多数円板の矩形内配置問題　　振動制御法によるアプローチ

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  • A Packing Problem of Many Circles into Rectangles. A New Approach by Vibration Control Method.
  • タスウ エンバン ノ クケイ ナイ ハイチ モンダイ シンドウ セイギョホウ

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This paper describes a new approach to solve a problem of packing circles into a given rectangular area. In our problem setting, we assume that the circles have different diameters and the number of circles is above one hundred. Starting from random allocation of circles in relatively large rectangular area, by giving external force, we vibrate the circles and obtain more dense allocation. Elasticity is assumed in resulting forces by collision between the circles. The circles will continue to collide with each other while changing their positions continually. While the circles being vibrated, the rectangular area will be shrunk to minimize resulting waste. Final positions of the circles and the size of the rectangle will be determined when the circles cease to move. To obtain effective vibration to move the circles, we give the vibration according to Lissajous's figures and we tune the parameters of the figures using Genetic Algorithms. Magnitudes of amplitude, frequency and phase of the figures are encoded as artificial chromosomes and manipulated by conventional genetic operators. In the paper, we carry out some simulation basis experiments, and examine the applicability of the proposed methodology.

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