球面上5点分布问题的数值解法

球面上5点分布问题的数值解法 5 Points on a Sphere is Solved by Numerical Method 杨承中 YANG Chen-zhong~1 1 2 3 4 5 first-author 康卓 KANG Zuo~2 1 2 3 4 5 周爱民 Zhou Ai-min~3 1 2 3 4 5 康立山 KANG Li-shan~3 1 2 3 4 5 贵州民族学院数学与计算机系 贵州民族学院数学与计算机系 Department of Mathematics and Computer, Guizhou College of Nationalities Department of Mathematics and Computer, Guizhou College of Nationalities 武汉大学计算中心 武汉大学计算中心 Computation Center, Wuhan University Computation Center, Wuhan University 武汉大学软件工程国家重点实验室 武汉大学软件工程国家重点实验室 State Key Laboratory of Software Engineering, Wuhan University State Key Laboratory of Software Engineering, Wuhan University 武汉大学软件工程国家重点实验室,贵州,贵阳,550025 武汉大学软件工程国家重点实验室,贵州,贵阳,550025 ,湖北,武汉,430072 ,湖北,武汉,430072 针对物理学家Thomson在研究核电子的平衡时提出球面上点的分布问题,本文设计了一个新型群体分裂演化算法PDEA（Population-DecompositionEvolutionaryAlgorithm）来求解该问题在各种能量意义下的5点分布问题:minV5（X,α）,得到了令人惊喜的结果:这些点的分布为两个点位于球的两极,其余3点位于赤道上形成一个等边三角形.特别是当α=1时,即Thomson问题minV5（X,1）,这时达到最小能量V5（X,1）=6.474691. It is just a century when physicist Thomson posed the question of distributing N points on the sphere for determining the stable equilibrium position of N classical electrons constrained to move on the surface of a sphere and repelling each other by an inverse square law in 1904. In this paper, a new population decomposition evolutionary algorithm PDEA is designed for solving the problem of 5 points on a sphere: minV 5 （X,α） under different energy circumstances, especially, for solving the Thomson’s problem: minV 5 （X,1）. Numerical results are obtained. These points are distributed as: two points are positioned at the poles of the sphere and the other three are positioned as an equilateral triangle on the equator. We get the minimum energy of Thomson’s problem: minV 5 （X,1）=6.474 691. 球面5点分布问题 演化算法 群体分裂 群体爬山 5 points on a sphere evolutionary algorithm population decomposition population hill-climbing O411.1 国家自然科学重点基金（60133010）;国家自然科学基金（60473081,40275034）;贵州省高教改革基金（黔教高发[2004]349） 2005-03-01 2021-04-01 3