求解特征值互补问题的遗传算法
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摘要
利用遗传算法求解特征值互补问题,构造了求解特征值互补问题的标准遗传算法,给出保留精英遗传算法的收敛性证明.数值例子验证了求解特征值互补问题的遗传算法的有效性.
Using genetic algorithm to solve the eigenvalue complementarity problem. the convergence of the retained elite genetic algorithm is proved. Numerical examples are presented to indicate the effectiveness of the algorithm.
Using genetic algorithm to solve the eigenvalue complementarity problem. the convergence of the retained elite genetic algorithm is proved. Numerical examples are presented to indicate the effectiveness of the algorithm.
引文
[1]Júdice J J,Sherali H D,Ribeiro I M.The eigenvalue complementarity problem[J].Computational Optimization and Application,2007,37(2):139-156.
[2]Costa A P D,Martins J A C,Figueiredo I N,et al.The Directional Instability Problem in Systems with frictional contacts[J].Computer Methods in Applied Mechanics and engineering,2004,193(3-5):357-384.
[3]Costa A P D,Seeger A.Cone-constrained eigenvalue problems:theory and algorithms[J].Computational Optimization and Applications,2010,45(1):25-57.
[4]Seeger A,Pérez J V.On cardinality of pareto spectra[J].The Electronic Journal of Linear Algebra,2011,22(1):758-766.
[5]Adly S,Seeger A.A nonsmooth algorithm for cone-constrained eigenvalue problems[J].Computational Optimization and Applications,2011,49(2):299-318.
[6]Costa A P D,Seeger A.Numerical resolution of cone-constrained eigenvalue problems[J].Computational and Applied Mathematics,2009,28(1):37-61.
[7]韩海山,黄迪帅.求解特征值互补问题的ABS算法[J].高等学校计算数学学报,2018,40(3):207-222.
[8]黄迪帅,韩海山.求解特征值互补问题的一类ABS算法[J].运筹与管理,2018,27(8):92-98.
[9]王梓坤.随机过程论[M].北京:科学出版社,1978.
[10]朱会霞,郝志云,王福林.二进制遗传算法编码长度的计算方法[J].辽宁工业大学学报(自然科学版),2016,36(2):138-140.
[11]刘英.遗传算法中适应度函数的研究[J].工业高等专科学校学报,2006,13(3):1-4.
[12]吴龙,任红民,毕惟红.遗传算法求解非线性方程组研究综述[J].电子科技,2014,27(4):173-178.
[13]陈磊,霍永亮.利用改进的遗传算法求解非线性方程组[J].西南师范大学学报(自然科学版),2015,40(1):23-26.
[14]恽为民,席裕庚.遗传算法的全局收敛性和计算效率分析[J].控制理论与应用,1996,13(4):455-460.
[15]曲中水,刘淑兰.基本遗传算法的收敛性分析方法[J].哈尔滨理工大学学报,2003,8(1):42-45.
[2]Costa A P D,Martins J A C,Figueiredo I N,et al.The Directional Instability Problem in Systems with frictional contacts[J].Computer Methods in Applied Mechanics and engineering,2004,193(3-5):357-384.
[3]Costa A P D,Seeger A.Cone-constrained eigenvalue problems:theory and algorithms[J].Computational Optimization and Applications,2010,45(1):25-57.
[4]Seeger A,Pérez J V.On cardinality of pareto spectra[J].The Electronic Journal of Linear Algebra,2011,22(1):758-766.
[5]Adly S,Seeger A.A nonsmooth algorithm for cone-constrained eigenvalue problems[J].Computational Optimization and Applications,2011,49(2):299-318.
[6]Costa A P D,Seeger A.Numerical resolution of cone-constrained eigenvalue problems[J].Computational and Applied Mathematics,2009,28(1):37-61.
[7]韩海山,黄迪帅.求解特征值互补问题的ABS算法[J].高等学校计算数学学报,2018,40(3):207-222.
[8]黄迪帅,韩海山.求解特征值互补问题的一类ABS算法[J].运筹与管理,2018,27(8):92-98.
[9]王梓坤.随机过程论[M].北京:科学出版社,1978.
[10]朱会霞,郝志云,王福林.二进制遗传算法编码长度的计算方法[J].辽宁工业大学学报(自然科学版),2016,36(2):138-140.
[11]刘英.遗传算法中适应度函数的研究[J].工业高等专科学校学报,2006,13(3):1-4.
[12]吴龙,任红民,毕惟红.遗传算法求解非线性方程组研究综述[J].电子科技,2014,27(4):173-178.
[13]陈磊,霍永亮.利用改进的遗传算法求解非线性方程组[J].西南师范大学学报(自然科学版),2015,40(1):23-26.
[14]恽为民,席裕庚.遗传算法的全局收敛性和计算效率分析[J].控制理论与应用,1996,13(4):455-460.
[15]曲中水,刘淑兰.基本遗传算法的收敛性分析方法[J].哈尔滨理工大学学报,2003,8(1):42-45.