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66
A Survey of Optimization by Building and Using Probabilistic Models
 COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
, 1999
"... This paper summarizes the research on populationbased 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 ge ..."
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Cited by 297 (88 self)
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This paper summarizes the research on populationbased 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.
Bayesian Optimization Algorithm: From Single Level to Hierarchy
, 2002
"... 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 decompositi ..."
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Cited by 90 (18 self)
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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 realworld 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
The CMA Evolution Strategy: A Comparing Review
 STUDFUZZ
, 2006
"... Derived from the concept of selfadaptation in evolution strategies, the CMA (Covariance Matrix Adaptation) adapts the covariance matrix of a multivariate normal search distribution. The CMA was originally designed to perform well with small populations. In this review, the argument starts out with ..."
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Cited by 58 (18 self)
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Derived from the concept of selfadaptation in evolution strategies, the CMA (Covariance Matrix Adaptation) adapts the covariance matrix of a multivariate normal search distribution. The CMA was originally designed to perform well with small populations. In this review, the argument starts out with large population sizes, reflecting recent extensions of the CMA algorithm. Commonalities and differences to continuous Estimation of Distribution Algorithms are analyzed. The aspects of reliability of the estimation, overall step size control, and independence from the coordinate system (invariance) become particularly important in small populations sizes. Consequently, performing the adaptation task with small populations is more intricate.
Continuous Iterated Density Estimation Evolutionary Algorithms Within The IDEA Framework
, 2000
"... 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 probabili ..."
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Cited by 47 (4 self)
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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.
Optimization in continuous domains by learning and simulation of Gaussian networks
"... This paper shows how the Gaussian network paradigm can be used to solve optimization problems in continuous domains. Some methods of structure learning from data and simulation of Gaussian networks are applied in the Estimation of Distribution Algorithm (EDA) as well as new methods based on in ..."
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Cited by 37 (4 self)
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This paper shows how the Gaussian network paradigm can be used to solve optimization problems in continuous domains. Some methods of structure learning from data and simulation of Gaussian networks are applied in the Estimation of Distribution Algorithm (EDA) as well as new methods based on information theory are proposed. Experimental results are also presented. 1 Estimation of Distribution Algorithms approaches in continuous domains Figure 1 shows a schematic of the EDA approach for continuous domains. We will use x = (x 1 ; : : : ; xn ) to denote individuals, and D l to denote the population of N individuals in the lth generation. Similarly, D Se l will represent the population of the selected Se individuals from D l . In the EDA [9] our interest will be to estimate f(x j D Se ), that is, the joint probability density function over one individual x being among the selected individuals. We denote as f l (x) = f l (x j D Se l 1 ) the joint density of the lth genera...
Expanding From Discrete To Continuous Estimation Of Distribution Algorithms: The IDEA
 In Parallel Problem Solving From Nature  PPSN VI
, 2000
"... . The direct application of statistics to stochastic optimization based on iterated density estimation has become more important and present in evolutionary computation over the last few years. The estimation of densities over selected samples and the sampling from the resulting distributions, i ..."
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Cited by 33 (8 self)
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. The direct application of statistics to stochastic optimization based on iterated density estimation has become more important and present in evolutionary computation over the last few years. The estimation of densities over selected samples and the sampling from the resulting distributions, is a combination of the recombination and mutation steps used in evolutionary algorithms. We introduce the framework named IDEA to formalize this notion. By combining continuous probability theory with techniques from existing algorithms, this framework allows us to dene new continuous evolutionary optimization algorithms. 1 Introduction Algorithms in evolutionary optimization guide their search through statistics based on a vector of samples, often called a population. By using this stochastic information, non{deterministic induction is performed in order to attempt to use the structure of the search space and thereby aid the search for the optimal solution. In order to perform induct...
