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## An introduction and survey of estimation of distribution algorithms (2011)

Venue: | SWARM AND EVOLUTIONARY COMPUTATION |

Citations: | 18 - 7 self |

### Citations

3755 | Particle swarm optimization
- Kennedy, Eberhart
- 1995
(Show Context)
Citation Context ... distributions centered around a population of high-quality solutions found so far. Similarly, many ant colony optimization (ACO) methods (Dorigo, 1992) and particle swarm optimization methods (PSO) (=-=Kennedy & Eberhart, 1995-=-) use models that explicitly define a probability distribution over candidate solutions. From this perspective, many evolutionary algorithms may be viewed as ”true” EDAs. Developed independently of ED... |

3725 |
Genetic Programming - On the programming of computers by means of natural selection
- Koza
- 1998
(Show Context)
Citation Context ...ter numerous successes in the design of EDAs for discrete and real-valued representations, a numberof researchers have attempted to replicate these successes in thedomain of genetic programming (GP) (=-=Koza, 1992-=-). In GP the task is to evolve a population of computer programs represented by labeled trees. In this domain, some additional challenges become evident. To start with, the length of candidate program... |

2240 |
Clustering Algorithms
- Hartigan
- 1975
(Show Context)
Citation Context ...ctive optimization. Aspecialselection operatorwasusedtoensurepreservationofdiversity alongthePareto front, guided by a single parameter δ. The population is then clustered using the leader algorithm (=-=Hartigan, 1975-=-), with the leader algorithm selected due its speed and the lack of any requirement to specify the number of clusters beforehand. A univariate model is built for each cluster and sampled to generate n... |

1909 | Multi-Objective Optimization Using Evolutionary Algorithms - Deb - 2001 |

1810 | A fast and elitist multiobjective genetic algorithm: Nsga-ii
- Deb, Pratap, et al.
- 2002
(Show Context)
Citation Context ...II on several interleaved deceptive problems. The multi-objective hierarchical BOA (mohBOA) (Pelikan, Sastry, & Goldberg, 2005) extended hBOA to the multi-objective domain by combining hBOA, NSGA-II (=-=Deb, Pratap, Agarwal, & Meyarivan, 2002-=-) and clustering. mohBOA uses the non-dominated crowding of NSGA-II to rank candidate solutions and assign crowding distances. This information is then used to select promising solutions using the sam... |

1289 |
An Introduction to Copulas
- Nelsen
- 1999
(Show Context)
Citation Context ...howntooutperformmIDEA onseveral real-valued deceptive problems. Recently a new approach to developing EDAs to solve real-valued optimization problem has been developed that is based on copula theory (=-=Nelsen, 1998-=-). Copulas are a way to describe the dependence between random variables, and according to copula theory a joint probability distribution can be decomposed into n marginal probability distributions an... |

1154 | Learning Bayesian networks: The combination of knowledge and statistical data
- Heckerman, Geiger, et al.
- 1995
(Show Context)
Citation Context ...metric has a tendency to favor overly complex models, usually an upper bound on the number of allowable parents is set or a prior bias on the network structure is introduced to prefer simpler models (=-=Heckerman, Geiger, & Chickering, 1994-=-). New candidate solutions are generated by sampling the probability distribution encoded by the built network using probabilistic logic sampling (Henrion, 1988). Theestimation of Bayesian network alg... |

876 | Approximating discrete probability distributions with dependence trees
- Chow, Liu
- 1968
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Citation Context ...is the tree that maximizes the mutual information between connected variables, which is the provably best tree model in terms of the Kullback-Leibler divergence with respect to the true distribution (=-=Chow & Liu, 1968-=-). The probability matrix is initialized so that it corresponds to the uniform distribution over all candidate solutions. In each iteration of the algorithm, a tree model is built and sampled to gener... |

439 | Multiobjective evolutionary algorithms: Classifications, analyses, and new innovations
- Veldhuizen
- 1999
(Show Context)
Citation Context ...ive by weighing the objectives in some way. However, it is often more desirable to find an optimal tradeoff between the objectives in the form of a diverse set of Pareto optimal solutions (Deb, 2001; =-=Coello & Lamont, 2004-=-). In short, a solution is Pareto optimal if it outperforms any other solution in at least one objective. In this section, we review several EDAs that aim to find diverse sets of Pareto optimal soluti... |

355 | Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning
- Baluja
- 1994
(Show Context)
Citation Context ...n, estimation of distribution algorithms, probabilistic models, model building, decomposable problems, evolutionary computation, problem solving 1 Introduction Estimation of distribution algorithmss (=-=Baluja, 1994-=-; Mühlenbein & Paaß, 1996a; Larrañaga & Lozano, 2002; Pelikan, Goldberg, & Lobo, 2002) arestochastic optimization techniques that explore the space of potential solutions by building and sampling expl... |

346 |
The design of innovation: Lessons from and for competent genetic algorithms
- Goldberg
- 2002
(Show Context)
Citation Context ...dimensional lattices (Pelikan & Hartmann, 2006), military antenna design (Yu, Santarelli, & Goldberg, 2006), multiobjective knapsack (Shah & Reed, 2010), groundwaterremediation design(Arst, Minsker, &=-=Goldberg, 2002-=-; Hayes &Minsker, 2005), aminoacid alphabet reduction for protein structure prediction (Bacardit, Stout, Hirst, Sastry, Llorà, & Krasnogor, 2007), identification of clusters of genes with similar expr... |

338 | A survey of optimization by building and using probabilistic models
- Pelikan, Goldberg, et al.
- 1999
(Show Context)
Citation Context ...del building, decomposable problems, evolutionary computation, problem solving 1 Introduction Estimation of distribution algorithmss (Baluja, 1994; Mühlenbein & Paaß, 1996a; Larrañaga & Lozano, 2002; =-=Pelikan, Goldberg, & Lobo, 2002-=-) arestochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. This model-based approach... |

329 | BOA: The Bayesian Optimization Algorithm. In
- Pelikan, Goldberg, et al.
- 1999
(Show Context)
Citation Context ...any given level may depend on interactions at a higher level, it is necessary that alternate solutions to each subproblem be stored over time. The hierarchical Bayesian Optimization Algorithm (hBOA) (=-=Pelikan, 2005-=-) is able to solve many difficult hierarchically decomposable problems by extending BOA in two key areas. In order to ensure that interactions of high order can be represented in a feasible manner, a ... |

313 |
Assignment problems and the location of economic activities
- Koopmans, Beckman
- 1957
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Citation Context ...s In many important real-world problems, candidate solutions are represented by permutations over a given set of elements. Two important classes of such problems are the quadratic assignment problem (=-=Koopmans & Beckmann, 1957-=-) and the traveling salesman problem. These types of problems often contain two specific types of features or constraints that EDAs need to capture. The first is the absolute position of a symbol in a... |

312 | From recombination of genes to estimation of distributions
- Mühlenbein, Paaß
- 1996
(Show Context)
Citation Context ...of distribution algorithms, probabilistic models, model building, decomposable problems, evolutionary computation, problem solving 1 Introduction Estimation of distribution algorithmss (Baluja, 1994; =-=Mühlenbein & Paaß, 1996-=-a; Larrañaga & Lozano, 2002; Pelikan, Goldberg, & Lobo, 2002) arestochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models... |

296 | Efficient and Accurate Parallel Genetic Algorithms
- Cantú-Paz
- 2000
(Show Context)
Citation Context ...ny problems contain highly overlapping subproblems that cannot be accurately modeled by dividing the problem into independent clusters. The Bayesian optimization algorithm (BOA) (Pelikan, Goldberg, & =-=Cantú-Paz, 2000-=-) uses Bayesian networks to model candidate solutions, which allow it to solve the large class of nearly decomposable problems, many of which cannot be decomposed into independent subproblems of bound... |

283 | A parameter-less genetic algorithm
- Harik, Lobo
- 1999
(Show Context)
Citation Context ...lity vector entry is also slightly varied each generation based on a mutation rate parameter. 8Figure 5: Examples of graphical models produced by different EDAs. The compact genetic algorithm (cGA) (=-=Harik, Lobo, & Goldberg, 1997-=-) is another incremental univariate EDA. Much like PBIL, cGA uses a probability vector to represent the entire population of solutions encoded by fixed-length binary strings. The main difference betwe... |

275 | Genetic algorithms, noise, and the sizing of populations
- Goldberg, Deb, et al.
- 1992
(Show Context)
Citation Context ...n infinite population is not possible. The population size in EDAs is closely related to the reliability and complexity of the search, similarly as for other population-based evolutionary algorithms (=-=Goldberg, Deb, & Clark, 1992-=-; Goldberg, Sastry, & Latoza, 2001; Harik, Cantú-Paz, Goldberg, & Miller, 1997). Using a population that is too small can lead to convergence to solutions of low quality and inability to reliably find... |

271 | Learning Bayesian networks with Local Structure
- Friedman, Goldszmidt
- 1996
(Show Context)
Citation Context ...der can be represented in a feasible manner, a more compact version of Bayesian networks is used. Specifically, hBOA uses Bayesian networks with local structures (Chickering, Heckerman, & Meek, 1997; =-=Friedman & Goldszmidt, 1999-=-) to allow feasible learning and sampling of more complex networks than would be possible with conventional Bayesian networks. In addition, the preservation of alternative solutions over time is ensur... |

232 | Linkage learning via probabilistic modeling in the ECGA,
- Harik
- 1999
(Show Context)
Citation Context ...rtition, we would expect the proportions of trap partitions with all 1s to increase over time. By merging the variables in each trap partition together, the extended compact genetic algorithm (ECGA) (=-=Harik, 1999-=-) explained further in section 3.1.3 does just that. Probabilistic models that combine groups of variables or bits into linkage groups and assume independence between the different linkage groups are ... |

211 |
Propagating Uncertainty in Bayesian Networks by Logic Sampling.
- Henrion
- 1988
(Show Context)
Citation Context ...simpler models (Heckerman, Geiger, & Chickering, 1994). New candidate solutions are generated by sampling the probability distribution encoded by the built network using probabilistic logic sampling (=-=Henrion, 1988-=-). Theestimation of Bayesian network algorithm (EBNA) (Etxeberria & Larrañaga, 1999) and the learning factorized distribution algorithm (LFDA) (Mühlenbein & Mahnig, 1999) also use Bayesian networks to... |

189 | A Bayesian approach to learning Bayesian networks with local structure
- Chickering, Heckerman, et al.
- 1997
(Show Context)
Citation Context ...o ensure that interactions of high order can be represented in a feasible manner, a more compact version of Bayesian networks is used. Specifically, hBOA uses Bayesian networks with local structures (=-=Chickering, Heckerman, & Meek, 1997-=-; Friedman & Goldszmidt, 1999) to allow feasible learning and sampling of more complex networks than would be possible with conventional Bayesian networks. In addition, the preservation of alternative... |

