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Algoritmos de estimação de distribuição Estimation of distribution algorithm Algoritmo de estimación de distribución Estimation of Distribution Algorithmus Algorithme à estimation de distribution
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Les algorithmes à estimation de distribution (Estimation of Distribution Algorithms, EDA, en anglais) forment une famille de métaheuristiques inspirée des algorithmes génétiques. Ils sont utilisés pour résoudre des problèmes d'optimisation, via la manipulation d'un échantillonnage de la fonction décrivant la qualité des solutions possibles. Comme toutes les métaheuristiques utilisant une population de points, ils sont itératifs. Algoritmos de estimação de distribuição (AED) são métodos evolutivos que utilizam técnicas de estimação de distribuição ao invés de operadores genéticos . AED's são consequência dos algoritmos genéticos, sendo motivados pela deficiência destes, principalmente pela sua incapacidade de representar e manipular as dependências entre as variáveis. Este problema é conhecido como linkage problem. Estimation of Distribution Algorithmen (EDA) (engl., etwa: Schätzung der Verteilung) sind evolutionäre Algorithmen, also Verfahren, die mit den Prinzipien der Evolution Optimierungsprobleme lösen. Im Fall von EDA wird während der Berechnung iterativ ein probabilistisches Modell entwickelt, das aufgrund der gemachten Stichproben das gesuchte Optimum schätzt. Während im Modell zu Beginn alle zulässigen Lösungen für das gegebene Problem gleich verteilt sind, wird im Erfolgsfall am Ende nur das gesuchte Optimum vorgeschlagen. Der Algorithmus stellt eine Verallgemeinerung des genetischen Algorithmus dar, der die Verteilung nur implizit schätzt. Die Motivation zur Entwicklung von EDA war die Tatsache, dass die Auswahl geeigneter Parameter für klassische evolutionäre Algorithmen (wie z. B. Mutati Los Algoritmos de Estimación de Distribución (AED) constituyen una familia de metaheurísticas derivadas de los algoritmos evolutivos. A diferencia de los algoritmos evolutivos "clásicos", en donde se busca encontrar una solución a un problema codificando directamente sus variables, los AED buscan estimar la distribución de probabilidad de cada variable. La población de soluciones candidatas se recrea en cada generación, a partir de la distribución de probabilidad obtenida a partir de los mejores individuos de la generación anterior. Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates of a probabilistic model, starting with the model encoding an uninformative prior over admissible solutions and ending with the model that generates only the global optima. The general procedure of an EDA is outlined in the following:
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Los Algoritmos de Estimación de Distribución (AED) constituyen una familia de metaheurísticas derivadas de los algoritmos evolutivos. A diferencia de los algoritmos evolutivos "clásicos", en donde se busca encontrar una solución a un problema codificando directamente sus variables, los AED buscan estimar la distribución de probabilidad de cada variable. La población de soluciones candidatas se recrea en cada generación, a partir de la distribución de probabilidad obtenida a partir de los mejores individuos de la generación anterior. Dado que la población no se regenera a partir de individuos, sino desde las distribuciones de probabilidad obtenidas, no existen operadores de ni de mutación Algoritmos de estimação de distribuição (AED) são métodos evolutivos que utilizam técnicas de estimação de distribuição ao invés de operadores genéticos . AED's são consequência dos algoritmos genéticos, sendo motivados pela deficiência destes, principalmente pela sua incapacidade de representar e manipular as dependências entre as variáveis. Este problema é conhecido como linkage problem. Em seu trabalho seminal sobre algoritmos genéticos, Holland já havia reconhecido que, se a interação das variáveis fosse utilizada, certamente traria benefícios aos algoritmos genéticos. Esta fonte de informação, até então inexplorada, foi chamada de informação de ligação (linkage information). Assim, para contornar estes obstáculos dos algoritmos genéticos, os AEDs representam explicitamente as dependências entre as variáveis através de modelos probabilísticos, como desde simples representação em vetores de probabilidades até modelos mais complexos, como rede bayesiana, estruturas em árvore (grafo), cadeias de Markov, entre outras. Os AEDs utilizam estes modelos probabilísticos como guias para desempenhar a busca em um determinado espaço de soluções. Considere o seguinte exemplo de um AED. Seja uma