Fitness inheritance in the Bayesian optimization algorithm

Sep 25, 20071 like618 views

This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions, but also for estimating their fitness. The results indicate that fitness inheritance is a promising concept in BOA, because population-sizing requirements for building appropriate models of promising solutions lead to good fitness estimates even if only a small proportion of candidate solutions is evaluated using the actual fitness function. This can lead to a reduction of the number of actual fitness evaluations by a factor of 30 or more.

Fitness inheritance in the Bayesian optimization algorithm

This document discusses various importance sampling methods for approximating marginal likelihoods, including regular importance sampling, bridge sampling, and harmonic means. It compares these methods on a probit model example using data on diabetes in Pima Indian women. Regular importance sampling uses the MLE distribution as an importance function. Bridge sampling introduces a pseudo-posterior to handle models with different parameter dimensions. Harmonic means directly uses the posterior sample but requires a proposal distribution with lighter tails than the posterior.

CVPR2010: higher order models in computer vision: Part 4 zukun

The schedule included an introduction from 830-900, a discussion of models with small cliques and special potentials from 900-1000, a tea break from 1000-1030, a discussion of inference techniques like LP relaxation, Lagrangian relaxation and dual decomposition from 1030-1200, and a discussion of models with global potentials and parameters from 1200-1230. The document concluded by outlining some open questions for future work, including exploiting new ideas in applications, exploring other higher-order cliques, comparing different inference techniques, and learning higher-order random fields models.

Sparsity with sign-coherent groups of variables via the cooperative-LassoLaboratoire Statistique et génome

The document presents the cooperative-Lasso, a regularization method for variable selection in regression that assumes sign-coherent group structure. It begins by introducing generalized linear models and the group Lasso estimator. It then notes two limitations of the group Lasso: it does not allow for single zeros within groups, and it does not enforce sign coherence within groups. The cooperative-Lasso is introduced as a penalty that assumes groups will have either all non-positive, non-negative, or null parameters. Examples of applications that could benefit from sign coherence between variables within groups are given.

Signal Processing Course : Sparse Regularization of Inverse ProblemsGabriel Peyré

The document discusses sparse regularization for inverse problems. It describes how sparse regularization can be used for tasks like denoising, inpainting, and image separation by posing them as optimization problems that minimize data fidelity and an L1 sparsity prior on the coefficients. Iterative soft thresholding is presented as an algorithm for solving the noisy sparse regularization problem. Examples are given of how sparse wavelet regularization can outperform other regularizers like Sobolev for tasks like image deblurring.

Tele3113 wk1wedVin Voro

The document provides an overview of probability theory and random variables including: 1) It defines probability as a measure of the chance of obtaining a particular outcome from an event. Common properties of probability such as mutually exclusive events and conditional probability are also covered. 2) Random variables are introduced as rules that assign real numbers to possible outcomes of an experiment. Both discrete and continuous random variables are defined. 3) Key concepts related to random variables are summarized including the cumulative distribution function, probability density function, expected value, variance, and common distributions like the uniform, binomial, and Gaussian distributions. 4) Finally, random processes are defined as sets of random variables indexed by time, with properties like the mean

Goodfellow, Bengio, Couville (2016) "Deep Learning", Chap. 7Ono Shigeru

Regularization is used in deep learning to reduce generalization error by modifying the learning algorithm. Common regularization techniques for deep neural networks include: 1) Parameter norm penalties like L2 and L1 regularization that penalize the weights of a network. This encourages simpler models that generalize better. 2) Early stopping which obtains the model parameters at the point of lowest validation error during training, rather than at the end of training. 3) Data augmentation which creates additional fake training data through techniques like translation to improve robustness.

Link-based document classification using Bayesian NetworksAlfonso E. Romero

This document summarizes a paper on using a Bayesian network model for link-based text classification. The authors propose learning the interactions between document categories from data using a Bayesian network, rather than fixing the network structure. They model the probability of a document's category given both its content and the categories of linked documents. Experimental results show their Bayesian network approach improves over baseline classifiers, particularly providing around a 10% boost when used with an OR gate classifier. The authors conclude the model is valuable and parametrizable, and they discuss exploring other base classifiers and more experiments.

