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Showing papers by "Enrique Alba published in 2007"


Journal ArticleDOI
TL;DR: This work tackles the problem of Project Scheduling Problem by using genetic algorithms (GAs) to solve many different software project scenarios and shows that GAs are quite flexible and accurate for this application, and an important tool for automatic project management.

253 citations


Proceedings ArticleDOI
01 Sep 2007
TL;DR: This work compares the use of a particle swarm optimization (PSO) and a genetic algorithm (GA) (both augmented with support vector machines SVM) for the classification of high dimensional microarray data and proves that PSOsvm is able to find interesting genes and to provide classification competitive performance.
Abstract: In this work we compare the use of a particle swarm optimization (PSO) and a genetic algorithm (GA) (both augmented with support vector machines SVM) for the classification of high dimensional microarray data. Both algorithms are used for finding small samples of informative genes amongst thousands of them. A SVM classifier with 10- fold cross-validation is applied in order to validate and evaluate the provided solutions. A first contribution is to prove that PSOsvm is able to find interesting genes and to provide classification competitive performance. Specifically, a new version of PSO, called Geometric PSO, is empirically evaluated for the first time in this work using a binary representation in Hamming space. In this sense, a comparison of this approach with a new GAsvm and also with other existing methods of literature is provided. A second important contribution consists in the actual discovery of new and challenging results on six public datasets identifying significant in the development of a variety of cancers (leukemia, breast, colon, ovarian, prostate, and lung).

220 citations


Journal ArticleDOI
TL;DR: This paper studies the fine-tuning of broadcasting strategies by using a cellular multi-objective genetic algorithm (cMOGA) which computes a Pareto front of solutions to empower a human designer with the ability of choosing the preferred configuration for the network.

89 citations


Journal ArticleDOI
TL;DR: Some aspects about the software design of the MALLBA library are introduced, details of the most recent implemented skeletons are revealed and computational results for a scheduling problem are offered to illustrate the utilisation of the library.
Abstract: In this paper we discuss on the MALLBA framework, a software tool for the resolution of combinatorial optimisation problems using generic algorithmic skeletons implemented in C++. Every skeleton in the MALLBA library implements an optimisation method (exacts, metaheuristics and hybrids) and provides three different implementations for it: sequential, parallel for Local Area Networks and parallel for Wide Area Networks. This paper introduces some aspects about the software design of the MALLBA library, details of the most recent implemented skeletons and offers computational results for a scheduling problem to illustrate the utilisation of our library.

84 citations


Book ChapterDOI
05 Mar 2007
TL;DR: This paper focuses here on the synchronous/asynchronous feature of the cGA, the feedback of the search experience contained in the archive into the algorithm, and two different replacement strategies, and evaluates the resulting algorithms using a benchmark of problems and compares the best of them against two state-of-the-art genetic algorithms for multiobjective optimization.
Abstract: In this paper we study a number of issues related to the design of a cellular genetic algorithm (cGA) for multiobjective optimization. We take as an starting point an algorithm following the canonical cGA model, i.e., each individual interacts with those ones belonging to its neighborhood, so that a new individual is obtained using the typical selection, crossover, and mutation operators within this neighborhood. An external archive is used to store the non-dominated solutions found during the evolution process. With this basic model in mind, there are many different design issues that can be faced. Among them, we focus here on the synchronous/asynchronous feature of the cGA, the feedback of the search experience contained in the archive into the algorithm, and two different replacement strategies. We evaluate the resulting algorithms using a benchmark of problems and compare the best of them against two state-of-the-art genetic algorithms for multiobjective optimization. The obtained results indicate that the cGA model is a promising approach to solve this kind of problem.