162 |
Analyzing deception in trap functions
- Deb, Goldberg
- 1993
(Show Context)
Citation Context ...lutions. However this situation is reversed for trap-5, for which the average fitness of solutions with a 0 in any position is greater than the average fitness of solutions with a 1 in that position (=-=Deb & Goldberg, 1991-=-), even though the optimum is still located in the string consisting of all 1s. This leads to the probability vector being strongly biased towards solutions with 0s in all positions. All is not lost, ... |

159 | Combining convergence and diversity in evolutionary multiobjective optimization
- Laumanns, Thiele, et al.
(Show Context)
Citation Context ... goal is to find a broad distribution of Pareto-optimal solutions. The Bayesian multi-objective optimization algorithm (BMOA) (Laumanns & Ocenasek, 2002) uses a special selection operator, ǫ-archive (=-=Laumanns, Thiele, Deb, & Zitzler, 2002-=-), to both ensure that Pareto-optimal solutions are maintained over time and that diversity is maintained so that an approximation of the entire Pareto set is preserved. The selection operator works b... |

154 | MIMIC: Finding Optima by Estimating Probability Densities. - Bonet, Isbell, et al. - 1996 |

154 |
Learning gaussian networks
- Geiger, Heckerman
- 1994
(Show Context)
Citation Context ...s arereal-valued andlocally each variablehasits meanandvariance computed by a linear function from its parents. The network structure is learned greedily using a continuous version of the BDe metric (=-=Geiger & Heckerman, 1994-=-), with a penalty term to prefer simpler models. In the IDEA framework, Bosman and Thierens (2000) proposed models capable of capturing multiple basins of attraction or clusters of points by storing t... |

149 |
Genetic algorithms and random keys for sequencing and optimization
- Bean
- 1994
(Show Context)
Citation Context ...and the absolute positions matter. It certainly is possible to use non-permutation based EDAs using specific encodings to solve permutation problems. For example, one may use the random key encoding (=-=Bean, 1994-=-) to solve permutation-based problems using EDAs for optimization of real-valued vectors (Bosman & Thierens, 2001b; Robles, de Miguel, & Larrañaga, 2002). Random key encoding represents a permutation ... |

131 | Using optimal dependency-trees for combinatorial optimization: Learning the structure of the search space. - Baluja, Davies - 1997 |

129 | Finding multimodal solutions using restricted tournament selection,”
- Harik
- 1995
(Show Context)
Citation Context ... possible with conventional Bayesian networks. In addition, the preservation of alternative solutions over time is ensured by using a niching technique called restricted tournament replacement (RTR) (=-=Harik, 1995-=-) which encourages competition among similar solutions rather than dissimilar ones. Combined together these changes allow hBOA to solve a broad class of nearly decomposable and hierarchical problems i... |

128 |
Genetic algorithms and the optimal allocation of trials.
- Holland
- 1973
(Show Context)
Citation Context ...ely related to EDAs. Evolutionary algorithms use operators of selection and variation to update a population of candidate solutions or a single candidate solution. For example, in genetic algorithms (=-=Holland, 1973-=-), binary tournament selection may be used to select promising solutions from the current population and the new population may be created by applying one-point crossover and bit-flip mutation to the ... |

114 | The Bivariate Marginal Distribution Algorithm. In
- Pelikan, Muhlenbein
- 1999
(Show Context)
Citation Context ...a tree model is built and sampled to generate several newcandidate solutions. Thebestof thesesolutions arethen usedtoupdatetheprobability matrix. The bivariate marginal distribution algorithm (BMDA) (=-=Pelikan & Mühlenbein, 1999-=-) uses a model based on a set of mutually independent trees (a forest). Each generation a dependency model is created by using Pearson’s chi-square statistics (Marascuilo & McSweeney, 1977) as the mai... |

112 | Adaptive global optimization with local search, Doctoral
- Hart
- 1994
(Show Context)
Citation Context ...ministic hill climber (DHC), which takes a candidate solution represented by a binary string and keeps 23performing single-bit flips on the solution that lead to the greatest improvement in fitness (=-=Hart, 1994-=-). While even incorporating simple local search techniques can lead to significant improvements in time complexity of EDAs, sometimes more advanced optimization techniques are available that are tailo... |

101 | Linkage Problem, Distribution Estimation, and Bayesian Networks.
- Pelikan, Goldberg, et al.
- 2000
(Show Context)
Citation Context ...hown in Figure 5b. Many problems contain highly overlapping subproblems that cannot be accurately modeled by dividing the problem into independent clusters. The Bayesian optimization algorithm (BOA) (=-=Pelikan, Goldberg, & Cantú-Paz, 2000-=-) uses Bayesian networks to model candidate solutions, which allow it to solve the large class of nearly decomposable problems, many of which cannot be decomposed into independent subproblems of bound... |

75 | FDA – a scalable evolutionary algorithm for the optimization of additively decomposed functions.
- Muhlenbein, Mahnig
- 1999
(Show Context)
Citation Context ...e model built in each generation captures the important features of selected solutions and generates new solutions with these features, then the EDA should be able to quickly converge to the optimum (=-=Mühlenbein & Mahnig, 1999-=-). However, as we will see later on, there is a tradeoff between the expressiveness of probabilistic models and the complexity of learning and sampling these models. Due to the importance of the class... |

74 |
Nonparametric and distribution-free methods for the social sciences
- Marascuilo, McSweeney
- 1977
(Show Context)
Citation Context ...rithm (BMDA) (Pelikan & Mühlenbein, 1999) uses a model based on a set of mutually independent trees (a forest). Each generation a dependency model is created by using Pearson’s chi-square statistics (=-=Marascuilo & McSweeney, 1977-=-) as the main measure of dependence. The model built is then sampled to generate new solutions based on the conditional probabilities learned from the population. 3.1.3 Multivariate Interactions While... |