Goodfellow, Bengio, Couville (2016) "Deep Learning", Chap. 6Ono Shigeru

The document discusses deep feedforward networks, also known as multilayer perceptrons. It begins with an introduction to feedforward networks, which apply vector-to-vector functions across multiple hidden layers without feedback connections between layers. Each hidden layer consists of units that resemble neurons. The document then covers gradient-based learning, different cost functions, types of output and hidden units like ReLU, and considerations for network architecture such as depth, width, and universal approximation properties.

Session 6vivek_shaw

This document provides an overview of continuous probability distributions including: - The probability of an event occurring between two values a and b is defined by the shaded area under the probability density function curve between a and b. - Key properties of continuous distributions include the mean, median, standard deviation, and cumulative distribution function. - The normal distribution is discussed as an important continuous distribution with properties like symmetry and effectiveness in modeling real-world data. - Methods for calculating normal probabilities using tables or Excel are presented with examples. - An example problem involving a quality control scenario and modeling the number of defective items using a binomial distribution is provided.

Principal component analysis and matrix factorizations for learning (part 2) ...zukun

1) Spectral clustering is a technique for clustering data based on the eigenvectors of the similarity matrix of the data. 2) It works by computing the generalized eigenvectors of the normalized graph Laplacian matrix, which leads to a low-dimensional embedding of the data that can then be clustered using k-means. 3) Spectral clustering is related to other graph clustering techniques like normalized cut that aim to minimize similarities between clusters while balancing cluster sizes.

MUMS: Bayesian, Fiducial, and Frequentist Conference - Multiscale Analysis of...The Statistical and Applied Mathematical Sciences Institute

The widespread popularity of Bayesian tree-structured regression methods has raised considerable interest in theoretical understanding of their empirical success. However, theoretical literature on methods such as Bayesian CART and BART is still in its infancy. This paper affords new insights about Bayesian CART in the context of structured wavelet shrinkage under the white noise model. We exhibit precise connections between tree-shaped sparsity priors and unstructured spike-and-slab priors, which are regarded as ideal but are rather theoretical in nature. We show that the more practical Bayesian CART priors lead to adaptive rate-minimax posterior concentration in the l∞sense, performing nearly as well as the theoretical ideal (up to a log term). To further explore the benefits of structured shrinkage, we propose the g-prior for trees, which departs from the typical wavelet product priors by harnessing correlation structure induced by the tree topology. While the majority of wavelet type theoretical results for CART focus on dyadic trees, here we do not require that splits are at dyadic locations. We introduce the library of weakly balanced Haar wavelets and show that Bayesian CART is equivalent to Bayesian basis selection from this library. To illustrate that l∞adaptation is an intricate phenomenon, where internal sparsity plays a key role, we show that dense trees are incapable of adaptation. While one of the major appeals of BART is uncertainty quantification via credible sets, asymptotic normality justifications have thus far been unavailable. Building on the l∞adaptation property, we provide new fully non-parametric and adaptive Bernstein-von Mises statements for Bayesian CART using multiscale techniques. (Joint work with Ismael Castillo)

Image denoisingYap Wooi Hen

1. Gibbs sampling is a technique for drawing samples from probability distributions by iteratively sampling each variable conditioned on the current values of the other variables. It can be used to sample from Markov random fields and Bayesian networks. 2. An Ising model is a Markov random field with binary variables on a grid that are correlated with their neighbors. Gibbs sampling in an Ising model samples each variable based on its neighbors' current values. 3. Boltzmann machines generalize the Ising model to arbitrary graph structures between variables. Restricted Boltzmann machines and Hopfield networks are specific types of Boltzmann machines.

Computational methods for Bayesian model choiceChristian Robert

This document discusses several computational methods for Bayesian model choice, including importance sampling, cross-model solutions, nested sampling, and approximate Bayesian computation (ABC) model choice. It introduces Bayes factors and marginal likelihoods as key quantities for Bayesian model comparison, and describes how Bayesian model choice involves allocating probabilities to different models and computing the marginal likelihood or evidence for each model.

Mesh Processing Course : Mesh ParameterizationGabriel Peyré

Rank awarealgs small11Jules Esp

This document discusses rank-aware algorithms for joint sparse recovery from multiple measurement vectors (MMV). It begins by introducing the MMV problem and showing that when the rank of the signal matrix is r, the necessary and sufficient conditions for unique recovery are less restrictive than in the single measurement vector case. Classical MMV algorithms like SOMP and l1/lq minimization are not rank-aware. The document then proposes two rank-aware pursuit algorithms: 1) Rank-Aware OMP, which modifies the atom selection step of SOMP but still suffers from rank degeneration over iterations. 2) Rank-Aware Order Recursive Matching Pursuit (RA-ORMP), which forces the sparsity

CVPR2010: Advanced ITinCVPR in a Nutshell: part 7: Future Trendzukun

The document discusses using wavelet representations for density estimation and shape analysis. It proposes using a constrained maximum likelihood objective to estimate density coefficients in a multi-resolution wavelet basis. Model selection criteria like MDL, AIC and BIC are compared for selecting the number of resolution levels in the wavelet expansion, with MDL shown to be invariant to the multi-resolution analysis used. The criteria are tested on 1D densities with different shapes, with MDL and MSE performing best in distinguishing the densities.

The multilayer perceptronESCOM

The document discusses the multilayer perceptron (MLP), a neural network architecture that can solve nonlinear classification problems. It describes the structure of an MLP with one hidden layer and discusses training an MLP using backpropagation. Backpropagation is a gradient descent algorithm that propagates error signals backward from the output to hidden layers to update weights. The document also introduces the resilient backpropagation (RPROP) algorithm, which uses individual adaptive learning rates, and discusses second-order learning algorithms like the Levenberg-Marquardt algorithm.

Alternating directionDerek Pang

This document provides an overview of the Alternating Direction Method of Multipliers (ADMM) for solving constrained convex optimization problems. It begins by discussing dual decomposition and the method of multipliers, which inspired ADMM. ADMM allows for problems to be decomposed and solved in parallel by alternating between optimizing one block of variables while fixing the others. The document outlines the ADMM algorithm, convergence properties, and common patterns. It provides examples of how ADMM can be applied to problems like lasso regression and sparse inverse covariance selection.

05 history of cv a machine learning (theory) perspective on computer visionzukun

This document provides an overview of machine learning algorithms used in computer vision from the perspective of a machine learning theorist. It discusses how the theorist got involved in a computer vision project in 2002 and summarizes key algorithms at that time like boosting, support vector machines, and their developments. It also provides historical context and comparisons of algorithms like perceptron and Winnow. The document uses examples to explain concepts like kernels and the kernel trick in support vector machines.

Bayesian inversion of deterministic dynamic causal modelskhbrodersen

1. The document discusses various methods for Bayesian inference and model comparison in dynamic causal models, including variational Laplace approximation, sampling methods, and computing model evidence. 2. Variational Laplace approximation involves factorizing the posterior distribution and iteratively optimizing a lower bound on the model evidence called the negative free energy. 3. Sampling methods like Markov chain Monte Carlo generate stochastic approximations to the posterior by constructing a Markov chain with the target distribution as its equilibrium distribution.

Physics of Algorithms Talkjasonj383

1. The document summarizes analysis of Gaussian belief propagation (GaBP) on graphical models, including walk-sum analysis of means and variances and orbit-product analysis of determinants. 2. GaBP provides an approximate inference algorithm that computes marginal distributions by passing messages between nodes. In tree models it is exact, but in loopy graphs it can underestimate variances. 3. The analysis shows that GaBP computes a complete walk-sum for the means but an incomplete walk-sum for the variances, accounting for its inexactness on loopy graphs. It also shows that the GaBP estimate of the partition function is equal to the totally backtracking orbit-product.

Maximum likelihood estimation of regularisation parameters in inverse problem...Valentin De Bortoli

This document discusses an empirical Bayesian approach for estimating regularization parameters in inverse problems using maximum likelihood estimation. It proposes the Stochastic Optimization with Unadjusted Langevin (SOUL) algorithm, which uses Markov chain sampling to approximate gradients in a stochastic projected gradient descent scheme for optimizing the regularization parameter. The algorithm is shown to converge to the maximum likelihood estimate under certain conditions on the log-likelihood and prior distributions.

IwsmbvsBob O'Hara

This document discusses Bayesian variable selection methods for regression models. It begins by reviewing traditional ANOVA tables and their limitations for modern applications with many variables, such as GWAS studies. It then introduces Bayesian approaches using priors to perform variable selection by building it into the regression model. Several variable selection methods are described that use different prior distributions, such as slab and spike priors, the stochastic search variable selection (SSVS) method, and the normal-exponential-gamma (NEG) distribution. The document discusses how these methods can be implemented using MCMC sampling and compares their performance. It also discusses some extensions like using random effects and polynomial terms.