83 citations


Proceedings ArticleDOI
26 Mar 2007
TL;DR: This work exploits the capabilities of cellular memetic algorithms (cMAs) for obtaining efficient batch schedulers for grid systems and shows that this heuristic approach is able to deliver very high quality planning of jobs to grid nodes and thus it can be used to design efficient dynamic schedULers for real grid systems.
Abstract: Computational grids are an important emerging paradigm for large-scale distributed computing. As grid systems become more wide-spread, techniques for efficiently exploiting the large amount of grid computing resources become increasingly indispensable. A key aspect in order to benefit from these resources is the scheduling of jobs to grid resources. Due to the complex nature of grid systems, the design of efficient grid schedulers becomes challenging since such schedulers have to be able to optimize many conflicting criteria in very short periods of time. In this work we exploit the capabilities of cellular memetic algorithms (cMAs) for obtaining efficient batch schedulers for grid systems. A careful design of the cMA methods and operators for the problem yielded to an efficient and robust implementation. Our experimental study, based on a known static benchmark for the problem, shows that this heuristic approach is able to deliver very high quality planning of jobs to grid nodes and thus it can be used to design efficient dynamic schedulers for real grid systems. Such dynamic schedulers can be obtained by running the cMA-based scheduler in batch mode for a very short time to schedule jobs arriving to the system since the last activation of the cMA scheduler.

74 citations


Proceedings ArticleDOI
07 Jul 2007
TL;DR: The use of a new kind of Ant Colony Optimization (ACO) model, ACOhg, is proposed to refute safety properties in concurrent systems with a reduced amount of resources, outperforming algorithms that are the state-of-the-art in model checking.
Abstract: Model Checking is a well-known and fully automatic technique forchecking software properties, usually given as temporal logicformulae on the program variables. Most model checkers found inthe literature use exact deterministic algorithms to check theproperties. These algorithms usually require huge amounts ofcomputational resources if the checked model is large. We proposehere the use of a new kind of Ant Colony Optimization (ACO) model, ACOhg, to refute safety properties in concurrent systems. ACO algorithms are stochastic techniques belonging to the class of metaheuristic algorithms and inspired by the foraging behaviour of real ants. The traditional ACO algorithms cannot deal with the model checking problem and thus we use ACOhg to tackle it. The results state that ACOhg algorithms find optimal or near optimal error trails in faulty concurrent systems with a reduced amount of resources, outperforming algorithms that are the state-of-the-art in model checking. This fact makes them suitable for checking safety properties in large concurrent systems, in which traditional techniques fail to find errors because of the model size.

73 citations


Proceedings ArticleDOI
07 Jul 2007
TL;DR: This paper solves the RND problem using a multi-objective version of the algorithm CHC, which is the metaheuristic having reported the best results when solving the single- objective formulation of RND, and indicates that MOCHC outperfoms NSGA-II and is more efficient finding the optimal solutions than single-objectives techniques.
Abstract: Radio network design (RND) is a fundamental problem in cellular networks for telecommunications. In these networks, the terrain must be covered by a set of base stations (or antennae), each of which defines a covered area called cell. The problem may be reduced to figure out the optimal placement of antennae out of a list of candidate sites trying to satisfy two objectives: to maximize the area covered by the radio signal and to reduce the number of used antennae. Consequently, RND is a bi-objective optimization problem. Previous works have solved the problem by using single-objective techniques which combine the values of both objectives. The used techniques have allowed to find optimal solutions according to the defined objective, thus yielding a unique solution instead of the set of Pareto optimal solutions. In this paper, we solve the RND problem using a multi-objective version of the algorithm CHC, which is the metaheuristic having reported the best results when solving the single-objective formulation of RND. This new algorithm, called MOCHC, is compared against a binary-coded NSGA-II algorithm and also against the provided results in the literature. Our experiments indicate that MOCHC outperfoms NSGA-II and, more importantly, it is more efficient finding the optimal solutions than single-objectives techniques.

63 citations


Book ChapterDOI
11 Apr 2007
TL;DR: This proposal is a very efficient assembler that allows to find optimal solutions for large instances of this problem, considerably faster than its competitors and with high accuracy.
Abstract: In this paper we propose and study the behavior of a new heuristic algorithm for the DNA fragment assembly problem: PALS. The DNA fragment assembly is a problem to be solved in the early phases of the genome project and thus is very important since the other steps depend on its accuracy. This is an NP-hard combinatorial optimization problem which is growing in importance and complexity as more research centers become involved on sequencing new genomes. Various heuristics, including genetic algorithms, have been designed for solving the fragment assembly problem, but since this problem is a crucial part of any sequencing project, better assemblers are needed. Our proposal is a very efficient assembler that allows to find optimal solutions for large instances of this problem, considerably faster than its competitors and with high accuracy.

