Algoritmos Evolutivos que utilizam modelos probabilísticos de distribuição dos valores das variáveis (para orientar o processo de busca da solução de problemas) são chamados Algoritmos de Estimação de Distribuição (AEDs). Esses algoritmos têm apresentado resultados relevantes para lidar com problemas relativamente complexos. O desempenho deles depende diretamente da qualidade dos modelos probabilísticos construídos que, por sua vez, dependem dos métodos de construção dos modelos. Os melhores modelos em geral são construídos por métodos computacionalmente complexos, resultando em AEDs que requerem tempo computacional alto, apesar de serem capazes de explorar menos pontos do espaço de busca para encontrar a solução de um problema. Este trabalho investiga modelos probabilísticos obtidos por algoritmos de reconstrução de filogenias, uma vez que alguns desses métodos podem produzir, de forma computacionalmente eficiente, modelos que representam bem as principais relações entre espécies (ou entre variáveis). Este trabalho propõe algumas estratégias para obter um melhor uso de modelos baseados em filogenia para o desenvolvimento de AEDs, dentre elas o emprego de um conjunto de filogenias em vez de apenas uma filogenia como modelo de correlação entre variáveis, a síntese das informações mais relevantes desse conjunto em uma estrutura de rede e a identificação de grupos de variáveis correlacionadas a partir de uma ou mais redes por meio de um algoritmo de detecção de comunidades. Utilizando esses avanços para a construção de modelos, foi desenvolvido uma nova técnica de busca, a Busca Exaustiva Composta, que possibilita encontrar a solução de problemas combinatórios de otimização de diferentes níveis de dificuldades. Além disso, foi proposta uma extensão do novo algoritmo para problemas multiobjetivos, que mostrou ser capaz de determinar a fronteira Pareto-ótima dos problemas combinatórios investigados. Por fim, o AED desenvolvido possibilitou obter um compromisso em termos de número de avaliações e tempo de computação, conseguindo resultados similares aos dos melhores algoritmos encontrados para cada um desses critérios de desempenho nos problemas testados. / Evolutionary Algorithms that use the distribution of values of variables as probabilistic models (to direct the search process of problem solving) are called Estimation of Distribution Algorithms (EDAs). These algorithms have presented relevant performance in handling relatively complex problems. The performance of such algorithms depends directly on the quality of probabilistic models constructed that, in turn, depend on the methods of model building. The best models are often constructed by computationally complex methods, resulting in AEDs that require high running time although they are able to explore less points in the search space to find the solution of a problem. This work investigates probabilistic models obtained by algorithms of phylogeny reconstruction since some of them can produce models in an efficient way representing the main relationships among species (or among variables). This work proposes some strategies for better use of phylogeny-based models in the development of EDAs, such as the employment of a set of phylogenies instead of only one phylogeny as a model of correlation among variables, the synthesis of the most relevant information from a set of phylogenies into a structure of network and the identification groups of correlated variables from one or more networks by an algorithm of community detection. Using those advances for model construction, a new search technique, called Composed Exhaustive Search, was developed in order to find solutions for combinatorial optimization problems with different levels of difficulty. In addition, an extension of the new algorithm for multi-objective problems was proposed, which was able to determine the Pareto-optimal front of the combinatorial problems investigated. Finally, the developed EDA makes possible to obtain a trade-off in terms of number of evaluations and running time, finding results that are similar to the ones achieved by the best algorithms found for each one of these performance criteria in the problems tested.

