基于嵌套Gumbel Copula函数的分布估计算法

Estimation of Distribution Algorithms Based on Nested Gumbel Copula

如何估计群体的联合概率分布及如何对其采样,是分布估计算法应用中需要解决的关键问题,尤其在多维情形下,该问题更显重要。Copula理论为研究多变量联合分布提供了一个有用的工具,它可以把随机变量的边缘分布和它们的相关结构分开来研究。提出基于嵌套Copula函数的分布估计算法。论文在介绍完全嵌套和部分嵌套两种嵌套copula模型的基础上,详细讨论了三维情形下,完全嵌套阿基米德Copula函数的采样算法,并给出了基于嵌套Copula函数的分布估计算法的框架。以Gumbel Copula函数为例,针对三维Benchmark函数优化问题的仿真实验,表明了该算法的有效性。

Two key issues for Estimation of Distribution Algorithms （EDAs） are how to estimate and sample the joint probability distribution, especially in multi-dimensional case. Copula theory separated joint probability distribution function into product of marginal distributions, and provided a useful tool for multivariate probability analysis. Two nested copula models were introduced, including fully nested Archimedean copula and partially nested Archimedean copula. The sampling method of three-dimensional fully nested Archimedean copula was discussed at length, and then the procedure of newly proposed paradigm, Ncopula-EDAs, was described, which indicated an innovative way to solve the multivariate and multiple dependences optimization problem. Based on Gumbel copula function, the experiment results validate the feasibility and efficiency of the algorithm.