Arturo Hernández-Aguirre

Using Copulas in Estimation of Distribution Algorithms

A new way of modeling probabilistic dependencies in Estimation of Distribution Algorithm (EDAs) is presented. By means of copulas it is possible to separate the structure of dependence from marginal distributions in a joint distribution. The use of copulas as a mechanism for modeling joint distributions and its application to EDAs is illustrated on several benchmark examples.

D-vine EDA: a new estimation of distribution algorithm based on regular vines

A new Estimation of Distribution Algorithm is presented. The proposed algorithm, called D-vine EDA, uses a graphical model which is based on pair copula decomposition. By means of copula functions it is possible to model the dependence structure in a joint distribution with marginals of different type. Thus, this paper introduces the D-vine EDA and performs experiments and statistical tests to assess the best algorithm. The set of experiments shows the potential of the D-vine EDA

G-Metric: an M-ary quality indicator for the evaluation of non-dominated sets

An open problem in multiobjective optimization using the Pareto optimality criteria, is how to evaluate the performance of different evolutionary algorithms that solve multi-objective problems. As the output of these algorithms is a non-dominated set (NS), this problem can be reduced to evaluate what NS is better than the others based on their projection on the objective space. In this work we propose a new performance measure for the evaluation of non-dominated sets, that ranks a set of NSs based on their convergence and dispersion. Its evaluations of the NSs agree with intuition. Also, we introduce a benchmark of test cases to evaluate performance measures, that considers several topologies of the Pareto Front.An open problem in multiobjective optimization using the Pareto optimality criteria, is how to evaluate the performance of different evolutionary algorithms that solve multi-objective problems. As the output of these algorithms is a non-dominated set (NS), this problem can be reduced to evaluate what NS is better than the others based on their projection on the objective space. In this work we propose a new performance measure for the evaluation of non-dominated sets, that ranks a set of NSs based on their convergence and dispersion. Its evaluations of the NSs agree with intuition. Also, we introduce a benchmark of test cases to evaluate performance measures, that considers several topologies of the Pareto Front.

Approximating the search distribution to the selection distribution in EDAs

In an Estimation of Distribution Algorithm (EDA) with an infinite sized population the selection distribution equals the search distribution. For a finite sized population these distributions are different. In practical EDAs the goal of the search distribution learning algorithm is to approximate the selection distribution. The source data is the selected set, which is derived from the population by applying a selection operator. The new approach described here eliminates the explicit use of the selection operator and the selected set. We rewrite for a finite population the selection distribution equations of four selection operators. The new equation is called the empirical selection distribution. Then we show how to build the search distribution that gives the best approximation to the empirical selection distribution. Our approach gives place to practical EDAs which can be easily and directly implemented from well established theoretical results. This paper also shows how common EDAs with discrete and real variables are adapted to take advantage of the empirical selection distribution. A comparison and discussion of performance is presented.In an Estimation of Distribution Algorithm (EDA) with an infinite sized population the selection distribution equals the search distribution. For a finite sized population these distributions are different. In practical EDAs the goal of the search distribution learning algorithm is to approximate the selection distribution. The source data is the selected set, which is derived from the population by applying a selection operator. The new approach described here eliminates the explicit use of the selection operator and the selected set. We rewrite for a finite population the selection distribution equations of four selection operators. The new equation is called the empirical selection distribution. Then we show how to build the search distribution that gives the best approximation to the empirical selection distribution. Our approach gives place to practical EDAs which can be easily and directly implemented from well established theoretical results. This paper also shows how common EDAs with discrete and real variables are adapted to take advantage of the empirical selection distribution. A comparison and discussion of performance is presented.

On the performance of nature inspired algorithms for the automatic segmentation of coronary arteries using Gaussian matched filters

Graphical abstractDisplay Omitted HighlightsNature inspired algorithms are used for the optimal parameter selection of Gaussian filters.Comparative analysis shows that differential evolution is efficient to work with GMF.The proposed GMF-DE method achieved a detection rate of 0.9402 on a training set.GMF-DE achieved a coronary artery segmentation rate of 0.9134 on a test set.The proposal reports the highest performance compared with state-of-the-art methods. This paper presents a comparative analysis of four nature inspired algorithms to improve the training stage of a segmentation strategy based on Gaussian matched filters (GMF) for X-ray coronary angiograms. The statistical results reveal that the method of differential evolution (DE) outperforms the considered algorithms in terms of convergence to the optimal solution. From the potential solutions acquired by DE, the area (Az) under the receiver operating characteristic curve is used as fitness function to establish the best GMF parameters. The GMF-DE method demonstrated high accuracy with Az=0.9402 with a training set of 40 angiograms. Moreover, to evaluate the performance of the coronary artery segmentation method compared to the ground-truth vessels hand-labeled by a specialist, measures of sensitivity, specificity and accuracy have been adopted. According to the experimental results, GMF-DE has obtained high coronary artery segmentation rate compared with six state-of-the-art methods provided an average accuracy of 0.9134 with a test set of 40 angiograms. Additionally, the experimental results in terms of segmentation accuracy, have also shown that the GMF-DE can be highly suitable for clinical decision support in cardiology.