Estimation of Distribution Algorithms (EDAs) belong to the class of population based optimisation algorithms. They are motivated by the idea of discovering and exploiting the interaction between variables in the solution. They estimate a probability distribution from population of solutions, and sample it to generate the next population. Many EDAs use probabilistic graphical modelling techniques for this purpose. In particular, directed graphical models (Bayesian networks) have been widely used in EDA. This thesis proposes an undirected graphical model (Markov Random Field (MRF)) approach to estimate and sample the distribution in EDAs. The interaction between variables in the solution is modelled as an undirected graph and the joint probability of a solution is factorised as a Gibbs distribution. The thesis describes a model of fitness function that approximates the energy in the Gibbs distribution, and shows how this model can be fitted to a population of solutions to estimate the parameters of the MRF. The estimated MRF is then sampled to generate the next population. This approach is applied to estimation of distribution in a general framework of an EDA, called Distribution Estimation using Markov Random Fields (DEUM). The thesis then proposes several variants of DEUM using different sampling techniques and tests their performance on a range of optimisation problems. The results show that, for most of the tested problems, the DEUM algorithms significantly outperform other EDAs, both in terms of number of fitness evaluations and the quality of the solutions found by them. There are two main explanations for the success of DEUM algorithms. Firstly, DEUM builds a model of fitness function to approximate the MRF. This contrasts with other EDAs, which build a model of selected solutions. This allows DEUM to use fitness in variation part of the evolution. Secondly, DEUM exploits the temperature coefficient in the Gibbs distribution to regulate the behaviour of the algorithm. In particular, with higher temperature, the distribution is closer to being uniform and with lower temperature it concentrates near some global optima. This gives DEUM an explicit control over the convergence of the algorithm, resulting in better optimisation.

Submitted by Caroline Xavier (caroline.xavier@pucrs.br) on 2017-06-29T11:51:00Z No. of bitstreams: 1 DIS_HENRY_EMANUEL_LEAL_CAGNINI_COMPLETO.pdf: 3650909 bytes, checksum: 55d52061a10460875dba677a9812fe9c (MD5) / Made available in DSpace on 2017-06-29T11:51:00Z (GMT). No. of bitstreams: 1 DIS_HENRY_EMANUEL_LEAL_CAGNINI_COMPLETO.pdf: 3650909 bytes, checksum: 55d52061a10460875dba677a9812fe9c (MD5) Previous issue date: 2017-03-20 / Extrair informa??es relevantes a partir de dados n?o ? uma tarefa f?cil. Tais dados podem vir a partir de lotes ou em fluxos cont?nuos, podem ser completos ou possuir partes faltantes, podem ser duplicados, e tamb?m podem ser ruidosos. Ademais, existem diversos algoritmos que realizam tarefas de minera??o de dados e, segundo o teorema do "Almo?o Gr?tis", n?o existe apenas um algoritmo que venha a solucionar satisfatoriamente todos os poss?veis problemas. Como um obst?culo final, algoritmos geralmente necessitam que hiper-par?metros sejam definidos, o que n?o surpreendentemente demanda um m?nimo de conhecimento sobre o dom?nio da aplica??o para que tais par?metros sejam corretamente definidos. J? que v?rios algoritmos tradicionais empregam estrat?gias de busca local gulosas, realizar um ajuste fino sobre estes hiper-par?metros se torna uma etapa crucial a fim de obter modelos preditivos de qualidade superior. Por outro lado, Algoritmos de Estimativa de Distribui??o realizam uma busca global, geralmente mais eficiente que realizar uma buscam exaustiva sobre todas as poss?veis solu??es para um determinado problema. Valendo-se de uma fun??o de aptid?o, algoritmos de estimativa de distribui??o ir?o iterativamente procurar por melhores solu??es durante seu processo evolutivo. Baseado nos benef?cios que o emprego de algoritmos de estimativa de distribui??o podem oferecer para as tarefas de agrupamento e indu??o de ?rvores de decis?o, duas tarefas de minera??o de dados consideradas NP-dif?cil e NP-dif?cil/completo respectivamente, este trabalho visa desenvolver novos algoritmos de estimativa de distribui??o a fim de obter melhores resultados em rela??o a m?todos tradicionais que empregam estrat?gias de busca local gulosas, e tamb?m sobre outros algoritmos evolutivos. / Extracting meaningful information from data is not an easy task. Data can come in batches or through a continuous stream, and can be incomplete or complete, duplicated, or noisy. Moreover, there are several algorithms to perform data mining tasks, and the no-free lunch theorem states that there is not a single best algorithm for all problems. As a final obstacle, algorithms usually require hyperparameters to be set in order to operate, which not surprisingly often demand a minimum knowledge of the application domain to be fine-tuned. Since many traditional data mining algorithms employ a greedy local search strategy, fine-tuning is a crucial step towards achieving better predictive models. On the other hand, Estimation of Distribution Algorithms perform a global search, which often is more efficient than performing a wide search through the set of possible parameters. By using a quality function, estimation of distribution algorithms will iteratively seek better solutions throughout its evolutionary process. Based on the benefits that estimation of distribution algorithms may offer to clustering and decision tree-induction, two data mining tasks considered to be NP-hard and NPhard/ complete, respectively, this works aims at developing novel algorithms in order to obtain better results than traditional, greedy algorithms and baseline evolutionary approaches.

