### Citations

8753 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
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Citation Context ... of xi The set pa i comprises the variables on which xi depends. This factorization is only possible because, for each i, xi is assumed to be independent of its nondescendants, given its parents pa i =-=[20]-=-. Figure 2 illustrates two possible factorization assumptions and figure 1 illustrates a Bayesian network learned at some stage of an evolutionary process for the concatenated trap-4 problem [11] with... |

1097 |
Adaptation in natural and artificial systems. Ann Arbor
- Holland
- 1975
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Citation Context ...g solutions and creation of new solutions in order to obtain a new population. Combination of genetic information is a major concern in evolutionary computation. In the simple genetic algorithm (sGA) =-=[1]-=- this mechanism is implemented as the crossover operator, which creates a new individual from two parents by combining portions of both strings. Recently, estimation of distribution algorithms (EDAs) ... |

667 |
Perceptrons: An introduction to computational geometry, expanded edition
- Minsky, Papert
- 1988
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Citation Context ...ables is an irreducible whole; a dependency which cannot be broken [14]. A classic example from machine learning literature related to the importance of interaction among variables is the XOR problem =-=[15]-=- which is not linearly separable and cannot be solved without capturing interactions. In genetic and evolutionary computation, the identification and preservation of important interactions among genes... |

378 |
Approximate is better than ‘exact’ for interval estimation of binomial proportions
- Agresti, Coull
- 1998
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Citation Context ...which changes slightly the binomial proportions estimated and, therefore, allows for an allele to be generated even if all individual possess the complementary allele. The Wilson estimator revised in =-=[24]-=- incorporates a degree of uncertainty by estimating the binomial proportion as ˆπi,j = ni ∑ c(x)=i xj + 2 ni + 4 (7) (8) 11Table 1: ϕ-PBIL parameters Parameter Description Default value N0 initial po... |

374 |
Messy genetic algorithms: Motivation, analysis, and first results
- Goldberg, Korb, et al.
- 1989
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Citation Context ...ently other approaches adopted alternative schemes ranging from the simple reordering of the genes to more complex mechanisms like subspecification and superspecification of solutions, as in Messy GA =-=[18]-=-. This algorithm adopts a two-stage evolutionary process where substructures are identified in a first stage and subsequently combined. This ensures that substructures were all correctly identified be... |

322 | BOA: The Bayesian Optimization Algorithm
- Pelikan, Goldberg, et al.
- 1999
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Citation Context ...pc, pold and pw all to 50%. 7 Some benchmark optimization problems This section discusses and revises the benchmark problems used in the empirical evaluation Section. The reader is referred to [3][12]=-=[11]-=-[13] for a more detailed description of the problems. A representative set of benchmark problems was chosen, which are known to be hard for a GA and most EDAs to solve. The existence of building block... |

296 |
Some methods for classification and analysis of multivariate observations
- McQueen
- 1967
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Citation Context ...articular [7]. It improves the identification of the problem structure as much as enhances the chances of finding a higher number of global optima on multimodal problems. K-means clustering algorithm =-=[8]-=- has recently been applied as a niching technique based on grouping genotypically similar solutions together. The performance of simpler low-order EDAs, however, was not show to be much improved by cl... |

278 | A parameter-less genetic algorithm," in
- Harik, Lobo
- 1999
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Citation Context ... models which assume independence among genes. This class of EDA is known for its simplicity and computational efficiency in model learning, since no search for model structures needs to be performed =-=[2]-=-. Further, the simple conception and implementation should make those algorithms very attractive. Their low effectiveness on harder benchmark problems, however, is unacceptable. This is a major drawba... |

208 | Removing the genetics from the standard genetic algorithm (Tech Rep
- Baluja, Caruana
- 1995
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Citation Context ...ons are considered and only order 1 statistics are used, those algorithms should be called order 1 EDAs. One of the most important member of this class is PBIL (Population Based Incremental Learning) =-=[19]-=-. In PBIL the population is represented by a probability vector p = (p1, vp, . . .,pm), as in (1), where pj represents the probability of an individual to possess a 1 in gene j. At each generation, M ... |

75 | Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms
- Harik
- 1997
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Citation Context ...inkage learning and this topic gained increasing attention from the community. Most linkage learning techniques aim at the identification of substructures which should be conserved during combination =-=[16]-=-. A similar concept in genomics, called genetic linkage, is defined as the association of genes on the same chromosome. When two genes are independent, the Mendelian law of independent assortment stat... |

66 |
Global Optimization Using Bayesian Networks
- Etxeberria, Larrañaga
- 1999
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Citation Context ...ions are considered. Two very representative higher-order EDAs which adopt Bayesian Networks are the Bayesian Optimization Algorithm (BOA) [11] and the Estimation of Bayesian Network Algorithm (EBNA) =-=[21]-=-. The difference among them is on the metric used to evaluate factorizations when searching for the model structure. 3 Related work It was already shown that clustering improves the performance of som... |

