S. Ivvan Valdez

A Boltzmann based estimation of distribution algorithm

This paper introduces a new approach for estimation of distribution algorithms called the Boltzmann Univariate Marginal Distribution Algorithm (BUMDA). It uses a Normal-Gaussian model to approximate the Boltzmann distribution, hence, formulae for computing the mean and variance parameters of the Gaussian model are derived from the analytical minimization of the Kullback-Leibler divergence. The resulting formulae explicitly introduces information about the fitness landscape for the Gaussian parameters computation, in consequence, the Gaussian distribution obtains a better bias to sample intensively the most promising regions than simply using the maximum likelihood estimator of the selected set. In addition, the BUMDA formulae needs only one user parameter. Accordingly to the experimental results, the BUMDA excels in its niche of application. We provide theoretical, graphical and statistical analysis to show the BUMDA performance contrasted with state of the art EDAs.

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.

Efficient Estimation of Distribution Algorithms by using the Empirical Selection Distribution

Estimation of Distribution Algorithms (EDAs) (Muhlenbein et al., 1996; Muhlenbein & PaaB, 1996) are a promising area of research in evolutionary computation. EDAs propose to create models that can capture the dependencies among the decision variables. The widely known Genetic Algorithm could benefit from the available dependencies if the building blocks of the solution were correlated. However, it was proved that the building blocks of a genetic algorithm have a limited capacity for discovering and using complex relationships (correlations) among variables. EDAs instead, focus on learning probability distributions which serve as the vehicle to capture the data dependencies and the data structure as well. In order to show how the proposed method unifies the theory for infinite sized population with the finite sized population case of practical EDAs, we explain them first. An EDA with infinite sized population would perform the steps shown in the algorithm in Table 1.

Structure-control design of a mechatronic system with parallelogram mechanism using an estimation of distribution algorithm

ABSTRACT In this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of a parallelogram linkage robot is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process along with the controller. Thus, proportional-integral-derivative (PID) control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure an optimal combination of the robot structure and controller gains is obtained. The global optimization problem is tackled by using an estimation of distribution algorithm (EDA) based on the Boltzmann distribution. The EDA seeks for the global optimum by estimating and sampling a probability distribution. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposal. This approach is generic and could be applied to other mechanisms in similar way when for concurrent process both kinematic and dynamic models are available along with the controller. In particular, the results are promising when the optimization parameters are uncorrelated, namely control and mechanical parameters.

Design Optimization of a Cable-Driven Parallel Robot in Upper Arm Training-Rehabilitation Processes

This paper presents an optimized design of a cable driven parallel manipulator which is intended in rehabilitation or exercise of patients with shoulder problems like illness, traumatic events or for the elderly who need to exercise their limbs. Cable based parallel manipulators have characteristics that make them suitable for rehabilitation-exercise purposes like large workspace, re-configurable architecture, portability and low cost. From these purposes, upper-limb movements are analyzed and different prescribed workspaces are defined. After kinematic and wrench analysis, the Jacobian matrix of the cable driven manipulator is derived, which is used as a quantitative representation of dexterity along the workspace. An optimization model is presented to simultaneously fulfill the prescribed workspace and to improve dexterity by selecting proper length cables and other structural parameters. Numerical examples delineate effectiveness of an Estimation of Distribution Algorithm (EDA), where correlation among variables are inserted in the optimization process.

Concurrent Structure-Control Design of Parallel Robots Using an Estimation of Distribution Algorithm

In this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of parallel robots is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process. Thus, PID control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure, an optimal combination of the robot structure and control gains is obtained. An estimation of distribution algorithm (EDA) is formulated and used as the search algorithm. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposed methodology. The presented approach is generic and can be applied to other mechanisms with similar structure.

