On Copula Estimation Of Distribution Algorithms Copula Function Research

To estimate the probability distribution model is the key of Estimation of Distribution Algorithm (EDA), with the complexity of the problem to be solved, it will cost more time to estimate the probability distribution model and to sample from it, improving EDA is the difficult and hot issues of the field.Copula theory is used in Estimation of Distribution Algorithm based on Copula (cEDA). Copula theory provides a new way to estimate joint probability distribution, it enable us to separate joint probability distribution into the product of univariate margins and a copula which represents the dependency structure of random variables. The estimation of the marginal probability distribution is much easier than that of the joint probability distribution, and the Copula is easier to sample.An Estimation of Distribution Algorithm based on Clayton Copula is presented in this paper, which uses empirical distribution as the univariate marginal. When the marginal distribution and Copula are fixed, the estimation of the parameters of the Copula is very important, because it directly influence the accuracy of the probability distribution. In this paper, we use some fixed value as the parameters first, which means the probability distribution model is fixed, the experimental results show the method is feasible. Then we utilize maximum likelihood estimation (MLE) to estimate the parameters to establish the more accurate probability distribution model, the experimental results show the effectiveness of the method. When the problem to be solved is complex, it is time-consuming to use MLE. At last we adopt non-parametric method, the experimental results show this method could establish the more accurate probability distribution model and cost spend less time.