size, is the number of decision variables in the linkage set and is the joint entropy of the variables in The linkage-learning in ECGA works as follows: (1) Insert each variable in a cluster, (2) compute CCC = MC + CPC of the current linkage sets, (3) verify the increase on CCC provided by joining pairs of clusters, (4) effectively joins those clusters with highest CCC improvement. This procedure is repeated until no CCC improvements are possible and produces a linkage model . The ECGA works with concrete populations, therefore, using the factorized distribution modeled by ECGA, it can be described as Bayesian optimization algorithm (BOA) The BOA uses Bayesian networks to model and sample promising solutions. Bayesian networks are directed acyclic graphs, with nodes representing variables and edges representing conditional probabilities between pair of variables. The value of a variable can be conditioned on a maximum of other variables, defined in . BOA builds a PGM encoding a factorized joint distribution, in which the parameters of the network, i.e. the conditional probabilities, are estimated from the selected population using the maximum likelihood estimator. The Bayesian network structure, on the other hand, must be built iteratively (linkage-learning). It starts with a network without edges and, at each step, adds the edge which better improves some scoring metric (e.g. Bayesian information criterion (BIC) or Bayesian-Dirichlet metric with likelihood equivalence (BDe)). The scoring metric evaluates the network structure according to its accuracy in modeling the selected population. From the built network, BOA samples new promising solutions as follows: (1) it computes the ancestral ordering for each variable, each node being preceded by its parents; (2) each variable is sampled conditionally to its parents. Given such scenario, every BOA step can be defined as Linkage-tree Genetic Algorithm (LTGA) The LTGA differs from most EDA in the sense it does not explicitly model a probability distribution but only a linkage model, called linkage-tree. A linkage is a set of linkage sets with no probability distribution associated, therefore, there is no way to sample new solutions directly from . The linkage model is a linkage-tree produced stored as a Family of sets (FOS). The linkage-tree learning procedure is a hierarchical clustering algorithm, which work as follows. At each step the two closest clusters and are merged, this procedure repeats until only one cluster remains, each subtree is stored as a subset . The LTGA uses