67 |
Global optimization using bayesian networks,”
- Exteberria, Larranaga
- 1999
(Show Context)
Citation Context ...e solutions are generated by sampling the probability distribution encoded by the built network using probabilistic logic sampling (Henrion, 1988). Theestimation of Bayesian network algorithm (EBNA) (=-=Etxeberria & Larrañaga, 1999-=-) and the learning factorized distribution algorithm (LFDA) (Mühlenbein & Mahnig, 1999) also use Bayesian networks to model the promising solutions. EBNA and LFDA use the Bayesian information criterio... |

66 |
An empirical study of bit vector function optimization. Genetic algorithms and simulated annealing,
- Ackley
- 1987
(Show Context)
Citation Context ...: Using an EDA to Solve Trap-5 To illustrate some of the limitations of EDAs based on the probability vector, let us consider a more complex problem such as the concatenated trap of order 5 (trap-5) (=-=Ackley, 1987-=-; Deb & 4Probability vector entries 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 Generation Figure 2: Proportions of 1s in a probability vector of a simple EDA on the onemax problem of n ... |

56 | Optimization by learning and simulation of Bayesian and Gaussian networks.
- Larranaga, Etxeberria, et al.
- 1999
(Show Context)
Citation Context ...etter in scenarios where certain variables have higher variance than others. As in SHCLVND, however, all variables are assumed to be independent. The estimation of Gaussian networks algorithm (EGNA) (=-=Larrañaga, Etxeberria, Lozano, & Peña, 1999-=-) works by creating a Gaussian network to model the interactions between variables in the selected population of solutions in each generation. This network is similar to a Bayesian network exceptthat ... |

56 | Hierarchical boa solves ising spin glasses and maxsat
- Pelikan, Goldberg
- 2003
(Show Context)
Citation Context ...ality solutions into the initial population. These high-quality solutions can be either obtained from previous runs on similar problems, provided by a specialized heuristic (Schwarz & Ocenasek, 2000; =-=Pelikan & Goldberg, 2003-=-), or created in some way from high-quality solutions of smaller instances of the same problem (Sastry, 2001a). 25While seeding can work with many types of algorithms, EDAs offer us a wealth of new o... |

52 | 2002. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation - Larrañaga, Lozano |

49 | Continuous iterated density estimation evolutionary algorithms within the IDEA framework, - Bosman, Thierens - 2000 |

48 | Convergence Theory and Applications of the Factorized Distribution Algorithm - Mühlenbein, Mahnig - 1999 |

47 | Scalability of the Bayesian optimization algorithm - Pelikan, Sastry, et al. |

44 | Linkage information processing in distribution estimation algorithms
- Bosman, Thierens
- 1999
(Show Context)
Citation Context ...ability to identify and exploit interactions between problem variables, using tree models is often not enough to solve problems with multivariate or highly-overlapping interactions between variables (=-=Bosman & Thierens, 1999-=-; Pelikan & Mühlenbein, 1999). This section describes several EDAs that are based on probabilistic models capable of capturing multivariate interactions between problem variables. The extended compact... |

36 | Linkage identification by non-monotonicity detection for overlapping functions
- Munemoto, Goldberg
- 1999
(Show Context)
Citation Context ...ed using only marginal statistics. One can envision several ways to alleviate this problem, such as limited probing (Heckendorn & Wright, 2004) and linkage identification by non-motonicity detection (=-=Munetomo & Goldberg, 1999-=-). However, it is questionable whether the ability to solve such a special class of problems will outweigh the disadvantages of giving up the use of Bayesian statistics in learning the probabilistic m... |

34 | On the supply of building blocks
- Goldberg, Sastry, et al.
- 2001
(Show Context)
Citation Context ...ossible. The population size in EDAs is closely related to the reliability and complexity of the search, similarly as for other population-based evolutionary algorithms (Goldberg, Deb, & Clark, 1992; =-=Goldberg, Sastry, & Latoza, 2001-=-; Harik, Cantú-Paz, Goldberg, & Miller, 1997). Using a population that is too small can lead to convergence to solutions of low quality and inability to reliably find the global optimum. On the other ... |

33 | Fitness inheritance in the bayesian optimization algorithm.,”
- Pelikan, Sastry
- 2004
(Show Context)
Citation Context ...ess function. Efficiency enhancement techniques based on this principle are called evaluation relaxation techniques (Goldberg, 2002; Smith, Dike, & Stegmann, 1995; Sastry, Goldberg, & Pelikan, 2001a; =-=Pelikan & Sastry, 2004-=-; Sastry, Pelikan, & Goldberg, 2004). There are two basic approaches to evaluation relaxation: (1) endogenous models (Smith, Dike, & Stegmann, 1995; Sastry, Goldberg, & Pelikan, 2001a; Pelikan & Sastr... |

32 | Real–valued evolutionary optimization using a flexible probability density estimator. - Gallagher, Frean, et al. - 1999 |

28 | Efficient linkage discovery by limited probing
- Heckendorn, Wright
- 2004
(Show Context)
Citation Context ...ion (CPF) for which pairwise correlations between variables cannot be easily detected using only marginal statistics. One can envision several ways to alleviate this problem, such as limited probing (=-=Heckendorn & Wright, 2004-=-) and linkage identification by non-motonicity detection (Munetomo & Goldberg, 1999). However, it is questionable whether the ability to solve such a special class of problems will outweigh the disadv... |

28 | Probabilistic Reasoning in Intelligent Systems; Networks of Plausibale Inference[M - unknown authors - 1988 |