58 citations


Proceedings ArticleDOI
07 Jul 2007
TL;DR: A new mathematical formulation of the problem in which the frequency plans are evaluated by using accurate interference information coming from a real GSM network is presented, and an ant colony optimization (ACO) algorithm is developed to tackle this problem.
Abstract: Frequency planning is a very important task for current GSM operators. In this work we present a new mathematical formulation of the problem in which the frequency plans are evaluated by using accurate interference information coming from a real GSM network. We have developed an ant colony optimization (ACO) algorithm to tackle this problem. After accurately tuning this algorithm, it has been compared against a (1,10) Evolutionary Algorithm (EA). The results show that the ACO clearly outperforms the EA when using different time limits as stopping condition for a rather extensive comparison.

55 citations


Journal ArticleDOI
17 Jan 2007
TL;DR: The conclusion is that this kind of systems can provide to the community with a large and precise set of Pareto fronts that would be otherwise unknown.
Abstract: This paper analyzes some technical and practical issues concerning the use of parallel systems to solve multi-objective optimization problems using enumerative search. This technique constitutes a conceptually simple search strategy, and it is based on evaluating each possible solution from a given finite search space. The results obtained by enumeration are impractical for most computer platforms and researchers, but they exhibit a great interest because they can be used to be compared against the values obtained by stochastic techniques. We analyze here the use of a grid computing system to cope with the limits of enumerative search. After evaluating the performance of the sequential algorithm, we present, first, a parallel algorithm targeted to multiprocessor systems. Then, we design a distributed version prepared to be executed on a federation of geographically distributed computers known as a computational grid. Our conclusion is that this kind of systems can provide to the community with a large and precise set of Pareto fronts that would be otherwise unknown.

Proceedings ArticleDOI
07 Jul 2007
TL;DR: A new ACO model that overcomes the difficulties found when working with a huge construction graph is studied and the results can help to understand the meaning of the new parameters introduced and to decide which parameterization is more suitable for a given problem.
Abstract: Ant Colony Optimization (ACO) has been successfully applied to those combinatorial optimization problems which can be translated into a graph exploration. Artificial ants build solutions step by step adding solution components that are represented by graph nodes. The existing ACO algorithms are suitable when the graph is not very large (thousands of nodes) but is not useful when the graph size can be a challenge for the computer memory and cannot be completely generated or stored in it. In this paper we study a new ACO model that overcomes the difficulties found when working with a huge construction graph. In addition to the description of the model, we analyze in the experimental section one technique used for dealing with this huge graph exploration. The results of the analysis can help to understand the meaning of the new parameters introduced and to decide which parameterization is more suitable for a given problem. For the experiments we use one real problem with capital importance in Software Engineering: refutation of safety properties in concurrent systems. This way, we foster an innovative research line related to the application of ACO to formal methods in Software Engineering.

Book ChapterDOI
12 Feb 2007
TL;DR: The experimental studies show that ACO finds optimal or near optimal error trails in faulty concurrent systems with a reduced amount of resources, outperforming in most cases the results of algorithms that are widely used in model checking, like Nested Depth First Search.
Abstract: Model Checking is a well-known and fully automatic technique for checking software properties, usually given as temporal logic formulae on the program variables. Most model checkers found in the literature use exact deterministic algorithms to check the properties. These algorithms usually require huge amounts of computational resources if the checked model is large. We propose here the use of Ant Colony Optimization (ACO) to refute safety properties in concurrent systems. ACO algorithms are stochastic techniques belonging to the class of metaheuristic algorithms and inspired by the foraging behaviour of real ants. The results state that ACO algorithms find optimal or near optimal error trails in faulty concurrent systems with a reduced amount of resources, outperforming algorithms that are the state-of-the-art in model checking. This fact makes them suitable for checking safety properties in large concurrent systems, in which traditional techniques fail to find errors because of the model size.