Approach in the Integrated Structure-Control Optimization of a 3RRR Parallel Robot

In this paper, an optimization methodology for the structure and control optimization of a 3RRR planar parallel robot is presented. The proposal consists of three stages in cascade: firstly, we optimize the geometry for a maximum workspace. Secondly, the kinematics is used to optimize dexterity for a set of desired paths inside the workspace that is found in the first stage, and, finally, a set of dynamic control gains are optimized for trajectories given by the same paths. The methodology permits to reduce the computational cost for the geometry optimization stages, while optimizing the control gains using high precision numerical simulation using SimWise 4D commercial software, with a reduced number of evaluations of candidate solutions, and as consequence, a reduced computational time. The results demonstrate that the final structure-control optimized design accurately follows the desired trajectories.

Designing the Boltzmann Estimation of Multivariate Normal Distribution: Issues, goals and solutions

This paper introduces a new Estimation of Distribution Algorithm (EDA) based on the multivariate Boltzmann distribution. In this work, the design variables and the energy function of the Boltzmann distribution are continuous. Note that since the population has finite size, it can only approximate a continuous Boltzmann distribution with some error. In order to tackle this issue, the parameter estimators for the mean vector and covariance matrix of a Multivariate Normal Density that approximate the Boltzmann density, are derived by minimizing the Kullback-Leibler divergence. The algorithm introduced here uses one energy function for the mean estimator and another for the covariance matrix estimator. The first function places the probability mass around the most promising regions by assigning larger weights to individuals with higher fitness. However, the second function orients the covariance matrix along improving directions by assigning larger weights to individuals with lower fitness. Our proposal combines the conveniences of linear weights with a simple annealing schedule to regulate the exploration and exploitation of the search process. The resulting algorithm is named the Boltzmann Estimation of Multivariate Normal Algorithm (BEMNA). By applying the developed formulae the BEMNA is capable of adapting the structure of a density model to the promisory search directions. BEMNA is tested with a benchmark of 16 functions and contrasted with the AMaLGaM algorithm, a state of the art EDA. Statistical tests of the experimental data show the competitiveness of the proposed algorithm.

A Boltzmann Multivariate Estimation of Distribution Algorithm for Continuous Optimization

This paper introduces an approach for continuous optimization using an Estimation of Distribution Algorithm (EDA), based on the Boltzmann distribution. When using the objective function as energy function, the Boltzmann function favors the most promising regions, making the probability exponentially proportional to the objective function. Using the Boltzmann distribution directly for sampling is not possible because it requires the computation of the objective function values in the complete search space. This work presents an approximation to the Boltzmann function by a multivariate Normal distribution. Formulae for computing the mean and covariance matrix are derived by minimizing the Kullback-Leibler divergence. The proposed EDA is competitive and often superior to similar algorithms as it is shown by statistical results reported here.

Effective Structure Learning in Bayesian Network Based EDAs

Estimation of Distribution Algorithms (EDAs) is a high impact area in evolutionary computation and global optimization. One of the main EDAs strengths is the explicit codification of variable dependencies. The search engine is a joint probability distribution (the search distribution), which is usually computed by fitting the best solutions in the current population. Even though using the best known solutions for biasing the search is a common rule in evolutionary computation, it is worth to notice that most evolutionary algorithms (EAs) derive the new population directly from the selected set, while EDAs do not. Hence, a different bias can be introduced for EDAs. In this article we introduce the so called Empirical Selection Distribution for biasing the search of an EDA based on a Bayesian Network. Bayesian networks based EDAs had shown impressive results for solving deceptive problems, by estimating the adequate structure (dependencies) and parameters (conditional probabilities) needed to tackle the optimum. In this work we show that a Bayesian Network based EDA (BN-EDA) can be enhanced by using the empirical selection distribution instead of the standard selection method. We introduce weighted estimators for the K2 metric which is capable of detecting better the variable correlations than the original BN-EDA, in addition, we introduce formulas to compute the conditional probabilities (local probability distributions). By providing evidence and performing statistical comparisons, we show that the enhanced version: 1) detects more true variable correlations, 2) has a greater probability of finding the optimum, and 3) requires less number of evaluations and/or population size than the original BN-EDA to reach the optimum. Our results suggest that the Empirical Selection Distribution provides to the algorithm more useful information than the usual selection step.