26 | Parallel Estimation of Distribution Algorithms
- Ocenasek
- 2002
(Show Context)
Citation Context ...ximizes all the 18goals simultaneously. Instead, the ultimate goal is to find a broad distribution of Pareto-optimal solutions. The Bayesian multi-objective optimization algorithm (BMOA) (Laumanns & =-=Ocenasek, 2002-=-) uses a special selection operator, ǫ-archive (Laumanns, Thiele, Deb, & Zitzler, 2002), to both ensure that Pareto-optimal solutions are maintained over time and that diversity is maintained so that ... |

25 | Analyzing probabilistic models in hierarchical BOA on traps and spin glasses - Hauschild, Pelikan, et al. - 2007 |

24 | Real-coded Bayesian optimization algorithm, bringing the strength of BOA into the continuous world.
- Ahn, Ramakrishna, et al.
- 2004
(Show Context)
Citation Context ...itional probabilities of particular values of these variables. On the other hand, normal kernel distributions are used for continuous variables. The real-coded Bayesian optimization algorithm (rBOA) (=-=Ahn, Ramakrishna, & Goldberg, 2004-=-) tries to bring the power of BOA to the real-valued domain. rBOA uses a Bayesian network to describe the underlying structure of the problem and a mixture of Gaussians to describe the local distribut... |

23 | Advancing continuous ideas with mixture distributions and factorization selection metrics - Bosman, Thierens - 2001 |

23 | Using time efficiently: Genetic-evolutionary algorithms and the continuation problem
- Goldberg
- 1999
(Show Context)
Citation Context ...ly marginal statistics. One can envision several ways to alleviate this problem, such as limited probing (Heckendorn & Wright, 2004) and linkage identification by non-motonicity detection (Munetomo & =-=Goldberg, 1999-=-). However, it is questionable whether the ability to solve such a special class of problems will outweigh the disadvantages of giving up the use of Bayesian statistics in learning the probabilistic m... |

23 | Bayesian optimization algorithm for multiobjective optimization
- Laumanns, Ocenasek
- 2009
(Show Context)
Citation Context ...ion that maximizes all the 18goals simultaneously. Instead, the ultimate goal is to find a broad distribution of Pareto-optimal solutions. The Bayesian multi-objective optimization algorithm (BMOA) (=-=Laumanns & Ocenasek, 2002-=-) uses a special selection operator, ǫ-archive (Laumanns, Thiele, Deb, & Zitzler, 2002), to both ensure that Pareto-optimal solutions are maintained over time and that diversity is maintained so that ... |

21 | Evolutionary optimization and the estimation of search distributions with applications to graph 10
- Muhlenbein, Mahnig
- 2002
(Show Context)
Citation Context ...1) bias the procedurefor generating the initial population (Schwarz & Ocenasek, 2000; Sastry, 2001a; Pelikan&Goldberg, 2003) and(2) biasorrestrictthemodelbuilding procedure (Schwarz & Ocenasek, 2000; =-=Mühlenbein & Mahnig, 2002-=-; Baluja, 2006). For both these approaches, we may either (1) hard code the modifications based on prior problem-specific knowledge (Hauschild, Pelikan, Sastry, & Goldberg, 2008; Baluja, 2006; Schwarz... |

20 |
Multi-layer perceptron error surfaces: visualization, structure and modelling
- Gallagher
- 2000
(Show Context)
Citation Context ...ed. One of the strengths of this method is that the complexity of the model can change over time, with additional components added if the current model does not correspond closely enough to the data (=-=Gallagher, 2000-=-). The mixed iterated density estimation evolutionary algorithm (mIDEA) (Bosman & Thierens, 2001a) also used mixtures of normal distributions. The model building in mIDEA starts by clustering the vari... |

20 | Using previous models to bias structural learning in the hierarchical BOA
- Hauschild, Pelikan, et al.
- 2012
(Show Context)
Citation Context ...ful in its own right, the obtained information can be used to design problem-specific optimization techniques or speed up solution of new problem instances of similar type (Hauschild & Pelikan, 2009; =-=Hauschild, Pelikan, Sastry, & Goldberg, 2008-=-; Baluja, 2006; Schwarz & Ocenasek, 2000). Prior knowledge exploitation. Practical solutions of enormously complex optimization problems often necessitates that the practitioners bias the optimization... |

20 | Substructural neighborhoods for local search in the Bayesian optimization algorithm - Lima, Pelikan, et al. - 2006 |

18 | Multiobjective Bayesian optimization algorithm - Khan, Goldberg, et al. - 2002 |

16 | The parallel bayesian optimization algorithm
- Ocenásek, Schwarz
- 2000
(Show Context)
Citation Context ...nsists of two parts: (1) learning the structure and (2) learning the parameters of the identified structure. Typically, learning the model structure is much more complex than learning the parameters (=-=Ocenasek & Schwarz, 2000-=-; Pelikan, 2005). However, since the model structure is expected to not change much between consequent iterations, one way to speed up model building is to use sporadic model building, in which the st... |

16 |
Searching for ground states of ising spin glasses with hierarchical BOA and cluster exact approximation,” Scalable Optimization Via Probabilistic Modeling. Berlin/Heidelberg
- Pelikan, Hartmann
- 2006
(Show Context)
Citation Context ...optimization has allowed EDAs to solve many large and complex problems. EDAs were successfully applied to optimization of large spin glass instances in two-dimensional and three-dimensional lattices (=-=Pelikan & Hartmann, 2006-=-), military antenna design (Yu, Santarelli, & Goldberg, 2006), multiobjective knapsack (Shah & Reed, 2010), groundwaterremediation design(Arst, Minsker, &Goldberg, 2002; Hayes &Minsker, 2005), aminoac... |

