等球Packing问题的序列对称换位算法

Serial symmetrical relocation algorithm for equal sphere Packing problem

为处理等球Packing问题,在基本拟物算法的基础上设计了序列对称换位策略,形成了一个启发式的序列对称换位算法。在球形容器内装填1～50个等球时,此算法改进了其中45项当前记录。特别地,此算法成功将68个半径为1的等球装进半径小于5的球形容器。此结果证否了一个猜想,该猜想认为半径为5的球形容器至多只能装下67个半径为1的等球。其结果的质量说明了序列对称换位算法的有效性。

To deal with the equal sphere Packing problem,this paper designed a serial symmetrical relocation strategy based on the basic quasi physical algorithm to form a serial symmetrical relocation algorithm.When packing up to 50 equal spheres in a spherical container,this algorithm improved 45 current records.Especially,it successfully packed 68 equal spheres of radius 1 into a spherical container whose radius is less than 5.This result proves wrong a conjecture which states the spherical container of radius 5 can at most contain 67 spheres of radius 1.The quality of the results justifies the serial symmetrical relocation algorithm.