Estimation of distribution algorithms based on copula functions

The main objective of this doctoral research is to study Estimation of Distribution Algorithms (EDAs) based on copula functions. This new class of EDAs has shown that it is possible to incorporate successfully copula functions in EDAs.

Dependence trees with copula selection for continuous estimation of distribution algorithms

In this paper, a new Estimation of Distribution Algorithm (EDA) is presented. The proposed algorithm employs a dependency tree as a graphical model and bivariate copula functions for modeling relationships between pairwise variables. By selecting copula functions it is possible to build a very flexible joint distribution as a probabilistic model. The experimental results show that the proposed algorithm has a better performance than EDAs based on Gaussian assumptions.

A novel Gaussian matched filter based on entropy minimization for automatic segmentation of coronary angiograms

A new method for automatic segmentation of coronary arteries in X-ray angiograms is proposed.The proposed entropy minimization function obtains 0:97 of similarity with respect to the optimal Az value with the whole set of angiograms.The proposed Gaussian matched filter demonstrated high detection performance with Az = 0:945 with a test set of 45 angiograms.The proposed vessel segmentation method provided the highest accuracy (0:961) with the test set of angiograms. Display Omitted This paper presents a new method for automatic detection and segmentation of coronary arteries in X-ray angiograms. In the vessel detection stage, a novel Gaussian matched filter (GMF) based on an entropy minimization fitness function is used to detect blood vessels in angiographic images. The detection results of the proposed Gaussian matched filter are compared with those obtained by five state-of-the-art GMF-based methods using the area (Az) under the receiver operating characteristic (ROC) curve. In the second stage, the inter-class variance thresholding method has proven to be the most efficient compared with six different methods in order to classify vessel and non vessel pixels from the Gaussian filter response using the accuracy measure and the ground-truth angiograms drawn by a specialist. Finally, the proposed method is compared with eight state-of-the-art vessel segmentation methods. Due to the high rating of similarity (0.97) between the highest Az value and the Az value acquired by the fitness function over the whole dataset of angiograms, the result of vessel detection using the proposed GMF demonstrated high performance achieving A z = 0.945 with a test set of 45 angiograms. In addition, the results of vessel segmentation with the inter-class variance thresholding method provided an accuracy of 0.961 with the test set of angiograms.

Optimization of an Ethanol Dehydration Process Using Differential Evolution Algorithm

Abstract Due to the increasing demand for new fuels that are economically attractive, and as part of the quest for energy alternatives to replace carbon-based fuels, the purification of ethanol plays a key role. Bioethanol is an environmentally-friendly fuel with less greenhouse gases emissions than gasoline, but with similar energy power. Nevertheless the large-scale production of bioethanol fuel requires energy demanding distillation steps to concentrate the diluted streams from the fermentation step and to overcome the azeotropic behavior of the ethanol-water mixture. This work presents the design and optimization of a dehydration process for ethanol, using two separation sequences: a conventional arrangement using distillation and extractive distillation and an alternative arrangement based on liquid-liquid extraction and extractive distillation. Moreover, different solvents were optimized simultaneously in the liquid-liquid extraction column, while ethylene glycol was used as extractive agent in the extractive distillation (ED). Both sequences were optimized using a stochastic global optimization algorithm of differential evolution (DE) coupled to rigorous Aspen Plus simulations. The economic feasibility of utilities for the two configurations was studied by changing the ethanol/water composition in the analyzed feed stream. The results demonstrate significant savings around 20% in total annual cost when the alternative arrangement is used.

Supervised probabilistic classification based on Gaussian copulas

This paper introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendalls τ. Hence, this work studies the performance of a simple probabilistic classifier based on the Gaussian copula function. Without additional preprocessing of the source data, a supervised pixel classifier is tested with a 50-images benchmark; the experiments show this simple classifier has an excellent performance.