This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the further exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated. All methods are classified into a few classes according to the complexity of the class of models they use. Algorithms from each of these classes are briefly described and their strengths and weaknesses are discussed.

The paper describes the hierarchical Bayesian optimization algorithm which combines the Bayesian optimization algorithm, local structures in Bayesian networks, and a powerful niching technique. The proposed algorithm is able to solve hierarchical traps and other difficult problems very efficiently.

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema denes the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distribution to generate search points. From BEDA a new algorithm, FDA, is derived. FDA uses a factorization of the distribution. The factorization captures the structure of the given function. The factorization problem is closely connected to the theory of conditional independence graphs. For the test functions considered, the performance of FDA- in number of generations till convergence- is similar to that of a genetic algorithm for the OneMax function. This result is theoretically explained.

To solve hierarchical problems, one must be able to learn the linkage, represent partial solutions efficiently, and assure effective niching. We propose the hierarchical ...

There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decomposition as opposed to decomposition on only a single level. Third, design a class of difficult hierarchical problems that can be used to test the algorithms that attempt to exploit hierarchical decomposition. Fourth, test the developed algorithms on the designed class of problems and several real-world applications. The dissertation proposes the Bayesian optimization algorithm (BOA), which uses Bayesian networks to model the promising solutions found so far and sample new candidate solutions. BOA is theoretically and empirically shown to be capable of both learning a proper decomposition of the problem and exploiting the learned decomposition to ensure robust and scalable search for the optimum across a wide range of problems. The dissertation then identifies important features that must be incorporated into the basic BOA to solve problems that are not decomposable on a single level, but that can still be solved by decomposition over multiple levels of difficulty. Hierarchical

This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. TheBOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

Abstract In this paper we introduce model-based search as a unifying framework accommodating some recently proposed heuristics for combinatorial optimization such as ant colony optimization, stochastic gradient ascent, cross-entropy and estimation of distribution methods. We discuss similarities as well as distinctive features of each method, propose some extensions and present a comparative experimental study of these algorithms. 1

Theoretical and empirical evidence exists that the hierarchical Bayesian optimization algorithm (hBOA) can solve challenging hierarchical problems and anything easier. This paper applies hBOA to two important classes of real-world problems: Ising spin-glass systems and maximum satis ability (MAXSAT). The paper shows how easy it is to apply hBOA to realworld optimization problems. The results indicate that hBOA is capable of solving enormously dicult problems that cannot be solved by other optimizers and still provide competitive or better performance than problem-speci c approaches on other problems. The results thus con- rm that hBOA is a practical, robust, and scalable technique for solving challenging real-world problems.

In this paper we perform a comparison among FSS-EBNA, a randomized, populationbased and evolutionary algorithm, and two genetic and other two sequential search approaches in the well known Feature Subset Selection (FSS) problem. In FSS-EBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm within the EDA (Estimation of Distribution Algorithm) approach. The EDA paradigm is born from the roots of the GA community in order to explicitly discover the relationships among the features of the problem and not disrupt them by genetic recombination operators. The EDA paradigm avoids the use of recombination operators and it guarantees the evolution of the population of solutions and the discovery of these relationships by the factorization of the probability distribution of best individuals in each generation of the search. In EBNA, this factorization is carried out by a Bayesian network induced by a chea...

In this paper, we formalize the notion of performing optimization by iterated density estimation evolutionary algorithms as the IDEA framework. These algorithms build probabilistic models and estimate probability densities based upon a selection of available points. We show how these probabilistic models can be built and used for dierent probability density functions within the IDEA framework. We put the emphasis on techniques for vectors of continuous random variables and thereby introduce new continuous evolutionary optimization algorithms.