Estimation of Distribution Algorithm (EDA) is a branch of evolutionary computation that learn a probabilistic model of good solutions. Probabilistic models are used to represent relationships between solution variables which may give useful, human-understandable insights into real-world problems. Also, developing an effective PM has been shown to significantly reduce function evaluations needed to reach good solutions. This is also useful for real-world problems because their representations are often complex needing more computation to arrive at good solutions. In particular, many real-world problems are naturally represented as permutations and have expensive evaluation functions. EDAs can, however, be computationally expensive when models are too complex. There has therefore been much recent work on developing suitable EDAs for permutation representation. EDAs can now produce state-of-the-art performance on some permutation benchmark problems. However, models are still complex and computationally expensive making them hard to apply to real-world problems. This study investigates some limitations of EDAs in solving permutation and scheduling problems. The focus of this thesis is on addressing redundancies in the Random Key representation, preserving diversity in EDA, simplifying the complexity attributed to the use of multiple local improvement procedures and transferring knowledge from solving a benchmark project scheduling problem to a similar real-world problem. In this thesis, we achieve state-of-the-art performance on the Permutation Flowshop Scheduling Problem benchmarks as well as significantly reducing both the computational effort required to build the probabilistic model and the number of function evaluations. We also achieve competitive results on project scheduling benchmarks. Methods adapted for solving a real-world project scheduling problem presents significant improvements.

This thesis studies grammar-based approaches in the application of Estimation of Distribution Algorithms (EDA) to the tree representation widely used in Genetic Programming (GP). Although EDA is becoming one of the most active fields in Evolutionary computation (EC), the solution representation in most EDA is a Genetic Algorithms (GA) style linear representation. The more complex tree representations, resembling GP, have received only limited exploration. This is unfortunate, because tree representations provide a natural and expressive way of representing solutions for many problems. This thesis aims to help fill this gap, exploring grammar-based approaches to extending EDA to GP-style tree representations. This thesis firstly provides a comprehensive survey of current research on EDA with emphasis on EDA with GP-style tree representation. The thesis attempts to clarify the relationship between EDA with conventional linear representations and those with a GP-style tree representation, and to reveal the unique difficulties which face this research. Secondly, the thesis identifies desirable properties of probabilistic models for EDA with GP-style tree representation, and derives the PRODIGY framework as a consequence. Thirdly, following the PRODIGY framework, three methods are proposed. The first method is Program Evolution with Explicit Learning (PEEL). Its incremental general-to-specific grammar learning method balances the effectiveness and efficiency of the grammar learning. The second method is Grammar Model-based Program Evolution (GMPE). GMPE realises the PRODIGY framework by introducing elegant inference methods from the formal grammar field. GMPE provides good performance on some problems, but also provides a means to better understand some aspects of conventional GP, especially the building block hypothesis. The third method is Swift GMPE (sGMPE), which is an extension of GMPE, aiming at reducing the computational cost. Fourthly, a more accurate Minimum Message Length metric for grammar learning in PRODIGY is derived in this thesis. This metric leads to improved performance in the GMPE system, but may also be useful in grammar learning in general. It is also relevant to the learning of other probabilistic graphical models.