15 |
Incorporating a priori knowledge in probabilistic-model based optimization
- Baluja
- 2006
(Show Context)
Citation Context ... can be used to design problem-specific optimization techniques or speed up solution of new problem instances of similar type (Hauschild & Pelikan, 2009; Hauschild, Pelikan, Sastry, & Goldberg, 2008; =-=Baluja, 2006-=-; Schwarz & Ocenasek, 2000). Prior knowledge exploitation. Practical solutions of enormously complex optimization problems often necessitates that the practitioners bias the optimization algorithm in ... |

14 | A parallel framework for loopy belief propagation. In,
- Mendiburu, Santana, et al.
- 2007
(Show Context)
Citation Context ...nded on mutated bits depending on the conditional probability of the new parent variable’s value. In further work, Lima, Pelikan, Lobo, and Goldberg (2009) used loopy belief propogation (Pearl, 1988; =-=Mendiburu, Santana, Lozano, & Bengoetxea, 2007-=-) to find a more accurate substructural neighborhood based on the Bayesian model information and used that for local search. 5.4 Time continuation In time continuation, the goal is to maximize perform... |

13 | Estimation of Distribution Algorithms and Minimum Relative Entropy, phd
- Hons
(Show Context)
Citation Context ...on was driven by fitness statistics incorporated into the model in hBOA. Related approaches have also been studied in the context of other probabilistic models (Ochoa, Höns, Soto, & Muhlenbein, 2003; =-=Höns, 2006-=-; Santana, 2006; Muhlenbein & Höns, 2006; Höns, Santana, Larrañaga, & Lozano, 2007). 6.4 Time continuation In time continuation, the goal is to maximize performance of evolutionary algorithms by explo... |

12 | Automated alphabet reduction method with evolutionary algorithms for protein structure prediction. Genetic and Evolutionary Computation Conference (GECCO-2007
- BACARDIT, STOUT, et al.
- 2007
(Show Context)
Citation Context ...2006), multiobjective knapsack (Shah & Reed, 2010), groundwaterremediation design(Arst, Minsker, &Goldberg, 2002; Hayes &Minsker, 2005), aminoacid alphabet reduction for protein structure prediction (=-=Bacardit, Stout, Hirst, Sastry, Llorà, & Krasnogor, 2007-=-), identification of clusters of genes with similar expression profiles (Peña, Lozano, & Larrañaga, 2004), economic dispatch (Chen & p. Chen, 2007), forest management (Ducheyne, De Baets, & De Wulf, 2... |

11 | Enhancing the performance of maximum– likelihood gaussian eDAs using anticipated mean shift. - Bosman, Grahl, et al. - 2008 |

11 | Space complexity of estimation of distribution algorithms - Gao, Culberson |

10 | Efficient genetic algorithms using discretization scheduling
- Albert
- 2001
(Show Context)
Citation Context ...laxation: (1) endogenous models (Smith, Dike, & Stegmann, 1995; Sastry, Goldberg, & Pelikan, 2001a; Pelikan & Sastry, 2004; Sastry, Pelikan, & Goldberg, 2004) and (2) exogenous models (Sastry, 2001b; =-=Albert, 2001-=-). With endogenous models, the fitness values for some of the new candidate solutions are estimated based on the fitness values of the previously generated and evaluated solutions. With exogenous mode... |

10 |
Crossing the road to efficient ideas for permutation problems
- Bosman, Thierens
- 2001
(Show Context)
Citation Context ...specific encodings to solve permutation problems. For example, one may use the random key encoding (Bean, 1994) to solve permutation-based problems using EDAs for optimization of real-valued vectors (=-=Bosman & Thierens, 2001-=-b; Robles, de Miguel, & Larrañaga, 2002). However, since these EDAs do not process the aforementioned types of interactions directly their performance can often be poor (Bosman & Thierens, 2001b). The... |

10 | Parallel Implementation of EDAs Based on Probabilistic Graphical Models - Mendiburu, Lozano, et al. - 2005 |

10 |
A mixed Bayesian optimization algorithm with variance adaptation.
- Ocenasek, Kern, et al.
- 2004
(Show Context)
Citation Context ... (BIC) (Schwarz, 1978b) metric is used. In EDAs described so far, the variables were treated either as all real-valued or as all discrete quantities. The mixed Bayesian optimization algorithm (mBOA) (=-=Ocenasek, Kern, Hansen, & Koumoutsakos, 2004-=-) can deal with both types of variables. Much as in hBOA, the probability distribution of each variable is represented as a decision tree. The internal nodes of each tree encode tests on variables tha... |

9 | The Value of Online Adaptive Search - A Performance Comparison of NSGAII, ε-NSGAII and εMOEA,” Evolutionary Multi-Criterion Optimization,
- Kollat, Reed
- 2005
(Show Context)
Citation Context ...ir results showed that the ǫhBOA (Kollat, Reed, & Kasprzyk, 2008) was able to outperform both the strength pareto evolutionary algorithm (SPEA2) (Zitzler, Laumanns, & Thiele, 2002) and the ǫ-NSGA-II (=-=Kollat & Reed, 2005-=-). The ǫ-hBOA uses the selection operator in NSGA-II to select promising candidate 19solutions each generation. hBOA is then used to generate a Bayesian network model and sampled to generate new cand... |

8 | Inexact graph matching using learning and simulation of Bayesian networks, An empirical comparison between di8erent approaches with synthetic data - Bengoetxea, Larrañaga, et al. - 2000 |

