In this section, we discuss the relation works with MAMEDA.
It composes of two subsections. In subsection A, the
framework of EDA is described, and we have tried to present
a category of the methods are used for estimation the
structures in multivariate EDAs. In subsection B, we review
some of the MAs, EAs and EADs method presented on the
The general steps of EDAs have been used in stationary
optimization problems are as follows :
1) Generate initial populations D with uniform distribution
of variables, and evaluate them.
2) Select N promising individuals from the populationD.
3) Estimate best structure based on the selected individuals.
4) Sampling new individuals based on the parameter
5) Evaluate new individuals, and replace old individuals.
6) If a termination criterion is not met, go to step 2.
The above steps usually are used for multivariate EADs. In
univariate EDA, there is not structure learning, and bivariate
EDAs are different in structure learning and sampling steps.
The structure learning is more important part and there are
several works in this field. So, we focus on this step.
We assume each individual in search space has n dimension
or n variables. In the structure learning we must calculate the
following probability, is parents set of variable , if univariate EDAs is used
then ∅. As we described in introduction, the probability
graphical models (PGM) are used for structure representation,
or presentation of the estimated structure. For example, in Fig.
I is represented a structure with four variables that used of
Structure learning consists of two components. First, with
attention to the selected individuals, the best structure is
estimated, approximately. Second, the parameters of structure
estimated would be calculated. There are several methods for
structure estimation and many statistical methods for
evaluation the goodness of structures ,  and .
In introduction, we discussed three models for represent the
structures. There are many statistical methods to estimate and
evaluate the structures. Some of these methods are utilized in
discrete environments. Some of the structure estimation
methods are similar in Bayesian and Gaussian networks. We
explain some of these methods.
In Gaussian networks, it is considered, each variable of
solutions is continuous and each local density function is the
linear-regression model. One of the methods to generate
Gaussian based models is to use the detecting independencies
between variables . Some of the methods that are based on
this idea are as follow :
1) The likelihood ratio test.
2) The Wald test.
3) The efficient score test.
4) The modified profile likelihood ratio test.
5) The fisher’s statistic.
is one of the algorithms uses likelihood ratio test
for structure learning . Another method which has been
presented to generate models in Gaussian networks is BG
, which is a continuous version of