An hybrid parallel algorithm for solving tridiagonal linear systems versus the Wang’s method in a Cray T3D BSP computer

In this paper we describe an hybrid algorithm for an even number of processors based on an algorithm for two processors and the Overlapping Partition Method for tridiagonal systems. Moreover, we compare this hybrid method with the Partition Wang’s method in a BSP computer. Finally, we compare the theoretical computation cost of both methods for a Cray T3D computer, using the cost model that BSP model provides.

An algorithm to hide information in binary images

The objective of this paper is to develop a method to hide information inside a binary image. An algorithm to embed data in scanned text or figures is proposed, based on the detection of suitable pixels, which verify some conditions in order to be not detected. In broad terms, the algorithm locates those pixels placed at the contours of the figures or in those areas where some scattering of the two colors can be found. The hidden information is independent from the values of the pixels where this information is embedded. Notice that, depending on the sequence of bits to be hidden, around half of the used pixels to keep bits of data will not be modified. The other basic characteristic of the proposed scheme is that it is necessary to take into consideration the bits that are modified, in order to perform the recovering process of the information, which consists on recovering the sequence of bits placed in the proper positions. An application to banking sector is proposed for hidding some information in signatures.

Computational cost of GNG3D algorithm for mesh simplification

In this paper we present a study of the computational cost of the GNG3D algorithm for mesh optimization. This algorithm has been implemented taking as a basis a new method which is based on neural networks and consists on two differentiated phases: an optimization phase and a reconstruction phase. The optimization phase is developed applying an optimization algorithm based on the Growing Neural Gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The computational cost of both phases is calculated, showing some examples.

A neural network algorithm to simplify 2D meshes

In this paper we propose a neural network model to simplify and 2D meshes. This model is based on the Growing Neural Gas model and is able to simplify any mesh with different topologies and sizes. A triangulation process is included with the objective to reconstruct the mesh. This model is applied to some problems related to urban networks.

A memetic algorithm for the delineation of local labour markets

Given a territory composed of basic geographical units, the delineation of local labour market areas (LLMAs) can be seen as a problem in which those units are grouped subject to multiple constraints. In previous research, standard genetic algorithms were not able to find valid solutions, and a specific evolutionary algorithm was developed. The inclusion of multiple ad hoc operators allowed the algorithm to find better solutions than those of a widely-used greedy method. However, the percentage of invalid solutions was still very high. In this paper we improve that evolutionary algorithm through the inclusion of (i) a reparation process, that allows every invalid individual to fulfil the constraints and contribute to the evolution, and (ii) a hillclimbing optimisation procedure for each generated individual by means of an appropriate reassignment of some of its constituent units. We compare the results of both techniques against the previous results and a greedy method.

A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

Logic hybrid simulation-optimization algorithm for distillation design

In this paper, we propose a novel algorithm for the rigorous design of distillation columns that integrates a process simulator in a generalized disjunctive programming formulation. The optimal distillation column, or column sequence, is obtained by selecting, for each column section, among a set of column sections with different number of theoretical trays. The selection of thermodynamic models, properties estimation etc., are all in the simulation environment. All the numerical issues related to the convergence of distillation columns (or column sections) are also maintained in the simulation environment. The model is formulated as a Generalized Disjunctive Programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation. Some examples involving from a single column to thermally coupled sequence or extractive distillation shows the performance of the new algorithm.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

A new betweenness centrality measure based on an algorithm for ranking the nodes of a network

We propose and discuss a new centrality index for urban street patterns represented as networks in geographical space. This centrality measure, that we call ranking-betweenness centrality, combines the idea behind the random-walk betweenness centrality measure and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm. We initially use a PageRank algorithm in which we are able to transform some information of the network that we want to analyze into numerical values. Numerical values summarizing the information are associated to each of the nodes by means of a data matrix. After running the adapted PageRank algorithm, a ranking of the nodes is obtained, according to their importance in the network. This classification is the starting point for applying an algorithm based on the random-walk betweenness centrality. A detailed example of a real urban street network is discussed in order to understand the process to evaluate the ranking-betweenness centrality proposed, performing some comparisons with other classical centrality measures.

Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Eyes With Previous Myopic Laser Refractive Surgery

Purpose: To calculate theoretically the errors in the estimation of corneal power when using the keratometric index (nk) in eyes that underwent laser refractive surgery for the correction of myopia and to define and validate clinically an algorithm for minimizing such errors. Methods: Differences between corneal power estimation by using the classical nk and by using the Gaussian equation in eyes that underwent laser myopic refractive surgery were simulated and evaluated theoretically. Additionally, an adjusted keratometric index (nkadj) model dependent on r1c was developed for minimizing these differences. The model was validated clinically by retrospectively using the data from 32 myopic eyes [range, −1.00 to −6.00 diopters (D)] that had undergone laser in situ keratomileusis using a solid-state laser platform. The agreement between Gaussian (PGaussc) and adjusted keratometric (Pkadj) corneal powers in such eyes was evaluated. Results: It was found that overestimations of corneal power up to 3.5 D were possible for nk = 1.3375 according to our simulations. The nk value to avoid the keratometric error ranged between 1.2984 and 1.3297. The following nkadj models were obtained: nkadj= −0.0064286r1c + 1.37688 (Gullstrand eye model) and nkadj = −0.0063804r1c + 1.37806 (Le Grand). The mean difference between Pkadj and PGaussc was 0.00 D, with limits of agreement of −0.45 and +0.46 D. This difference correlated significantly with the posterior corneal radius (r = −0.94, P < 0.01). Conclusions: The use of a single nk for estimating the corneal power in eyes that underwent a laser myopic refractive surgery can lead to significant errors. These errors can be minimized by using a variable nk dependent on r1c.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Algorithm for the detection of outliers based on the theory of rough sets

Outliers are objects that show abnormal behavior with respect to their context or that have unexpected values in some of their parameters. In decision-making processes, information quality is of the utmost importance. In specific applications, an outlying data element may represent an important deviation in a production process or a damaged sensor. Therefore, the ability to detect these elements could make the difference between making a correct and an incorrect decision. This task is complicated by the large sizes of typical databases. Due to their importance in search processes in large volumes of data, researchers pay special attention to the development of efficient outlier detection techniques. This article presents a computationally efficient algorithm for the detection of outliers in large volumes of information. This proposal is based on an extension of the mathematical framework upon which the basic theory of detection of outliers, founded on Rough Set Theory, has been constructed. From this starting point, current problems are analyzed; a detection method is proposed, along with a computational algorithm that allows the performance of outlier detection tasks with an almost-linear complexity. To illustrate its viability, the results of the application of the outlier-detection algorithm to the concrete example of a large database are presented.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.