中文摘要：

为了从传统进化策略的角度分析并改进云进化策略，研究云分布的峰度统计量及其应用．云分布在固定标准差时，也可通过调整峰度来改变噪声形状，可能产生更有效的变异．推导云分布峰度计算公式，以支持熵-超熵空间和标准差一峰度空间的相互转换．比较峰度和峰比对云分布噪声的影响，证明峰度更适宜自适应演化．给出峰度驱动的云进化策略，它的参数演化结合基于1／5规则的标准差演化和自适应峰度演化．对8个测试函数的实验结果显示，高峰度利于全局寻优，低峰度利于局部寻优，而峰度的自适应调整可综合二者优势．

英文摘要：

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.