Enrique R. Villa-Diharce

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

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.

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.

An estimation distribution algorithm with the spearman's rank correlation index

This article arguments that rank correlation coefficients are powerful association measures and how can they be adopted by EDAs. A new EDA implements the proposed ideas: the Non-Parametric Real-valued Estimation Distribution Algorithm (NOPREDA). The paper fully describes the rank correlation coefficient, and the procedure to build a non parametric model for the probability distribution of the source data. A benchmark of global optimization problems is solved with NOPREDA.

Using the value of Lin’s concordance correlation coefficient as a criterion for efficient estimation of areas of leaves of eelgrass from noisy digital images

BackgroundEelgrass is a cosmopolitan seagrass species that provides important ecological services in coastal and near-shore environments. Despite its relevance, loss of eelgrass habitats is noted worldwide. Restoration by replanting plays an important role, and accurate measurements of the standing crop and productivity of transplants are important for evaluating restoration of the ecological functions of natural populations. Traditional assessments are destructive, and although they do not harm natural populations, in transplants the destruction of shoots might cause undesirable alterations. Non-destructive assessments of the aforementioned variables are obtained through allometric proxies expressed in terms of measurements of the lengths or areas of leaves. Digital imagery could produce measurements of leaf attributes without the removal of shoots, but sediment attachments, damage infringed by drag forces or humidity contents induce noise-effects, reducing precision. Available techniques for dealing with noise caused by humidity contents on leaves use the concepts of adjacency, vicinity, connectivity and tolerance of similarity between pixels. Selection of an interval of tolerance of similarity for efficient measurements requires extended computational routines with tied statistical inferences making concomitant tasks complicated and time consuming. The present approach proposes a simplified and cost-effective alternative, and also a general tool aimed to deal with any sort of noise modifying eelgrass leaves images. Moreover, this selection criterion relies only on a single statistics; the calculation of the maximum value of the Concordance Correlation Coefficient for reproducibility of observed areas of leaves through proxies obtained from digital images.ResultsAvailable data reveals that the present method delivers simplified, consistent estimations of areas of eelgrass leaves taken from noisy digital images. Moreover, the proposed procedure is robust because both the optimal interval of tolerance of similarity and the reproducibility of observed leaf areas through digital image surrogates were independent of sample size.ConclusionThe present method provides simplified, unbiased and non-destructive measurements of eelgrass leaf area. These measurements, in conjunction with allometric methods, can predict the dynamics of eelgrass biomass and leaf growth through indirect techniques, reducing the destructive effect of sampling, fundamental to the evaluation of eelgrass restoration projects thereby contributing to the conservation of this important seagrass species.

The gaussian polytree EDA for global optimization

This paper explains how to construct Gaussian polytrees and their application to estimation of distribution algorithms in continuous variables.

Using Gaussian Copulas in Supervised Probabilistic Classification

This chapter 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 Kendall’s τ. Hence, this chapter 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.

Particle Evolutionary Swarm Multi-Objective Optimization for Vehicle Routing Problem with Time Windows

The Vehicle Routing Problem with Time Windows (VRPTW), is an extension to the standard vehicle routing problem. VRPTW includes an additional constraint that restricts every customer to be served within a given time window. An approach for the VRPTW with the next three objectives is presented: 1)total distance (or time), 2)total waiting time, 3)number of vehicles. A data mining strategy, namely space partitioning, is adopted in this work. Optimal routes are extracted as features hidden in variable size regions where depots and customers are located. This chapter proposes the sector model for partitioning the space into regions. A new hybrid Particle Swarm Optimization algorithm (PSO), and combinatorial operators ad-hoc with space partitioning are described. A set of well-known benchmark functions in VRPTW are used to compare the effectiveness of the proposed method. The results show the importance of examining characteristics of a set of non-dominated solutions, that fairly consider the three dimensions, when a user should select only one solution according to problem conditions.