Journal ArticleDOI
TL;DR: This work describes the development of three parallel metaheuristic methods, a parallel genetic algorithm, a Parallel scatter search, and a parallel hybrid genetic algorithm which can find high-quality solutions to 20 different problem instances.
Abstract: Workforce planning is an important activity that enables organizations to determine the workforce needed for continued success. A workforce planning problem is a very complex task requiring modern techniques to be solved adequately. In this work, we describe the development of three parallel metaheuristic methods, a parallel genetic algorithm, a parallel scatter search, and a parallel hybrid genetic algorithm, which can find high-quality solutions to 20 different problem instances. Our experiments show that parallel versions do not only allow to reduce the execution time but they also improve the solution quality.

Posted Content
TL;DR: A Bayesian method for seasonal data is described and illustrated and it is shown that it can outperform traditional time series methods for short time series.
Abstract: This article by Enrique de Alba and Manuel Mendoza extends Foresight’s previous coverage of methods for forecasting seasonal data when the historical series is short (less than 2-3 years of data). The authors describe and illustrate a Bayesian method for seasonal data and show that it can outperform traditional time series methods for short time series. Copyright International Institute of Forecasters, 2007

Book ChapterDOI
11 Apr 2007
TL;DR: In this article, a (1, λ) EA for real-world GSM networks is proposed and analyzed using evolutionary algorithms, and the results show that this EA is able to compute accurate frequency plans for realworld instances.
Abstract: Frequency assignment is a well-known problem in Operations Research for which different mathematical models exist depending on the application specific conditions. However, most of these models are far from considering actual technologies currently deployed in GSM networks (e.g. frequency hopping). These technologies allow the network capacity to be actually increased to some extent by avoiding the interferences provoked by channel reuse due to the limited available radio spectrum, thus improving the Quality of Service (QoS) for subscribers and an income for the operators as well. Therefore, the automatic generation of frequency plans in real GSM networks is of great importance for present GSM operators. This is known as the Automatic Frequency Planning (AFP) problem. In this paper, we focus on solving this problem for a realistic-sized, real-world GSM network by using Evolutionary Algorithms (EAs). To be precise, we have developed a (1, λ) EA for which very specialized operators have been proposed and analyzed. Results show that this algorithmic approach is able to compute accurate frequency plans for real-world instances.

Journal ArticleDOI
TL;DR: The aim of this paper is to report experimental results on the behaviour of two types of parallel ACO algorithms on large instances of the mentioned problem with the goal of improving existing solutions significantly.
Abstract: Ant Colony Optimisation (ACO) algorithms are intrinsically distributed algorithms where independent agents are in charge of building solutions collaboratively. Stigmergy or indirect communication is the way in which each agent learns from the experience of the whole colony. In this sense, explicit communication models of ACO can be defined directly giving birth to parallel algorithms of high numerical and real time efficiency. We do so in this work and apply the resulting algorithms to the Minimum Tardy Task Problem (MTTP), a scheduling problem that has been faced with other metaheuristics in the past. The aim of this paper is to report experimental results on the behaviour of two types of parallel ACO algorithms on large instances of the mentioned problem with the goal of improving existing solutions significantly.

Book ChapterDOI
01 Jan 2007
TL;DR: This work analyzes the role of the mutation operator in the three algorithms and the impact of the frequency of dynamic changes in the resulting difficulty of the problem, and concludes that the steady-state GA is the best in fast adapting its search to a new problem definition, while the cellular GA isThe best in preserving diversity to finally get accurate solutions.
Abstract: In order to solve a Non-Stationary Optimization Problem (NSOP) it is necessary that the used algorithms have a set of suitable properties for being able to dynamically adapt the search to the changing fitness landscape. Our aim in this work is to improve our knowledge of existing canonical algorithms (steady-state, generational, and structured –cellular– genetic algorithms) in such a scenario. We study the behavior of these algorithms in a basic Dynamic Knapsack Problem, and utilize quantitative metrics for analyzing the results. In this work, we analyze the role of the mutation operator in the three algorithms and the impact of the frequency of dynamic changes in the resulting difficulty of the problem. Our conclusions outline that the steady-state GA is the best in fast adapting its search to a new problem definition, while the cellular GA is the best in preserving diversity to finally get accurate solutions. The generational GA is a tradeoff algorithm showing performances in between the other two.