Les métaheuristiques sont une famille d'algorithmes stochastiques destinés à résoudre des problèmes d 'optimisation difficile . Utilisées dans de nombreux domaines, ces méthodes présentent l'avantage d'être généralement efficaces, sans pour autant que l'utilisateur ait à modifier la structure de base de l'algorithme qu'il utilise. Parmi celles-ci, l'Optimisation par Essaim Particulaire (OEP) est une nouvelle classe d'algorithmes proposée pour résoudre les problèmes à variables continues. Les algorithmes d'OEP s'inspirent du comportement social des animaux évoluant en essaim, tels que les oiseaux migrateurs ou les poissons. Les particules d'un même essaim communiquent de manière directe entre elles tout au long de la recherche pour construire une solution au problème posé, en s'appuyant sur leur expérience collective. Reconnues depuis de nombreuses années pour leur efficacité, les métaheuristiques présentent des défauts qui rebutent encore certains utilisateurs. Le réglage des paramètres des algorithmes est un de ceux-ci. Il est important, pour chaque problème posé, de trouver le jeu de paramètres qui conduise à des performances optimales de l'algorithme. Cependant, cette tâche est fastidieuse et coûteuse en temps, surtout pour les utilisateurs novices. Pour s'affranchir de ce type de réglage, des recherches ont été menées pour proposer des algorithmes dits adaptatifs . Avec ces algorithmes, les valeurs des paramètres ne sont plus figées, mais sont modifiées, en fonction des résultats collectés durant le processus de recherche. Dans cette optique-là, Maurice Clerc a proposé TRIBES, qui est un algorithme d'OEP mono-objectif sans aucun paramètre de contrôle. Cet algorithme fonctionne comme une boîte noire , pour laquelle l'utilisateur n'a qu'à définir le problème à traiter et le critère d'arrêt de l'algorithme. Nous proposons dans cette thèse une étude comportementale de TRIBES, qui permet d'en dégager les principales qualités et les principaux défauts. Afin de corriger certains de ces défauts, deux modules ont été ajoutés à TRIBES. Une phase d'initialisation régulière est insérée, afin d'assurer, dès le départ de l'algorithme, une bonne couverture de l'espace de recherche par les particules. Une nouvelle stratégie de déplacement, basée sur une hybridation avec un algorithme à estimation de distribution, est aussi définie, afin de maintenir la diversité au sein de l'essaim, tout au long du traitement. Le besoin croissant de méthodes de résolution de problèmes multiobjectifs a conduit les concepteurs à adapter leurs méthodes pour résoudre ce type de problème. La complexité de cette opération provient du fait que les objectifs à optimiser sont souvent contradictoires. Nous avons élaboré une version multiobjectif de TRIBES, dénommée MO-TRIBES. Nos algorithmes ont été enfin appliqués à la résolution de problèmes de seuillage d'images médicales et au problème de dimensionnement de composants de circuits analogiques

[pt] Algoritmos de estimação de distribuição (EDAs – Estimation of Distribution Algorithms) são uma classe de algoritmos evolutivos capazes de extrair e utilizar conhecimento ao longo do processo de busca. O passo mais importante e um gargalo, que estabelece diferenciação entre esses algoritmos, é a estimação da distribuição de probabilidade conjunta das soluções mais promissoras determinadas pela função de avaliação. Recentemente, uma nova abordagem baseada em teoria das cópulas foi desenvolvida. Este trabalho apresenta um algoritmo de estimação baseado em cópulas para problemas de otimização numérica. Este modelo implementa um EDA através da expansão multivariada de cópulas (EDA-MEC – Estimation of Distribution Algorithm based on Multivariate Extension of Copulas) para estimar a distribuição de probabilidade da qual é gerada uma população de indivíduos. O EDA-MEC difere de outros EDAs baseados em cópulas em alguns aspectos: o parâmetro de cópula é estimado de forma dinâmica, através de medidas de dependência; utiliza uma variação da distribuição de probabilidade aprendida para gerar indivíduos que ajudam a evitar a convergência prematura; e utiliza uma heurística para reinicializar a população ao longo da evolução elitista