51 | Modeling building-block interdependency
- Watson, Hornby, et al.
- 1998
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Citation Context ...al optima of any benchmark problem tested. The problems adopted here illustrate several aspects which have been recently considered as tricky for EDAs, such as deception [11], symmetry [9], hierarchy =-=[12]-=-, global multimodality [3] and the presence of overlapping building blocks [13]. The structured fashion of those and other classes of problems makes them hard for low-order and even for high-order EDA... |

44 |
Statistical genomics: Linkage, mapping, and QTL analysis
- Liu
- 1998
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Citation Context ...ion of genes on the same chromosome. When two genes are independent, the Mendelian law of independent assortment states that the segregation of one gene is independent of the segregation of the other =-=[17]-=-. Simple genetic algorithm (sGA) with one-point crossover relies on the ordering of the genes in the codification of the problem. In order to achieve success it is required that interacting variables ... |

30 |
Niching Methods for Genetic Algorithms", Doctoral Dissertation
- Mahfoud
- 1995
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Citation Context ...s to make EDAs more effective is to adopt clustering as a strong niching approach, inducing the preservation of diversity in the population. Niching is crutial for evolutionary computation in general =-=[6]-=- and for EDAs in particular [7]. It improves the identification of the problem structure as much as enhances the chances of finding a higher number of global optima on multimodal problems. K-means clu... |

27 | Genetic Algorithms, Clustering, and the Breaking of Symmetry
- Pelikan, Goldberg
- 2000
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Citation Context ...owever, was not show to be much improved by clustering except for some simple unstructured multimodal problems. Low-order clustered EDAs have not been able to solve hard deceptive structured problems =-=[9]-=-. The main contribution of this paper is to show that a simple low-order EDA aided by clustering the population and guided by information measures is able to perform linkage learning and, therefore, s... |

26 | Testing the significance of attribute interactions
- Jakulin, Bratko
- 2004
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Citation Context ...ning and Estimation of Distribution Algorithms Interacting variables are more informative together than alone. Interaction among variables is an irreducible whole; a dependency which cannot be broken =-=[14]-=-. A classic example from machine learning literature related to the importance of interaction among variables is the XOR problem [15] which is not linearly separable and cannot be solved without captu... |

23 | Advancing continuous ideas with mixture distributions and factorization selection metrics
- Bosman, Thierens
- 2001
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Citation Context ...ntributions. Another motivation for clustering is (iii) to allow the identification of a mixture of distributions in continuous optimization. This last motivation is often described in the literature =-=[23]-=-[7], but it is not directly related to the work herein presented. The relevance of the motivation (i) is clear since diversity maintenance prevents premature convergence to local optima and allows for... |

19 | On the importance of diversity maintenance in estimation of distribution algorithms
- Yuan, Gallagher
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Citation Context ... associated to the model induction stage is imposed in this class of EDAs. Finding a factorization can be a computationally expensive process and the resulting graph is often a suboptimal solution [4]=-=[5]-=-. One of the most important efforts to make EDAs more effective is to adopt clustering as a strong niching approach, inducing the preservation of diversity in the population. Niching is crutial for ev... |

8 | Globally multimodal problem optimization via an estimation of distribution algorithm based on unsupervised learning of bayesian networks
- Peña, Lozano, et al.
- 2005
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Citation Context ...eir low effectiveness on harder benchmark problems, however, is unacceptable. This is a major drawback, since genetic and evolutionary algorithms are known for their wide applicability and robustness =-=[3]-=-. High order EDAs, by the other side, are based on learning the linkage among genes by inferring expressive probabilistic models based on searching for a factorization, which captures the dependencies... |

6 | Sporadic model building for efficiency enhancement of hBOA
- Pelikan, Sastry, et al.
- 2006
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Citation Context ...ructures. It was already recognized that learning the structure of a Bayesian network at each generation may become a bottleneck for EDAs and some attempts to overcome this problem have been proposed =-=[4]-=-. By the other side, incorporating even more elements into the model, as in [3] where clustering labels are used, seems to be worthy and should be considered, whereas this approach results models at i... |

4 |
R.S.: Multiple-deme parallel estimation of distribution algorithms: Basic framework and application
- Ahn, Goldberg, et al.
- 2003
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Citation Context ... used for an efficient scale-up behavior on low-order EDAs on difficult problems. A similar approach to clustering is the parallelization of EDAs by adopting multiple subpopulations and migration. In =-=[22]-=-, a simple recombination operator called PV-wise uniform crossover is proposed, which is similar to GA uniform crossover. After two parent PVs were selected for combination a new temporary PV is built... |

2 |
Clustering-based probabilistic model fitting in estimation of distribution algorithms
- Ahn, Ramakrishna
(Show Context)
Citation Context ...s to adopt clustering as a strong niching approach, inducing the preservation of diversity in the population. Niching is crutial for evolutionary computation in general [6] and for EDAs in particular =-=[7]-=-. It improves the identification of the problem structure as much as enhances the chances of finding a higher number of global optima on multimodal problems. K-means clustering algorithm [8] has recen... |

2 | Linkage learning, overlapping building blocks, and systematic strategy for recombination - Goldberg, Johnson - 2005 |