Semi-Supervised Regression using Cluster EnsembleAlexander Litvinenko

This document summarizes a semi-supervised regression method that combines graph Laplacian regularization with cluster ensemble methodology. It proposes using a weighted averaged co-association matrix from the cluster ensemble as the similarity matrix in graph Laplacian regularization. The method (SSR-LRCM) finds a low-rank approximation of the co-association matrix to efficiently solve the regression problem. Experimental results on synthetic and real-world datasets show SSR-LRCM achieves significantly better prediction accuracy than an alternative method, while also having lower computational costs for large datasets. Future work will explore using a hierarchical matrix approximation instead of low-rank.

Asymptotics for discrete random measuresJulyan Arbel

This document provides an introduction to asymptotics for discrete random measures, specifically the Dirichlet process and two-parameter Poisson-Dirichlet process. It discusses several key aspects in 3 sentences or less: 1) It outlines the stick-breaking construction of the two-parameter Poisson-Dirichlet process and defines related notation. 2) It introduces the truncation error Rn and discusses how its asymptotic behavior differs between the Dirichlet and two-parameter Poisson-Dirichlet cases. 3) It briefly describes some applications of these processes in mixture modeling and summarizes different sampling approaches like blocked Gibbs and slice sampling that rely on truncation of the infinite-dimensional distributions.

Approximate Bayesian Computation on GPUsMichael Stumpf

This document discusses using graphics processing units (GPUs) to perform approximate Bayesian computation (ABC) for parameter estimation of complex models. It describes how GPUs are well-suited for ABC due to their ability to perform linear computations on many threads in parallel. The document provides examples of applying ABC to GPUs for problems involving dynamical systems, network evolution models, and parameter estimation for protein interaction networks.

Linear Bayesian update surrogate for updating PCE coefficientsAlexander Litvinenko

This is our joint work with colleagues from TU Braunschweig. Prof. H. G. Matthies had an excellent idea to develop a Bayesian surrogate formula for updating not probability densities (like in classical Bayesian formula), but PCE coefficients of the given random variable. Bojana Rosic implemented the linear case. I (with help of Elmar Zander) implemented non-linear case. Later on Elmar significantly simplified the algorithm.

Macrocanonical models for texture synthesisValentin De Bortoli

This document discusses macrocanonical models for texture synthesis. It begins by introducing the goal of texture synthesis and providing a brief history. It then describes the parametric question of combining randomness and structure in images. Specifically, it discusses maximizing entropy under geometric constraints. The document goes on to discuss links to statistical physics, defining microcanonical and macrocanonical models. It focuses on studying the macrocanonical model, describing how to find optimal parameters through gradient descent and how to sample from the model using Langevin dynamics. The document provides examples of texture synthesis and compares results to other methods.

Effects of a Deterministic Hill climber on hBOAMartin Pelikan

Hybridization of global and local search algorithms is a well-established 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.

Intelligent Bias of Network Structures in the Hierarchical BOAMartin Pelikan

This document describes research on intelligently biasing the network structures learned by the hierarchical Bayesian Optimization Algorithm (hBOA) to improve its performance. The researchers developed a method called split probability matrix (SPM) biasing, which uses prior information stored in an SPM to bias hBOA's network building process towards structures with a certain number of splits. They tested SPM biasing on two problems: Trap-5 and 2D Ising spin glasses. The experiments showed that SPM biasing significantly reduced hBOA's execution time, number of evaluations, and bits examined on both problems, with the best speedups achieved around a tuning parameter κ value of 1.

More Related Content

What's hot (20)

Session 6vivek_shaw

Principal component analysis and matrix factorizations for learning (part 2) ...zukun

MUMS: Bayesian, Fiducial, and Frequentist Conference - Multiscale Analysis of...The Statistical and Applied Mathematical Sciences Institute

Image denoisingYap Wooi Hen

Computational methods for Bayesian model choiceChristian Robert

Mesh Processing Course : Mesh ParameterizationGabriel Peyré

Rank awarealgs small11Jules Esp

CVPR2010: Advanced ITinCVPR in a Nutshell: part 7: Future Trendzukun

The multilayer perceptronESCOM

Alternating directionDerek Pang

05 history of cv a machine learning (theory) perspective on computer visionzukun

Bayesian inversion of deterministic dynamic causal modelskhbrodersen

Physics of Algorithms Talkjasonj383

Maximum likelihood estimation of regularisation parameters in inverse problem...Valentin De Bortoli

