste   is usually the main objective of these combinatorial optimization problems.
  In nesting problems the combinatorial problem coexists with a geometric problem, since solutions must
  be geometrically feasible and triangles may not overlap and must completely fit inside the plate.

  Packing problems   are optimization problems that are concerned with searching a  good arrangement
  of multiple items   in   a   2d regions.  The usual objective   of the allocation is to maximize the material
  utilization   and to minimize the wasted area.   This  is of  particular interest to industries involved with
  mass-production   as  small improvements in   the layout   can result   in   savings   of   material   and a
  considerable reduction   in production costs.   The goal in the cutting stock problem is to determine the
  optimal   plan   to cut   a 2 dimensional sheet   to satisfy   a set of customers demands. Cutting triangle
  problems may involve a variety  of objectives,   minimizing trim loss, minimizing the number of cutting
  lines,   maximizing profit,   and so on.   In order   to solve the cutting triangle problem,  we use a cutting
  pattern optimizer and mathematical programming. In general, the cutting triangle 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 cutting stock problem may also be reduced to a bin-packing problem. The rectangular
  cutting stock problem is to determine how to cut a number of rectangular pieces 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 irregular   cutting stock problem.   The   2 dimensional cutting stock
  problem   is a   classic combinatorial optimization problem in which a number of parts 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   rectangular pieces 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 pieces and meets all
  technological requirements.    The stock cutting problem has gained a lot of attention in many industrial
  sectors.     Stock Cutting Problems  is  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 stock cutting problem is an example of a large scale
  optimization   problem.   This   means   that   this   problem requires   a   computing effort that increases
  exponentially   with   the problem size.     Since   the stock cutting problem is an efficient approximation
  algorithms,   namely,   algorithms that   do not produce optimal but rather   close-to-optimal   solutions,
  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.