A further result on the Markov chain model of genetic algorithms and its application to a simulated annealing-like strategy

“…Diversos trabalhos buscam analisar a estabilidade e a convergência de um algoritmo de busca (algoritmos genéticos, programação evolucionária e otimização por enxame de partículas, por exemplo) usando desde critérios de estabilidade assintótica derivados do Controle de Processos [29][30][31], dado que um algoritmo pode ser considerado um processo dinâmico, até a modelagem do algoritmo de busca como uma cadeia de Markov [32][33][34][35][36][37][38][39], uma vez que o espaço de buscaé finito e contável, dadas as limitações de representação numérica em sistemas computacionais, sendo o ponto de máximo/mínimo considerado um estado da cadeia.…”

Section: Análise Pelo Método Da Máxima Entropiaunclassified

Avaliação do Método Dialético na Quantização de Imagens Multiespectrais

Santos¹,

Assis²

2010

L&NLM

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Resumo -A classificação não supervisionada tem um papel muito importante na análise de imagens multiespectrais, dada a sua capacidade para auxiliar a extração de conhecimento a priori de imagens. Algoritmos como k-médias e fuzzy c-médias tem sido muito utilizados nessa tarefa. A Inteligência Computacional tem-se mostrado como um importante campo para auxiliar na construção de classificadores otimizados, tanto quantoà qualidade do agrupamento de classes, quantoà avaliação da qualidade da quantização vetorial. Diversos trabalhos têm mostrado que a Filosofia, em especial o Método Dialético, tem servido como importante inspiração para a construção de novos métodos computacionais. Este trabalho apresenta uma avaliação de quatro métodos baseados na Dialética: o Classificador Dialético Objetivo e o Método Dialético de Otimização adaptadoà construção de uma versão do k-médias otimizada segundoíndices de qualidade de agrupamento, cada um desses em uma versão canônica e em outra versão obtida pela aplicação do Princípio da Máxima Entropia. Esses métodos foram comparados aos métodos k-médias, fuzzy c-médias e mapa auto-organizado de Kohonen. Os resultados mostraram que os métodos baseados na Dialética são robustos ao ruído e podem atingir resultados de quantização tão bons quanto aqueles obtidos com o mapa de Kohonen, considerado um quantizadorótimo.Palavras-chave -Segmentação de imagens, k-médias, dialética, otimização, princípio da máxima entropia, computação evolucionária. Abstract -The unsupervised classification has a very important role in the analysis of multispectral images, given its ability to assist the extraction of a priori knowledge of images. Algorithms like k-means and fuzzy c-means has long been used in this task. Computational Intelligence has proven to be an important field to assist in building classifiers optimized according to the quality of the grouping of classes and the evaluation of the quality of vector quantization. Several studies have shown that Philosophy, especially the Dialectical Method, has served as an important inspiration for the construction of new computational methods. This paper presents an evaluation of four methods based on the Dialectics: the Objective Dialectical Classifier and the Dialectical Optimization Method adapted to build a version of k-means with optimal quality indices; each of them is presented in two versions: a canonical version and another version obtained by applying the Principle of Maximum Entropy. These methods were compared to k-means, fuzzy c-means and Kohonen's self-organizing maps. The results showed that the methods based on Dialectics are robust to noise, and quantization can achieve results as good as those obtained with the Kohonen map, considered an optimal quantizer. Keywords -Image segmentation, k-means, dialectics, optimization, principle of maximum entropy, evolutionary computation. IntroduçãoDiversos trabalhos mostram queé possível construir um algoritmo para classificação não supervisionada de imagens baseado no método dialético [1][2][3][4][5]....

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“…It is well known that EAs can be measured by Markov chain [15], [33], [34]. Consequently, the following concept of first hitting time defined for Markov chains can be used to measure the time complexity of EAs.…”

Section: B Mathematical Concepts and Toolsmentioning

confidence: 99%

“…In this paper, we develop a new general approach to analyze the time complexity of the population-based EAs on unimodal problems, which is based on some well-known concept and models of EAs, such as the takeover time [11], the Markov chain model [9], [15], [33], [34], and the supermartingale model [12], [13], [16], [29]. First, we generalize the original concept of takeover time introduced by Goldberg and Deb [11]: Rather than for a selection operator alone, the takeover time is generalized for EAs with mutation operators in this paper.…”

mentioning

confidence: 99%

A New Approach for Analyzing Average Time Complexity of Population-Based Evolutionary Algorithms on Unimodal Problems

Chen

Sun

et al. 2009

IEEE Trans. Syst., Man, Cybern. B

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Abstract-In the past decades, many theoretical results related to the time complexity of evolutionary algorithms (EAs) on different problems are obtained. However, there is not any general and easy-to-apply approach designed particularly for populationbased EAs on unimodal problems. In this paper, we first generalize the concept of the takeover time to EAs with mutation, then we utilize the generalized takeover time to obtain the mean first hitting time of EAs and, thus, propose a general approach for analyzing EAs on unimodal problems. As examples, we consider the so-called (N + N ) EAs and we show that, on two well-known unimodal problems, LEADINGONES and ONEMAX, the EAs with the bitwise mutation and two commonly used selection schemes both need O(n ln n + n 2 /N ) and O(n ln ln n + n ln n/N ) generations to find the global optimum, respectively. Except for the new results above, our approach can also be applied directly for obtaining results for some population-based EAs on some other unimodal problems. Moreover, we also discuss when the general approach is valid to provide us tight bounds of the mean first hitting times and when our approach should be combined with problem-specific knowledge to get the tight bounds. It is the first time a general idea for analyzing population-based EAs on unimodal problems is discussed theoretically.

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A further result on the Markov chain model of genetic algorithms and its application to a simulated annealing-like strategy

Cited by 71 publications

References 14 publications

On the stationary distribution of GAs with fixed crossover probability

On the stationary distribution of GAs with fixed crossover probability

Avaliação do Método Dialético na Quantização de Imagens Multiespectrais

A New Approach for Analyzing Average Time Complexity of Population-Based Evolutionary Algorithms on Unimodal Problems

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