Packing Equal Circles in a Square II. — New Results for up to 100 Circles Using the TAMSASS-PECS Algorithm
Packing Equal Circles in a Square II. — New Results for up to 100 Circles Using the TAMSASS-PECS Algorithm
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DOI：
10.1007/978-1-4613-0295-7_15
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
L. G. Casado;I. García;P. Szabó;T. Csendes
中科院分区：
文献类型：
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作者：
L. G. Casado;I. García;P. Szabó;T. Csendes
在这项工作中，我们提出了一个新的随机优化算法解决问题的最佳包装的n个不重叠的平等的圆圈在一个正方形。它将被证明，我们的程序可以找到大多数的最优解，以前解决的所有问题，并在文献中报道。通过我们的算法获得的结果，最多100圈给出相关的数值和图形形式。对于n = 32，37，47，62和72，该算法得到了比文献中报道的填充更好的解决方案。此外，还报道了40个新的和未发表的布局结果，并通过区间算术计算验证了所得到的布局。
In this work we propose a new stochastic optimization algorithm for solving the problem of optimal packing of n non-overlapping equal circles in a square. It will be shown that our procedure can find most of the optimal solutions for all the problems previously solved and reported in the literature. Results obtained by our algorithm for up to 100 circles are given in relevant numerical and graphical form. Forn= 32, 37, 47, 62 and 72 the algorithm has obtained better solutions than those reported on in the literature on packing. In addition, forty new and unpublished packing results are reported on. The arrangements obtained were validated by interval arithmetic computations.