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The current system has several input parameters, they are as follows:
Initial Population Size
Number of Generations
Set of Polygons
In this section we will study the effect of various parameters on the output of the algorithm. While studying one parameter we will keep other parameters constant and observe the output. For all the experiment conducted below, 7 polygons were used with a total vertex count of 191.
Since we relaxed ourselves from rotating the polygons, their orientation becomes static. As polygons would be dropped from the top of the strip with fixed/static orientation we can precalculate lots of collision data beforehand while loading the polygons .
It can be noted that when a polygon is to be dropped from the top of the trip, only the points/vertices of the front-facing lines can collide with the back-facing lines of the polygons that had already been dropped. On the other hand, only the points/vertices of the back-facing lines of the polygon already dropped in the strip can collide with the front facing lines of the polygon to be dropped. This prunes out half of the vertices and lines to be tested for collision on average and reduces the collision test to 1/4. The fact is demonstrated below. Continue reading →
The approach that has been taken to solve the given Strip-Packing problem was based on Genetic Algorithm. The first issue was to represent the arbitrary shapes into some geometric form.
2. Object definition
Each arbitrary shape was represented by an n-sided polygon. Each side of the polygon was a straight line. Curves and other smoother shapes were approximated by sampling a curve at many points and joining them with small lines. Therefore an arbitrary shape was represented by Continue reading →
Our simulation framework is basically a stand-alone software that was built with a GUI support. There are basically 3 modules, polygon input module, output module and GA-parameter input module.
1.1 Our simulation framework consists of the following parameters
1.1.1 n number of arbitrary polygons.
Polygons are stored in simple text files which are read in by the simulation program.
1.1.2 Initial Population, k
Initially k number of chromosomes/individuals are created randomly. These k chromosomes act as the first generation.
1.1.3 Number of Generations
This is basically the number of iterations or generations to be simulated for. Since the problem is a NP-Hard problem, there is no particular sentinel condition so we need to set this parameter manually. Continue reading →
Genetic algorithm (GA) is based on the natural evolution theory. GA begins with a set of k randomly generated states, called population. Each state, or individual, is represented as a string over a finite alphabet, most commonly a string of 0s and 1s. Each state must be one candidate solution or an acceptable configuration of the problem which may or may not be optimal. For example, in 8-queens-problem, which asks to arrange 8 chess queens on a chess board in such a way that no queen can attack another queen, a state must specify positions of 8 queens. A common representation of the state can be a string of 8 numbers. Each number will be associated with a queen in one particular column of the chess board, and the number it self will represent the row that queen belongs to. This representation is illustrated in Figure 3.1 below. 8 such numbers can fully represent the positions of all 8 queens on the chess board. Randomly generating one such state may have queens attacking another queen. Continue reading →
Nesting problem is interesting to many industries like garment, paper, ship building, and sheet metal industries since small improvements of the layout can result in a large saving of material. In some cases both the pieces and the containing region are rectangular, and a considerable mount of effective solutions have been proposed for rectangular nesting problems in the past decades. However, there are also many other cases where either the pieces or the containing region is irregular in shape, due to the geometrical complexity introduced by irregular shapes, such problems are not studied as well as rectangular nesting problem. Today even a purely automatic algorithm is still difficult to outperform an experienced operator, hence irregular nesting problem is still an attractive research topic. Continue reading →