8 |
A new epsilondominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems.” Adv
- Kollat, Reed, et al.
- 2008
(Show Context)
Citation Context ...erg, 2006). Shah and Reed (2011) compared three different multi-objective evolutionary algorithms when solving the multi-objective d-dimensional knapsack problem. Their results showed that the ǫhBOA (=-=Kollat, Reed, & Kasprzyk, 2008-=-) was able to outperform both the strength pareto evolutionary algorithm (SPEA2) (Zitzler, Laumanns, & Thiele, 2002) and the ǫ-NSGA-II (Kollat & Reed, 2005). The ǫ-hBOA uses the selection operator in ... |

7 | Model accuracy in the Bayesian optimization algorithm - Lima, Lobo, et al. - 2010 |

6 | Adaptive discretization for probabilistic model building genetic algorithms.
- Chen, Liu, et al.
- 2006
(Show Context)
Citation Context ...tization than others. To deal with these difficulties, various approaches to adaptive discretization were developed using EDAs (Tsutsui, Pelikan, & Goldberg, 2001; Pelikan, Goldberg, & Tsutsui, 2003; =-=Chen, Liu, & Chen, 2006-=-; Suganthan, Hansen, Liang, Deb, Chen, Auger, & Tiwari, 2005; Chen & Chen, 2010). We discuss some of these next. Tsutsui, Pelikan, and Goldberg (2001) proposed to divide the search space of each varia... |

6 | Intelligent bias of network structures in the hierarchical boa
- Hauschild, Pelikan
- 2009
(Show Context)
Citation Context ...f the problem domain is useful in its own right, the obtained information can be used to design problem-specific optimization techniques or speed up solution of new problem instances of similar type (=-=Hauschild & Pelikan, 2009-=-; Hauschild, Pelikan, Sastry, & Goldberg, 2008; Baluja, 2006; Schwarz & Ocenasek, 2000). Prior knowledge exploitation. Practical solutions of enormously complex optimization problems often necessitate... |

6 |
Getting the best of both worlds: Discrete and continuous genetic and evolutionary algorithms in concert
- Pelikan, Goldberg, et al.
- 2003
(Show Context)
Citation Context ... regions require a more dense discretization than others. To deal with these difficulties, various approaches to adaptive discretization were developed using EDAs (Tsutsui, Pelikan, & Goldberg, 2001; =-=Pelikan, Goldberg, & Tsutsui, 2003-=-; Chen, Liu, & Chen, 2006; Suganthan, Hansen, Liang, Deb, Chen, Auger, & Tiwari, 2005; Chen & Chen, 2010). We discuss some of these next. Tsutsui, Pelikan, and Goldberg (2001) proposed to divide the s... |

5 | New IDEAs and more ICE by learning and using unconditional permutation factorizations - Bosman, Thierens - 2001 |

5 |
A maximum entropy approach to sampling in EDA- the single connected case
- Ochoa, Höns, et al.
- 2003
(Show Context)
Citation Context ...obabilities, the loopy belief propagation was driven by fitness statistics incorporated into the model in hBOA. Related approaches have also been studied in the context of other probabilistic models (=-=Ochoa, Höns, Soto, & Muhlenbein, 2003-=-; Höns, 2006; Santana, 2006; Muhlenbein & Höns, 2006; Höns, Santana, Larrañaga, & Lozano, 2007). 6.4 Time continuation In time continuation, the goal is to maximize performance of evolutionary algorit... |

4 | The effectiveness of mutation operation in the case of estimation of distribution algorithms - Handa - 2006 |

4 | Optimization by max-propagation using Kikuchi approximations
- Höns, Santana, et al.
- 2007
(Show Context)
Citation Context ...o the model in hBOA. Related approaches have also been studied in the context of other probabilistic models (Ochoa, Höns, Soto, & Muhlenbein, 2003; Höns, 2006; Santana, 2006; Muhlenbein & Höns, 2006; =-=Höns, Santana, Larrañaga, & Lozano, 2007-=-). 6.4 Time continuation In time continuation, the goal is to maximize performance of evolutionary algorithms by exploiting the trade-off between making more runs with a small population size and maki... |

4 |
Loopy substructural local search for the bayesian optimization algorithm
- Lima, Pelikan, et al.
- 2009
(Show Context)
Citation Context ...posed the use of loopy belief propagation (Pearl, 1988) to generate the most likely instance from the Bayesian network learned in each iteration of EBNA. A similar approach has later been studied by (=-=Lima, Pelikan, Lobo, & Goldberg, 2009-=-), who also used loopy belief propagation but instead of conditional probabilities, the loopy belief propagation was driven by fitness statistics incorporated into the model in hBOA. Related approache... |

4 | Convergence of estimation of distribution algorithms for finite samples. Unpublished manuscript
- Mühlenbein
- 2007
(Show Context)
Citation Context ...e function, a Markov network that ensures convergence to the global optimum may sometimes be considerably less complex than an adequate Bayesian network, at least with respect to the number of edges (=-=Mühlenbein, 2008-=-). Nonetheless, sampling Markov networks is more difficult than sampling Bayesian networks. In other words, some of the difficulty moves from learning to sampling the probabilistic model compared to E... |

