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23
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
Designing competent mutation operators via probabilistic model building of neighborhoods
 In Deb, K., & et al. (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2004), Part II, LNCS 3103
, 2004
"... This paper presents a competent selectomutative genetic algorithm (GA), that adapts linkage and solves hard problems quickly, reliably, and accurately. A probabilistic model building process is used to automatically identify key building blocks (BBs) of the search problem. The mutation operator uses ..."
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Cited by 32 (20 self)
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This paper presents a competent selectomutative genetic algorithm (GA), that adapts linkage and solves hard problems quickly, reliably, and accurately. A probabilistic model building process is used to automatically identify key building blocks (BBs) of the search problem. The mutation operator uses the probabilistic model of linkage groups to find the best among competing building blocks. The competent selectomutative GA successfully solves additively separable problems of bounded difficulty, requiring only subquadratic number of function evaluations. The results show that for additively separable problems the probabilistic model building BBwise mutation scales as O(2 k m 1.5), and requires O ( √ k log m) less function evaluations than its selectorecombinative counterpart, confirming theoretical results reported elsewhere (Sastry & Goldberg, 2004). 1
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.
The hierarchical fair competition (hfc) framework for sustainable evolutionary algorithms
 Evolutionary Computation
"... Many current Evolutionary Algorithms (EAs) suffer from a tendency to converge prematurely or stagnate without progress for complex problems. This may be due to the loss of or failure to discover certain valuable genetic material or the loss of the capability to discover new genetic material before c ..."
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Cited by 19 (5 self)
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Many current Evolutionary Algorithms (EAs) suffer from a tendency to converge prematurely or stagnate without progress for complex problems. This may be due to the loss of or failure to discover certain valuable genetic material or the loss of the capability to discover new genetic material before convergence has limited the algorithm’s ability to search widely. In this paper, the Hierarchical Fair Competition (HFC) model, including several variants, is proposed as a generic framework for sustainable evolutionary search by transforming the convergent nature of the current EA framework into a nonconvergent search process. That is, the structure of HFC does not allow the convergence of the population to the vicinity of any set of optimal or locally optimal solutions. The sustainable search capability of HFC is achieved by ensuring a continuous supply and the incorporation of genetic material in a hierarchical manner, and by culturing and maintaining, but continually renewing, populations of individuals of intermediate fitness levels. HFC employs an assemblyline structure in which subpopulations are hierarchically organized into different fitness levels, reducing the selection
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.
Efficiency enhancement of probabilistic model building algorithms
 In Proceedings of the Optimization by Building and Using Probabilistic Models Workshop at the Genetic and Evolutionary Computation Conference
, 2004
"... Abstract. This paper presents two different efficiencyenhancement techniques for probabilistic model building genetic algorithms. The first technique proposes the use of a mutation operator which performs local search in the subsolution neighborhood identified through the probabilistic model. The ..."
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Cited by 9 (6 self)
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Abstract. This paper presents two different efficiencyenhancement techniques for probabilistic model building genetic algorithms. The first technique proposes the use of a mutation operator which performs local search in the subsolution neighborhood identified through the probabilistic model. The second technique proposes building and using an internal probabilistic model of the fitness along with the probabilistic model of variable interactions. The fitness values of some offspring are estimated using the probabilistic model, thereby avoiding computationally expensive function evaluations. The scalability of the aforementioned techniques are analyzed using facetwise models for convergence time and population sizing. The speedup obtained by each of the methods is predicted and verified with empirical results. The results show that for additively separable problems the competent mutation operator requires O ( √ k log m)—where k is the buildingblock size, and m is the number of building blocks—less function evaluations than its selectorecombinative counterpart. The results also show that the use of an internal probabilistic fitness model reduces the required number of function evaluations to as low as 110 % and yields a speedup of 2–50. 1