Substructural local search in discrete estimation of distribution algorithms

Tese dout., Engenharia Electrónica e Computação, Universidade do Algarve, 2009SFRH/BD/16980/2004The last decade has seen the rise and consolidation of a new trend of stochastic optimizers known as estimation of distribution algorithms (EDAs). In essence, EDAs build probabilistic models of promising solutions and sample from the corresponding probability distributions to obtain new solutions. This approach has brought a new view to evolutionary computation because, while solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. This dissertation proposes the integration of substructural local search (SLS) in EDAs to speedup the convergence to optimal solutions. Substructural neighborhoods are de ned by the structure of the probabilistic models used in EDAs, generating adaptive neighborhoods capable of automatic discovery and exploitation of problem regularities. Speci cally, the thesis focuses on the extended compact genetic algorithm and the Bayesian optimization algorithm. The utility of SLS in EDAs is investigated for a number of boundedly di cult problems with modularity, overlapping, and hierarchy, while considering important aspects such as scaling and noise. The results show that SLS can substantially reduce the number of function evaluations required to solve some of these problems. More importantly, the speedups obtained can scale up to the square root of the problem size O( p `).Fundação para a Ciência e Tecnologia (FCT

Application of substructural local search in the MAXSAT problem

Dissertação de mest., Engenharia Informática, Faculdade de Ciências e Tecnologia, Univ. do Algarve, 2011Genetic Algorithms (GAs) are stochastic optimizers usually applied to problems where the use of deterministic methods is not practical or when information about how to solve the problem is scarce. Although traditional GAs show good results in a broad range of problems, they do not take into account the dependencies that may exist among the variables of a given problem. Without respecting these links, achieving the optimum can be very hard or even impossible. Estimation of Distribution Algorithms (EDAs) are methods inspired on GAs that are able to learn the linkage between variables without providing any information about the problem structure. These methods use machine learning techniques to build a probabilistic model that captures the regularities present in the population (a set of candidate solutions for our problem). The learned model is used to generate new solutions similar to those present in the population but also with some innovation. The Substructural Local Search (SLS) is a method recently proposed that takes advantage from the model built by the EDA and performs local search in each substructure of the model, providing in the end a high quality solution. This method has shown to improve the e_ciency of the search when applied to di_erent EDAs in several arti_cial problems of bounded di_culty. In this thesis, the utility of SLS in the hierarchical Bayesian Optimization Algorithm (hBOA) (an EDA that uses Bayesian networks as probabilistic model), is investigated in the MAXSAT problem. Results show that SLS is able to improve the e_ciency of hBOA, but only on MAXSAT instances with a small number of variables. For larger instances that behavior is not observed. Additionally, the SLS execution is analyzed in order to better understand the obtained results. Finally, some observations and suggestions are exposed for an improvement of SLS

New methods for generating populations in Markov network based EDAs: Decimation strategies and model-based template recombination

Methods for generating a new population are a fundamental component of estimation of distribution algorithms (EDAs). They serve to transfer the information contained in the probabilistic model to the new generated population. In EDAs based on Markov networks, methods for generating new populations usually discard information contained in the model to gain in efficiency. Other methods like Gibbs sampling use information about all interactions in the model but are computationally very costly. In this paper we propose new methods for generating new solutions in EDAs based on Markov networks. We introduce approaches based on inference methods for computing the most probable configurations and model-based template recombination. We show that the application of different variants of inference methods can increase the EDAs’ convergence rate and reduce the number of function evaluations needed to find the optimum of binary and non-binary discrete functions

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Analyzing limits of effectiveness in different implementations of estimation of distribution algorithms

Conducting research in order to know the range of problems in which a search algorithm is effective constitutes a fundamental issue to understand the algorithm and to continue the development of new techniques. In this work, by progressively increasing the degree of interaction in the problem, we study to what extent different EDA implementations are able to reach the optimal solutions. Specifically, we deal with additively decomposable functions whose complexity essentially depends on the number of sub-functions added. With the aim of analyzing the limits of this type of algorithms, we take into account three common EDA implementations that only differ in the complexity of the probabilistic model. The results show that the ability of EDAs to solve problems quickly vanishes after certain degree of interaction with a phase-transition effect. This collapse of performance is closely related with the computational restrictions that this type of algorithms have to impose in the learning step in order to be efficiently applied. Moreover, we show how the use of unrestricted Bayesian networks to solve the problems rapidly becomes inefficient as the number of sub-functions increases. The results suggest that this type of models might not be the most appropriate tool for the the development of new techniques that solve problems with increasing degree of interaction. In general, the experiments proposed in the present work allow us to identify patterns of behavior in EDAs and provide new ideas for the analysis and development of this type of algorithms

MATEDA: A suite of EDA programs in Matlab

This paper describes MATEDA-2.0, a suite of programs in Matlab for estimation of distribution algorithms. The package allows the optimization of single and multi-objective problems with estimation of distribution algorithms (EDAs) based on undirected graphical models and Bayesian networks. The implementation is conceived for allowing the incorporation by the user of different combinations of selection, learning, sampling, and local search procedures. Other included methods allow the analysis of the structures learned by the probabilistic models, the visualization of particular features of these structures and the use of the probabilistic models as fitness modeling tools

Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods