In “BOA: The Bayesian Optimization Algorithm“, Pelikan, Goldberg, and Cant´u-Paz introduce an adaptive improvement over genetic optimization algorithms (See also [1]). They write, “In this paper, an algorithm based on the concepts of genetic algorithms that uses an estimation of a probability distribution of promising solutions in order to generate new candidate solutions is proposed. To estimate the distribution, techniques for modeling multivariate data by Bayesian networks are used.” and

“The algorithm proposed in this paper is also capable of covering higher order interactions. It uses techniques from the ﬁeld of modeling data by Bayesian networks in order to estimate the joint distribution of promising solutions. The class of distributions that are considered is identical to the class of conditional distributions used in the FDA. Therefore, the theory of the FDA can be used in order to demonstrate the power of the proposed algorithm to solve decomposable problems. However, unlike the FDA, our algorithm does not require any prior information about the problem. It discovers the structure of a problem on the ﬂy.”

where FDA refers to the Factorized Distribution Algorithm (Mühlenbein et al., 1998). The algorithm consists of the following steps

The Bayesian Optimization Algorithm (BOA)

(1) set t ← 0 randomly generate initial population P(0)

(2) select a set of promising strings S(t) from P(t)

(3) construct the network B using a chosen metric and constraints

(4) generate a set of new strings O(t) according to the joint distribution encoded by B

(5) create a new population P(t+1) by replacing some strings from P(t) with O(t) set t ← t + 1

(6) if the termination criteria are not met, go to (2)

where B is a Bayesian network.

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