população representada por vetores binários de comprimento 4. O AED pode empregar um único vetor composto por 4 probabilidades onde cada é a probabilidade da posição receber o valor 1. Usando este vetor de probabilidades é possível criar qualquer quantidade de soluções candidatas. Ao fim de cada geração, este vetor de probabilidades vai sendo atualizado segundo os melhores indivíduos da geração corrente. Estimation of Distribution Algorithmen (EDA) (engl., etwa: Schätzung der Verteilung) sind evolutionäre Algorithmen, also Verfahren, die mit den Prinzipien der Evolution Optimierungsprobleme lösen. Im Fall von EDA wird während der Berechnung iterativ ein probabilistisches Modell entwickelt, das aufgrund der gemachten Stichproben das gesuchte Optimum schätzt. Während im Modell zu Beginn alle zulässigen Lösungen für das gegebene Problem gleich verteilt sind, wird im Erfolgsfall am Ende nur das gesuchte Optimum vorgeschlagen. Der Algorithmus stellt eine Verallgemeinerung des genetischen Algorithmus dar, der die Verteilung nur implizit schätzt. Die Motivation zur Entwicklung von EDA war die Tatsache, dass die Auswahl geeigneter Parameter für klassische evolutionäre Algorithmen (wie z. B. Mutationsstärke oder Populationsgröße) selbst ein Optimierungsproblem darstellt. John H. Holland vermutete schon 1975, dass die Abhängigkeiten der zu optimierenden Variablen einen Ansatzpunkt darstellen, den evolutionäre Algorithmen ausnutzen könnten. Les algorithmes à estimation de distribution (Estimation of Distribution Algorithms, EDA, en anglais) forment une famille de métaheuristiques inspirée des algorithmes génétiques. Ils sont utilisés pour résoudre des problèmes d'optimisation, via la manipulation d'un échantillonnage de la fonction décrivant la qualité des solutions possibles. Comme toutes les métaheuristiques utilisant une population de points, ils sont itératifs. À l'inverse des algorithmes évolutionnaires « classiques », le cœur de la méthode consiste à estimer les relations entre les différentes variables d'un problème d'optimisation, grâce à l'estimation d'une distribution de probabilité, associée à chaque point de l'échantillon. Ils n'emploient donc pas d'opérateurs de croisement ou de mutation, l'échantillon étant directement construit à partir des paramètres de distribution, estimés à l'itération précédente. Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates of a probabilistic model, starting with the model encoding an uninformative prior over admissible solutions and ending with the model that generates only the global optima. EDAs belong to the class of evolutionary algorithms. The main difference between EDAs and most conventional evolutionary algorithms is that evolutionary algorithms generate new candidate solutions using an implicit distribution defined by one or more variation operators, whereas EDAs use an explicit probability distribution encoded by a Bayesian network, a multivariate normal distribution, or another model class. Similarly as other evolutionary algorithms, EDAs can be used to solve optimization problems defined over a number of representations from vectors to LISP style S expressions, and the quality of candidate solutions is often evaluated using one or more objective functions. The general procedure of an EDA is outlined in the following: t := 0initialize model M(0) to represent uniform distribution over admissible solutionswhile (termination criteria not met) do P := generate N>0 candidate solutions by sampling M(t) F := evaluate all candidate solutions in P M(t + 1) := adjust_model(P, F, M(t)) t := t + 1 Using explicit probabilistic models in optimization allowed EDAs to feasibly solve optimization problems that were notoriously difficult for most conventional evolutionary algorithms and traditional optimization techniques, such as problems with high levels of epistasis. Nonetheless, the advantage of EDAs is also that these algorithms provide an optimization practitioner with a series of probabilistic models that reveal a lot of information about the problem being solved. This information can in turn be used to design problem-specific neighborhood operators for local search, to bias future runs of EDAs on a similar problem, or to create an efficient computational model of the problem. For example, if the population is represented by bit strings of length 4, the EDA can represent the population of promising solution using a single vector of four probabilities (p1, p2, p3, p4) where each component of p defines the probability of that position being a 1. Using this probability vector it is possible to create an arbitrary number of candidate solutions.
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