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Analyzing probabilistic models in hierarchical boa on traps and spin glasses
 Genetic and Evolutionary Computation Conference (GECCO2007), I
, 2007
"... The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common t ..."
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Cited by 25 (17 self)
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The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common test problems: concatenated traps and 2D Ising spin glasses with periodic boundary conditions. We argue that although Bayesian networks with local structures can encode complex probability distributions, analyzing these models in hBOA is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying problem, the models do not change significantly in subsequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem. Categories and Subject Descriptors
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 20 (11 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.
An introduction and survey of estimation of distribution algorithms
 SWARM AND EVOLUTIONARY COMPUTATION
, 2011
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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 17 (9 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.
Influence of selection and replacement strategies on linkage learning in BOA
 In Proceedings of 2007 IEEE Congress on Evolutionary Computation (CEC 2007
, 2007
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Model Accuracy in the Bayesian Optimization Algorithm
, 2010
"... Evolutionary algorithms (EAs) are particularly suited to solve problems for which there is not much information available. From this standpoint, estimation of distribution algorithms (EDAs), which guide the search by using probabilistic models of the population, have brought a new view to evolutiona ..."
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Cited by 7 (4 self)
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Evolutionary algorithms (EAs) are particularly suited to solve problems for which there is not much information available. From this standpoint, estimation of distribution algorithms (EDAs), which guide the search by using probabilistic models of the population, have brought a new view to evolutionary computation. While solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. However, as the complexity of the used models increases, the chance of overfitting and consequently reducing model interpretability, increases as well. This paper investigates the relationship between the probabilistic models learned by the Bayesian optimization algorithm (BOA) and the underlying problem structure. The purpose of the paper is threefold. First, model building in BOA is analyzed to understand how the problem structure is learned. Second, it is shown how the selection operator can lead to model overfitting in Bayesian EDAs. Third, the scoring metric that guides the search for an adequate model structure is modified to take into account the nonuniform distribution of the mating pool generated by tournament selection. Overall, this paper makes a contribution towards
Spurious Dependencies and EDA Scalability
, 2010
"... Numerous studies have shown that advanced estimation of distribution algorithms (EDAs) often discover spurious (unnecessary) dependencies. Nonetheless, only little prior work exists that would study the effects of spurious dependencies on EDA performance. This paper examines the effects of spurious ..."
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Cited by 5 (2 self)
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Numerous studies have shown that advanced estimation of distribution algorithms (EDAs) often discover spurious (unnecessary) dependencies. Nonetheless, only little prior work exists that would study the effects of spurious dependencies on EDA performance. This paper examines the effects of spurious dependencies on the performance and scalability of EDAs with the main focus on EDAs with marginal product models and the onemax problem. A theoretical model is proposed to analyze the effects of spurious dependencies on the population sizing in EDAs and the theory is verified with experiments. The effects of spurious dependencies on the number of generations are studied empirically.
Let’s Get Ready to Rumble Redux: Crossover Versus Mutation Head to Head on Exponentially Scaled Problems
"... This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems with substructures of nonuniform salience. This study assumes that the recombination and mutation operators have the knowledge of the building blocks ( ..."
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Cited by 4 (1 self)
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This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems with substructures of nonuniform salience. This study assumes that the recombination and mutation operators have the knowledge of the building blocks (BBs) and effectively exchange or search among competing BBs. Facetwise models of convergence time and population sizing have been used to determine the scalability of each algorithm. The analysis shows that for deterministic exponentiallyscaled additively separable, problems, the BBwise mutation is more efficient than crossover yielding a speedup of o(ℓ log ℓ), where ℓ is the problem size. For the noisy exponentiallyscaled problems, the outcome depends on whether scaling on noise is dominant. When scaling dominates, mutation is more efficient than crossover yielding a speedup of o(ℓ log ℓ). On the other hand, when noise dominates, crossover is more efficient than mutation yielding a speedup of o(ℓ).
Effects of a Deterministic Hill climber on hBOA
, 2009
"... Hybridization of global and local search algorithms is a wellestablished technique for enhancing the efficiency of search algorithms. Hybridizing estimation of distribution algorithms (EDAs) has been repeatedly shown to produce better performance than either the global or local search algorithm alo ..."
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Cited by 2 (1 self)
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Hybridization of global and local search algorithms is a wellestablished technique for enhancing the efficiency of search algorithms. Hybridizing estimation of distribution algorithms (EDAs) has been repeatedly shown to produce better performance than either the global or local search algorithm alone. The hierarchical Bayesian optimization algorithm (hBOA) is an advanced EDA which has previously been shown to benefit from hybridization with a local searcher. This paper examines the effects of combining hBOA with a deterministic hill climber (DHC). Experiments reveal that allowing DHC to find the local optima makes model building and decision making much easier for hBOA. This reduces the minimum population size required to find the global optimum, which substantially improves overall performance.