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19
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 101 (19 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
Evaluationrelaxation schemes for genetic and evolutionary algorithms
, 2002
"... Genetic and evolutionary algorithms have been increasingly applied to solve complex, large scale search problems with mixed success. Competent genetic algorithms have been proposed to solve hard problems quickly, reliably and accurately. They have rendered problems that were difficult to solve by th ..."
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Cited by 68 (27 self)
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Genetic and evolutionary algorithms have been increasingly applied to solve complex, large scale search problems with mixed success. Competent genetic algorithms have been proposed to solve hard problems quickly, reliably and accurately. They have rendered problems that were difficult to solve by the earlier GAs to be solvable, requiring only a subquadratic number of function evaluations. To facilitate solving largescale complex problems, and to further enhance the performance of competent GAs, various efficiencyenhancement techniques have been developed. This study investigates one such class of efficiencyenhancement technique called evaluation relaxation. Evaluationrelaxation schemes replace a highcost, lowerror fitness function with a lowcost, higherror fitness function. The error in fitness functions comes in two flavors: Bias and variance. The presence of bias and variance in fitness functions is considered in isolation and strategies for increasing efficiency in both cases are developed. Specifically, approaches for choosing between two fitness functions with either differing variance or differing bias values have been developed. This thesis also investigates fitness inheritance as an evaluation
Let’s get ready to rumble: Crossover versus mutation head to head
 In GECCO ’04: Proc. of the Genetic and Evolutionary Computation Conference
, 2004
"... This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems. This study assumes that the recombination and mutation operators have the knowledge of the building blocks (BBs) and effectively exchange or search amo ..."
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Cited by 28 (20 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. 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 additively separable deterministic problems, the BBwise mutation is more efficient than crossover, while the crossover outperforms the mutation on additively separable problems perturbed with additive Gaussian noise. The results show that the speedup of using BBwise mutation on deterministic problems is O ( √ k log m), where k is the BB size, and m is the number of BBs. Likewise, the speedup of using crossover on stochastic problems with fixed noise variance is O(m √ k / logm). 1
Genetic Algorithms
, 2005
"... Genetic algorithms (GAs) are search methods based on principles of natural selection and genetics (Fraser, 1957; Bremermann, 1958; Holland, 1975). We start with a brief introduction to simple genetic algorithms and associated terminology. GAs encode ..."
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Cited by 21 (3 self)
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Genetic algorithms (GAs) are search methods based on principles of natural selection and genetics (Fraser, 1957; Bremermann, 1958; Holland, 1975). We start with a brief introduction to simple genetic algorithms and associated terminology. GAs encode
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.
A Matrix Approach for Finding Extrema: PROBLEMS WITH MODULARITY, HIERARCHY, AND OVERLAP
, 2006
"... Unlike most simple textbook examples, the real world is full with complex systems, and researchers in many different fields are often confronted by problems arising from such systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve lar ..."
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Cited by 9 (0 self)
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Unlike most simple textbook examples, the real world is full with complex systems, and researchers in many different fields are often confronted by problems arising from such systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve large and difficult problems, proper decomposition according to the complex system is the key. In this research project, investigating and analyzing interactions between components of complex systems shed some light on problem decomposition. By recognizing three barebone types of interactions—modularity, hierarchy, and overlap, theories and models are developed to dissect and inspect problem decomposition in the context of genetic algorithms. This dissertation presents a research project to develop a competent optimization method to solve boundedly difficult problems with modularity, hierarchy, and overlap by explicit problem decomposition. The proposed genetic algorithm design utilizes a matrix representation of an interaction graph to analyze and decompose the problem. The results from this thesis should benefit research both technically and scientifically. Technically, this thesis develops an automated dependency structure matrix clustering technique and utilizes it to design a competent blackbox problem solver. Scientifically, the explicit interaction
Sporadic model building for efficiency enhancement of hBOA
 Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2006
, 2006
"... 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). With sporadic model building, the structure of the probabilistic model is updated ..."
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Cited by 6 (3 self)
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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). With sporadic model building, the structure of the probabilistic model is updated once 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 that decreases the asymptotic time complexity of model building in hBOA by a factor of Θ(n 0.26) to Θ(n 0.65), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, for decomposable problems, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building.
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).