IwsmbvsBob O'Hara

Semi-Supervised Regression using Cluster EnsembleAlexander Litvinenko

Asymptotics for discrete random measuresJulyan Arbel

Approximate Bayesian Computation on GPUsMichael Stumpf

Linear Bayesian update surrogate for updating PCE coefficientsAlexander Litvinenko

Macrocanonical models for texture synthesisValentin De Bortoli

Session 6vivek_shaw

Principal component analysis and matrix factorizations for learning (part 2) ...zukun

MUMS: Bayesian, Fiducial, and Frequentist Conference - Multiscale Analysis of...The Statistical and Applied Mathematical Sciences Institute

Image denoisingYap Wooi Hen

Computational methods for Bayesian model choiceChristian Robert

Mesh Processing Course : Mesh ParameterizationGabriel Peyré

Rank awarealgs small11Jules Esp

CVPR2010: Advanced ITinCVPR in a Nutshell: part 7: Future Trendzukun

The multilayer perceptronESCOM

Alternating directionDerek Pang

05 history of cv a machine learning (theory) perspective on computer visionzukun

Bayesian inversion of deterministic dynamic causal modelskhbrodersen

Physics of Algorithms Talkjasonj383

Maximum likelihood estimation of regularisation parameters in inverse problem...Valentin De Bortoli

IwsmbvsBob O'Hara

Semi-Supervised Regression using Cluster EnsembleAlexander Litvinenko

Asymptotics for discrete random measuresJulyan Arbel

Approximate Bayesian Computation on GPUsMichael Stumpf

Linear Bayesian update surrogate for updating PCE coefficientsAlexander Litvinenko

Macrocanonical models for texture synthesisValentin De Bortoli

Viewers also liked (17)

Effects of a Deterministic Hill climber on hBOAMartin Pelikan

Intelligent Bias of Network Structures in the Hierarchical BOAMartin Pelikan

Analysis of Evolutionary Algorithms on the One-Dimensional Spin Glass with Po...Martin Pelikan

The document analyzes evolutionary algorithms for solving instances of the one-dimensional spin glass problem with power-law interactions. It generates 610,000 problem instances with varying system size (n=20-150) and power-law decay parameter (σ=0-2). It compares the performance of genetic algorithms, hierarchical Bayesian optimization, and local search methods on these instances, measuring the number of evaluations required to find the optimal solution. The results show how performance depends on the power-law decay and effective interaction range.

Empirical Analysis of ideal recombination on random decomposable problemskknsastry

This paper analyzes the behavior of a selectorecombinative genetic algorithm (GA) with an ideal crossover on a class of random additively decomposable problems (rADPs). Specifically, additively decomposable problems of order k whose subsolution fitnesses are sampled from the standard uniform distribution U[0,1] are analyzed. The scalability of the selectorecombinative GA is investigated for 10,000 rADP instances. The validity of facetwise models in bounding the population size, run duration, and the number of function evaluations required to successfully solve the problems is also verified. Finally, rADP instances that are easiest and most difficult are also investigated.

Efficiency Enhancement of Estimation of Distribution AlgorithmsMartin Pelikan

This document discusses enhancing the efficiency of estimation of distribution algorithms (EDAs). EDAs guide search by building and sampling an explicit probabilistic model of high-quality solutions and can solve hard problems scalably. However, for very large problems with complex evaluations, their performance may not be sufficient. The authors from the University of Missouri propose methods for improving the efficiency of EDAs.

Towards billion bit optimization via parallel estimation of distribution algo...kknsastry

The document describes research into using efficient estimation of distribution algorithms (EDAs) like the compact genetic algorithm (cGA) to solve optimization problems involving billions of variables. Key aspects discussed include the cGA's memory and computational efficiency through techniques like parallelization and vectorization. The researchers were able to solve a noisy OneMax problem involving over 33 million variables to optimality and a problem with 1.1 billion variables with relaxed convergence. The document argues this research is important because many real-world problems involving nanotechnology, biology, and information systems require solving optimization problems at massive scales.

iBOA: The Incremental Bayesian Optimization AlgorithmMartin Pelikan

This paper proposes the incremental Bayesian optimization algorithm (iBOA), which modifies standard BOA by removing the population of solutions and using incremental updates of the Bayesian network. iBOA is shown to be able to learn and exploit unrestricted Bayesian networks using incremental techniques for updating both the structure as well as the parameters of the probabilistic model. This represents an important step toward the design of competent incremental estimation of distribution algorithms that can solve difficult nearly decomposable problems scalably and reliably.