Realvalued Evolutionary Optimization using a Flexible Probability Density Estimator
 Proceedings of the GECCO 1999 Genetic and Evolutionary Computation Conference
, 1999
"... PopulationBased Incremental Learning (PBIL) is an abstraction of a genetic algorithm, which solves optimization problems by explicitly constructing a probabilistic model of the promising regions of the search space. At each iteration the model is used to generate a population of candidate sol ..."
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Cited by 29 (1 self)
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PopulationBased Incremental Learning (PBIL) is an abstraction of a genetic algorithm, which solves optimization problems by explicitly constructing a probabilistic model of the promising regions of the search space. At each iteration the model is used to generate a population of candidate solutions and is itself modified in response to these solutions. Through the extension of PBIL to Realvalued search spaces, a more powerful and general algorithmic framework arises which enables the use of arbitrary probability density estimation techniques in evolutionary optimization. To illustrate the usefulness of the framework, we propose and implement an evolutionary algorithm which uses a finite Adaptive Gaussian mixture model density estimator. This method offers considerable power and flexibility in the forms of the density which can be effectively modeled. We discuss the general applicability of the framework, and suggest that future work should lead to the developmen...
Parallel estimation of distribution algorithms
, 2002
"... The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion ..."
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Cited by 25 (4 self)
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The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion of a new formal description of EDA algorithm. This high level concept can be used to compare the generality of various probabilistic models by comparing the properties of underlying mappings. Also, some convergence issues are discussed and theoretical ways for further improvements are proposed. 2. Development of new probabilistic model and methods capable of dealing with continuous parameters. The resulting Mixed Bayesian Optimization Algorithm (MBOA) uses a set of decision trees to express the probability model. Its main advantage against the mostly used IDEA and EGNA approach is its backward compatibility with discrete domains, so it is uniquely capable of learning linkage between mixed continuousdiscrete genes. MBOA handles the discretization of continuous parameters as an integral part of the learning process, which outperforms the histogrambased
An Algorithmic Framework For Density Estimation Based Evolutionary Algorithms
, 1999
"... The direct application of statistics to stochastic optimization in evolutionary computation has become more important and present over the last few years. With the introduction of the notion of the Estimation of Distribution Algorithm (EDA), a new line of research has been named. The application are ..."
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Cited by 24 (5 self)
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The direct application of statistics to stochastic optimization in evolutionary computation has become more important and present over the last few years. With the introduction of the notion of the Estimation of Distribution Algorithm (EDA), a new line of research has been named. The application area so far has mostly been the same as for the classic genetic algorithms, being the binary vector encoded problems. The most important aspect in the new algorithms is the part where probability densities are estimated. In probability theory, a distinction is made between discrete and continuous distributions and methods. Using the rationale for density estimation based evolutionary algorithms, we present an algorithmic framework for them, named IDEA. This allows us to define such algorithms for vectors of both continuous and discrete random variables, combining techniques from existing EDAs as well as density estimation theory. The emphasis is on techniques for vectors of continuous random variables, for which we present new algorithms in the field of density estimation based evolutionary algorithms, using two different density estimation models.
Analyzing the PBIL Algorithm by Means of Discrete Dynamical Systems
 Complex Systems
"... this paper the convergence behavior of the Population Based Incremental Learning algorithm (PBIL) is analyzed using discrete dynamical systems. A discrete dynamical system is associated with the PBIL algorithm. We demonstrate that the behavior of the PBIL algorithm follows the iterates of the discre ..."
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Cited by 18 (3 self)
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this paper the convergence behavior of the Population Based Incremental Learning algorithm (PBIL) is analyzed using discrete dynamical systems. A discrete dynamical system is associated with the PBIL algorithm. We demonstrate that the behavior of the PBIL algorithm follows the iterates of the discrete dynamical system for a long time when the parameter # is near zero. We show that all the points of the search space are fixed points of the dynamical system, and that the local optimum points for the function to optimize coincide with the stable fixed points. Hence it can be deduced that the PBIL algorithm converges to the global optimum in unimodal functions. 1. Introduction