|
|
|
| Cloud Model Based Evolution Strategy Driven by Kurtosis |
| HE Zhen-Feng1, XIONG Fan-Lun2 |
1.College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108
2.Research Center of Intelligent Information System,Institute of Intelligent Machines,Chinese Academy of Sciences,Hefei 230031 |
|
|
|
|
Abstract The Cloud Distribution’s kurtosis statistic and its application are considered to analyze and improve cloud model based evolution strategy (CMES) from the angle of the classical evolution strategy. By adjusting the kurtosis, the Cloud Distribution with a fixed standard deviation changes the shape of noise, which makes the mutation more effective. The formula of the cloud distribution’s kurtosis is derived, which enables the transformation between the entropy-hyper entropy space and the standard deviation-kurtosis space. The influences of the kurtosis and the kurtosis ratio on the cloud distribution noises are compared to prove that the kurtosis is more suitable for self-adaptive. A kurtosis driven CMES, whose parameter evolution combines a 1/5 rule based standard deviation evolution and a self-adaptive kurtosis evolution, is presented. The experimental results of 8 test functions show that a high kurtosis benefits global optimization, a low kurtosis is in favor of local optimization, and the self-adaptive adjustment of the kurtosis can integrate the benefits from both.
|
|
Received: 19 April 2011
|
|
|
|
|
|
[1] Beyer H,Schwefel H.Evolution Strategies: A Comprehensive Introduction.Natural Computing: An International Journal,2002,1(1): 3-52
[2] Hansen N,Ostermeier A.Completely Derandomized Self-Adaptation in Evolution Strategies.Evolutionary Computation,2001,9(2): 159-195
[3] Colutto S,Fruhauf F,Fuchs M,et al.The CMA-ES on Riemannian Manifolds to Reconstruct Shapes in 3-D Voxel Images.IEEE Trans on Evolutionary Computation,2010,14(2): 227-245
[4] Yao Xin,Liu Yong.Fast Evolution Strategies.Control and Cybernetics,1997,26(3): 467-496
[5] Zhang Guangwei,He Rui,Liu Yu,et al.An Evolutionary Algorithm Based on Cloud Model.Chinese Journal of Computers,2008,31(7): 1082-1091 (in Chinese)
(张光卫,何 锐,刘 禹,等.基于云模型的进化算法.计算机学报,2008,31(7): 1082-1091)
[6] Liu Yu,Li Deyi,Zhang Guangwei,et al.Atomized Feature in Cloud Based Evolutionary Algorithm.Acta Electronica Sinica,2009,37(8): 1651-1658 (in Chinese)
(刘 禹,李德毅,张光卫,等.云模型雾化特性及在进化算法中的应用.电子学报,2009,37(8): 1651-1658)
[7] Li Deyi.Uncertainty in Knowledge Representation.Engineering Science,2000,2(10): 73-79 (in Chinese)
(李德毅.知识表示中的不确定性.中国工程科学,2000,2(10): 73-79)
[8] Liu Changyu,Li Deyi,Du Yi,et al.Some Statistical Analysis of the Normal Cloud Model.Information and Control,2005,34(2): 236-239 (in Chinese)
(刘常昱,李德毅,杜 鹢,等.正态云模型的统计分析.信息与控制,2005,34(2): 236-239)
[9] de Carlo L T.On the Meaning and Use of Kurtosis.Psychological Methods,1997,2(3): 292-307
[10] Chen Lin,Liu Weiqi.Classes of Heavy-Tailed Distribution and Venn Diagrams of Their Relations.Applied Mathematics: A Journal of Chinese Universities,2009,24(2): 166-174 (in Chinese)
(陈 琳,刘维奇.重尾分布族及其关系图.高校应用数学学报,2009,24(2): 166-174)
[11] Luo Ziqiang,Zhang Guangwei,Li Deyi.Probability Statistics Analysis of One Dimensional Normal Cloud.Information and Control,2007,36(4): 471-475 (in Chinese)
(罗自强,张光卫,李德毅.一维正态云的概率统计分析.信息与控制,2007,36(4): 471-475) |
|
|
|
2012, Vol. 25 