Simplified Runtime Analysis of Estimation of Distribution AlgorithmsPer Kristian Lehre

Spurious Dependencies and EDA ScalabilityMartin Pelikan

Using Previous Models to Bias Structural Learning in the Hierarchical BOAMartin Pelikan

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 problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific 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.

Initial-Population Bias in the Univariate Estimation of Distribution AlgorithmMartin Pelikan

This document studies the effects of biasing the initial population in the Univariate Marginal Distribution Algorithm (UMDA) on the onemax and noisy onemax problems. Theoretical models are developed to predict the impact on population size, number of generations, and number of evaluations for different levels of initial bias. Experiments match the theoretical predictions, showing that a positively biased initial population improves performance while a negatively biased population harms performance. Introducing noise does not change these effects.

Transfer Learning, Soft Distance-Based Bias, and the Hierarchical BOAMartin Pelikan

An automated technique has recently been proposed to transfer learning in the hierarchical Bayesian optimization algorithm (hBOA) based on distance-based statistics. The technique enables practitioners to improve hBOA efficiency by collecting statistics from probabilistic models obtained in previous hBOA runs and using the obtained statistics to bias future hBOA runs on similar problems. The purpose of this paper is threefold: (1) test the technique on several classes of NP-complete problems, including MAXSAT, spin glasses and minimum vertex cover; (2) demonstrate that the technique is effective even when previous runs were done on problems of different size; (3) provide empirical evidence that combining transfer learning with other efficiency enhancement techniques can often yield nearly multiplicative speedups.

Using Problem-Specific Knowledge and Learning from Experience in Estimation o...Martin Pelikan

Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin GlassesMartin Pelikan

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 optimization 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.

The Bayesian Optimization Algorithm with Substructural Local SearchMartin Pelikan

This work studies the utility of using substructural neighborhoods for local search in the Bayesian optimization algorithm (BOA). The probabilistic model of BOA, which automatically identifies important problem substructures, is used to define the structure of the neighborhoods used in local search. Additionally, a surrogate fitness model is considered to evaluate the improvement of the local search steps. The results show that performing substructural local search in BOA significatively reduces the number of generations necessary to converge to optimal solutions and thus provides substantial speedups.

Order Or Not: Does Parallelization of Model Building in hBOA Affect Its Scala...Martin Pelikan

1. Martin Pelikan and James D. Laury Jr. study the effects of parallelizing the model building process in hBOA on its scalability. 2. They find that parallelizing model building provides nearly linear speedups but can slightly increase the number of function evaluations needed. 3. However, the negative effects of parallelizing model building are negligible compared to the performance gains, so parallelizing model building is beneficial when it is the bottleneck.

Estimation of Distribution Algorithms TutorialMartin Pelikan

Probabilistic model-building algorithms (PMBGAs), also called estimation of distribution algorithms (EDAs) and iterated density estimation algorithms (IDEAs), replace traditional variation of genetic and evolutionary algorithms by (1) building a probabilistic model of promising solutions and (2) sampling the built model to generate new candidate solutions. PMBGAs are also known as estimation of distribution algorithms (EDAs) and iterated density-estimation algorithms (IDEAs). Replacing traditional crossover and mutation operators by building and sampling a probabilistic model of promising solutions enables the use of machine learning techniques for automatic discovery of problem regularities and exploitation of these regularities for effective exploration of the search space. Using machine learning in optimization enables the design of optimization techniques that can automatically adapt to the given problem. There are many successful applications of PMBGAs, for example, Ising spin glasses in 2D and 3D, graph partitioning, MAXSAT, feature subset selection, forest management, groundwater remediation design, telecommunication network design, antenna design, and scheduling. This tutorial provides a gentle introduction to PMBGAs with an overview of major research directions in this area. Strengths and weaknesses of different PMBGAs will be discussed and suggestions will be provided to help practitioners to choose the best PMBGA for their problem. The video of this tutorial presented at GECCO-2008 can be found at http://medal.cs.umsl.edu/blog/?p=293