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62
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.
Escaping Hierarchical Traps with Competent Genetic Algorithms
 Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2001
, 2001
"... To solve hierarchical problems, one must be able to learn the linkage, represent partial solutions efficiently, and assure effective niching. We propose the hierarchical ... ..."
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Cited by 91 (49 self)
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To solve hierarchical problems, one must be able to learn the linkage, represent partial solutions efficiently, and assure effective niching. We propose the hierarchical ...
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
Bayesian Optimization Algorithm, Decision Graphs, and Occam's Razor
 Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2001), 519–526. Also IlliGAL
, 2001
"... This paper discusses the use of various scoring metrics in the Bayesian optimization algorithm (BOA) which uses Bayesian networks to model promising solutions and generate the new ones. The use of decision graphs in Bayesian networks to improve the performance of the BOA is proposed. To favor simple ..."
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Cited by 39 (22 self)
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This paper discusses the use of various scoring metrics in the Bayesian optimization algorithm (BOA) which uses Bayesian networks to model promising solutions and generate the new ones. The use of decision graphs in Bayesian networks to improve the performance of the BOA is proposed. To favor simple models, a complexity measure is incorporated into the BayesianDirichlet metric for Bayesian networks with decision graphs. The presented modi cations are compared on a number of interesting problems.
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
Evolutionary Optimization and the Estimation of Search Distributions with Applications to Graph Bipartitioning
 Journal of Approximate Reasoning
, 2002
"... We present a theory of population based optimization methods using approximations of search distributions. We prove convergence of the search distribution to the global optima for the Factorized Distribution Algorithm FDA if the search distribution is a Boltzmann distribution and the size of the pop ..."
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Cited by 18 (4 self)
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We present a theory of population based optimization methods using approximations of search distributions. We prove convergence of the search distribution to the global optima for the Factorized Distribution Algorithm FDA if the search distribution is a Boltzmann distribution and the size of the population is large enough. Convergence is defined in a strong sense  the global optima are attractors of a dynamical system describing mathematically the algorithm. We investigate an adaptive annealing schedule and show its similarity to truncation selection. The inverse temperature beta is changed inversely proportionally to the standard deviation of the population. We extend FDA by using a Bayesian hyper parameter. The hyper parameter is related to mutation in evolutionary algorithms. We derive an upper bound on the hyper parameter to ensure that FDA still generates the optima with high probability. We discuss the relation of the FDA approach to methods used in statistical physics to approximate a Boltzmann distribution and to belief propagation in probabilistic reasoning. In the last part, we apply the algorithm to an important practical problem, the bipartioning of large graphs. We assume that the graphs are sparsely connected. Our empirical results are as good or even better than any other method used for this problem.
Substructural Neighborhoods for Local Search in the Bayesian Optimization Algorithm
, 2006
"... This paper studies the utility of using substructural neighborhoods for local search in the Bayesian optimization algorithm (BOA). The probabilistic model of BOA, which automatically identifies important problem substructures, is used to define the structure of the neighborhoods used in local search ..."
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Cited by 17 (14 self)
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This paper studies the utility of using substructural neighborhoods for local search in the Bayesian optimization algorithm (BOA). The probabilistic model of BOA, which automatically identifies important problem substructures, is used to define the structure of the neighborhoods used in local search. Additionally, a surrogate fitness model is considered to evaluate the improvement of the local search steps. The results show that performing substructural local search in BOA significatively reduces the number of generations necessary to converge to optimal solutions and thus provides substantial speedups.
On Stability of Fixed Points of Limit Models of Univariate Marginal Distribution Algorithm and Factorized Distribution Algorithm
 IEEE Trans. on Evolutionary Computation, Accepted
, 2003
"... Abstract—This paper aims to study the advantages of using higher order statistics in estimation distribution of algorithms (EDAs). We study two EDAs with twotournament selection for discrete optimization problems. One is the univariate marginal distribution algorithm (UMDA) using only firstorder s ..."
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Cited by 16 (6 self)
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Abstract—This paper aims to study the advantages of using higher order statistics in estimation distribution of algorithms (EDAs). We study two EDAs with twotournament selection for discrete optimization problems. One is the univariate marginal distribution algorithm (UMDA) using only firstorder statistics and the other is the factorized distribution algorithm (FDA) using higher order statistics. We introduce the heuristic functions and the limit models of these two algorithms and analyze stability of these limit models. It is shown that the limit model of UMDA can be trapped at any local optimal solution for some initial probability models. However, degenerate probability density functions (pdfs) at some local optimal solutions are unstable in the limit model of FDA. In particular, the degenerate pdf at the global optimal solution is the unique asymptotically stable point in the limit model of FDA for the optimization of an additively decomposable function. Our results suggest that using higher order statistics could improve the chance of finding the global optimal solution. Index Terms—Estimation of distribution algorithms (EDAs), factorized distribution algorithm (FDA), heuristic function, stability, univariate marginal distribution algorithm (UMDA). I.
Sporadic model building for efficiency enhancement of hierarchical BOA
, 2007
"... Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and ..."
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Cited by 14 (8 self)
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Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant modelbuilding speedup, which decreases the asymptotic time complexity of model building in hBOA by a factor of Θ(n 0.26) to Θ(n 0.5), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, if model building is the bottleneck, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structurebuilding period, which is the only parameter of the proposed sporadic modelbuilding approach. The paper then tests the proposed method and the rule for setting the structurebuilding period on the problem of finding ground states of 2D and 3D Ising spin glasses.
Using previous models to bias structural learning in the hierarchical BOA
, 2008
"... Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at l ..."
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Cited by 13 (9 self)
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Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problemspecific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problemspecific information has been practically ignored by the EDA community. This paper takes the first step towards the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.