3 | D.E.: Comparing Advanced Genetic Algorithms and Simple Genetic Algorithms for Groundwater Management
- Minsker, Goldberg
- 2002
(Show Context)
Citation Context ...nal and three-dimensional lattices (Pelikan & Hartmann, 2006), military antenna design (Yu, Santarelli, & Goldberg, 2006), multiobjective knapsack (Shah & Reed, 2010), groundwater remediation design (=-=Arst, Minsker, & Goldberg, 2002-=-; Hayes & Minsker, 2005), aminoacid alphabet reduction for protein structure prediction (Bacardit, Stout, Hirst, Sastry, Llorà, & Krasnogor, 2007), identification of clusters of genes with similar exp... |

3 | Real-coded ECGA for economic dispatch. - Chen, Chen - 2007 |

3 | Diculty of linkage learning in estimation of distribution algorithms
- Chen, Yu
- 2009
(Show Context)
Citation Context ...ther the ability to solve such a special class of problems will outweigh the disadvantages of giving up the use of Bayesian statistics in learning the probabilistic models. Furthermore, it was shown (=-=Chen & Yu, 2009-=-) that the difficulties of EDAs when solving CPF are mainly due to spurious linkages; therefore, using methods to reduce spurious linkages may provide yet another solution to this problem. 6 Efficienc... |

3 |
Enabling the extended compact genetic algorithm for real-parameter optimization by using adaptive discretization
- Chen, Chen
- 2010
(Show Context)
Citation Context ... discretization were developed using EDAs (Tsutsui, Pelikan, & Goldberg, 2001; Pelikan, Goldberg, & Tsutsui, 2003; Chen, Liu, & Chen, 2006; Suganthan, Hansen, Liang, Deb, Chen, Auger, & Tiwari, 2005; =-=Chen & Chen, 2010-=-). We discuss some of these next. Tsutsui, Pelikan, and Goldberg (2001) proposed to divide the search space of each variable into subintervalsusingahistogram. Twodifferent typesofhistogram modelswereu... |

3 | Towards understanding EDAs based on Bayesian networks through a quantitative analysis - Echegoyen, Mendiburu, et al. |

2 | Why is parity hard for estimation of distribution algorithms - Coffin, Smith - 2007 |

2 | Probabilistic models for linkage learning in forest management - Ducheyne, Baets, et al. - 2004 |

2 |
Evaluation of advanced genetic algorithms applied to groundwater remediation design
- Hayes, Minsker
- 2005
(Show Context)
Citation Context ...s (Pelikan & Hartmann, 2006), military antenna design (Yu, Santarelli, & Goldberg, 2006), multiobjective knapsack (Shah & Reed, 2010), groundwater remediation design (Arst, Minsker, & Goldberg, 2002; =-=Hayes & Minsker, 2005-=-), aminoacid alphabet reduction for protein structure prediction (Bacardit, Stout, Hirst, Sastry, Llorà, & Krasnogor, 2007), identification of clusters of genes with similar expression profiles (Peña,... |

2 | ECGA vs. BOA in discovering stock market trading experts
- Lipinski
- 2007
(Show Context)
Citation Context ...s of genes with similar expression profiles (Peña, Lozano, & Larrañaga, 2004), economic dispatch (Chen & p. Chen, 2007), forest management (Ducheyne, De Baets, & De Wulf, 2004), portfolio management (=-=Lipinski, 2007-=-), cancer chemotherapy optimization (Petrovski, Shakya, & Mccall, 2006), environmental monitoring network design (Kollat, 1Reed, & Kasprzyk, 2008), and others. It is important to stress that in most ... |

1 |
Multi-objective optimization with the naive MIDEA
- Bosman, Thierens
- 2006
(Show Context)
Citation Context ...nd the improved strength Pareto evolutionary algorithm (SPEA2) (Zitzler, Laumanns, & Thiele, 2002). The naive mixture-based multi-objective iterated density-estimation evolutionary algorithm (MIDEA) (=-=Bosman & Thierens, 2006-=-) extended the IDEA framework to multi-objective optimization. Aspecialselection operatorwasusedtoensurepreservationofdiversity alongthePareto front, guided by a single parameter δ. The population is ... |

1 | Optimization, learning and natural algorithms. Doctoral dissertation, Politecnico di - unknown authors - 1992 |

1 |
Towards automated selection of estimation of distribution algorithms
- Lobo, Lima
- 2010
(Show Context)
Citation Context ... 2005; Zhang, Zhou, & Jin, 2008). However, adaptation in EDAs is usually limited by the initial choice of the probabilistic model. As a consequence, adaptive EDAs (Santana, Larrañaga, & Lozano, 2008; =-=Lobo & Lima, 2010-=-) have been proposed that dynamically change the type of model used while solving a problem. Problem structure. Besides just providing the solution to the problem, EDAs also provide optimization pract... |

1 |
11 December). Competent program evolution
- Looks
- 2006
(Show Context)
Citation Context ...otic nature of program spaces, finding an accurate problem decomposition can be difficult over the entire search space of candidate programs. The meta-optimizing semantic evolutionary search (MOSES) (=-=Looks, 2006-=-) deals with this problem by first dynamically splitting up the search space into separate program subspaces called demes that are maintained simultaneously. hBOA is then applied to each individual de... |

1 |
Multiobjective hBOA, clustering, andscalability
- Pelikan, Sastry, et al.
- 2005
(Show Context)
Citation Context ...to generate new candidate solutions for the next generation. The multi-objective BOA outperformed the NSGA-II on several interleaved deceptive problems. The multi-objective hierarchical BOA (mohBOA) (=-=Pelikan, Sastry, & Goldberg, 2005-=-) extended hBOA to the multi-objective domain by combining hBOA, NSGA-II (Deb, Pratap, Agarwal, & Meyarivan, 2002) and clustering. mohBOA uses the non-dominated crowding of NSGA-II to rank candidate s... |