como uma técnica adicional para tentar preservar a diversidade de soluções. Após um conjunto de testes de parâmetros, inclusive das distribuições marginais, este trabalho mostra que estas abordagens melhoram o desempenho global da otimização comparativamente a outros EDAs baseados em cópulas, com a perspectiva promissora de ser um algoritmo competitivo frente a outras heurísticas comprovadamente eficientes, tais como a Estratégia Evolutiva com Adaptação da Matriz de Covariância (CMA-ES - Covariance Matrix Adaptation Evolution Strategy). / [en] Estimation of distribution algorithms constitute a class of evolutionary algorithms that can extract and use knowledge acquired throughout the search process. Its most important step that differs most among EDAs, and also a bottleneck, is the estimation of the joint probability distribution associated with the variables from the most promising solutions determined by the evaluation function. Recently, a new approach to EDAs has been developed that is based on copula theory. This work presents a copula-based estimation of distribution algorithm for numeric optimization problems. This model implements an estimation of distribution algorithm using a Multivariate Extension of Copulas (EDA-MEC) to estimate the probability distribution for generating a population of individuals. EDA-MEC differs from other copula-based EDAs in some aspects: the copula parameter is estimated dynamically, using dependency measures; it uses a variation of the learned probability distribution to generate individuals that help to avoid premature convergence; and it uses a heuristic to reinitialize the population throughout an elitist evolution as an additional technique to try to preserve the diversity of solutions. After a set of parametric tests, including marginal distributions, this work shows that these approaches improve the overall performance of the optimization compared to other copula-based EDAs and promises to be a competitive algorithm compared to other efficient heuristics, such as Covariance Matrix Adaptation Evolution Strategy (CMA-ES).

Tato diplomová práce se zabývá Weibullovými modely, přesněji dvouparametrickým Weibullovým rozdělením. Práce se zabývá odhady parametrů, a to čtyřmi variantami kvantilové metody, metodou maximální věrohodnosti a grafickou metodou Weibullova pravděpodobnostního grafu. Je uvedeno odvození odhadu parametrů pro jednovýběrovou analýzu rozptylu pro Weibullovo rozdělení. Jsou zde odvozeny vztahy pro model s konstantním parametrem alfa, s konstantním parametrem beta a s oběma konstantními parametry. Také jsou uvedeny testové statistiky pro rušivé parametry - skórový test, Waldův test a test založený na věrohodnostním poměru. V poslední kapitole je provedena aplikace jednotlivých představených metod. Srovnání metod je ukázáno pomocí grafů, histogramů a tabulek. Metody jsou naprogramovány v~softwaru R. Jejich funkčnost a vlastnosti jsme ověřili na dvou simulovaných souborech dat. Diplomová práce je zakončena příkladem tří simulovaných náhodných výběrů, na kterých byla provedena analýza pomocí zavedených metod.

In my thesis I~ deal with the design, implementation and testing of the advanced parallel Estimation of Distribution Algorithm (EDA) utilizing copula theory to create a~ probabilistic model. A~new population is created by the process of sampling the joint distribution function, which models the current distribution of the subpopulation of promising individuals . The usage of copulas increases the efficiency of the learning process and sampling the probabilistic model. It can be separated into mutually independent marginal distributions and the copula , which represents the correlations between the variables of the solved problem. This concept initiated the usage of the parallel island architecture , in which the migration of probabilistic models belonging to individual islands ' subpopulations was used instead of the migration of individuals . The statistical tests used in the comparison of the proposed algorithm ( mCEDA = migrating Copula - based Estimation of Distribution Algorithm ) and the algorithms of other authors confirmed the effectiveness of the proposed concept .