Journal ArticleDOI
TL;DR: A comparative study of pure and hybrid EAs applied to the GSP, codified over MALLBA, a general purpose library for combinatorial optimization is presented.
Abstract: Several evolutionary algorithms (EAs) applied to a wide class of communication network design problems modelled under the generalized Steiner problem (GSP) are evaluated. In order to provide a fault-tolerant design, a solution to this problem consists of a preset number of independent paths linking each pair of potentially communicating terminal nodes. This usually requires considering intermediate non-terminal nodes (Steiner nodes), which are used to ensure path redundancy, while trying to minimize the overall cost. The GSP is an NP-hard problem for which few algorithms have been proposed. This article presents a comparative study of pure and hybrid EAs applied to the GSP, codified over MALLBA, a general purpose library for combinatorial optimization. The algorithms were tested on several GSPs, and asset efficient numerical results are reported for both serial and distributed models of the evaluated algorithms.

Proceedings ArticleDOI
07 Jul 2007
TL;DR: Find a subset of features F that maximizes a scoring function G such that F ′ = argmaxG⊂Γ{Θ(G)}, (1)
Abstract: Feature selection for gene expression analysis in cancer prediction often uses wrapper classification methods to discriminate a type of tumor, to reduce the number of genes to investigate in case of a new patient. By creating clusters a big reduction of the number of considered genes and an improvement of the classification accuracy can be finally achieved. The definition of the feature selection problem is this: given a set of features F = {f1, ..., fi, ..., fn}, find a subset F ′ ⊆ F that maximizes a scoring function Θ : Γ → G such that F ′ = argmaxG⊂Γ{Θ(G)}, (1)

Proceedings ArticleDOI
07 Jul 2007
TL;DR: This work aims at optimizing injection networks, which consist in adding a set of long-range links in mobile multi-hop ad hoc networks so as to improve connectivity and overcome network partitioning using small-world network properties, that comprise a high clustering coefficient and a low characteristic path length.
Abstract: This work aims at optimizing injection networks, which consist in adding a set of long-range links (called bypass links) in mobile multi-hop ad hoc networks so as to improve connectivity and overcome network partitioning. To this end, we rely on small-world network properties, that comprise a high clustering coefficient and a low characteristic path length. We investigate the use of two genetic algorithms (generational and steady-state) to optimize three instances of this topology control problem and present results that show initial evidence of their capacity to solve it.

Proceedings ArticleDOI
07 Jul 2007
TL;DR: Jose Garcia-Nieto Dpto.
Abstract: Jose Garcia-Nieto Dpto. Lenguajes y Ciencias de la Computacion E.T.S. Ingenieria Informatica University of Malaga, Spain jnieto@lcc.uma.es Enrique Alba Dpto. Lenguajes y Ciencias de la Computacion E.T.S. Ingenieria Informatica University of Malaga, Spain eat@lcc.uma.es Francisco Chicano Dpto. Lenguajes y Ciencias de la Computacion E.T.S. Ingenieria Informatica University of Malaga, Spain chicano@lcc.uma.es

Book ChapterDOI
12 Feb 2007
TL;DR: This work uses omnidirectional antennas for RND (Radio Network Design) and uses not only sequential algorithms, but also grid computing with BOINC in order to execute thousands of experiments in only several days using around 100 computers.
Abstract: RND (Radio Network Design) is an important problem in mobile telecommunications (for example in mobile/cellular telephony), being also relevant in the rising area of sensor networks. This problem consists in covering a certain geographical area by using the smallest number of radio antennas achieving the biggest cover rate. To date, several radio antenna models have been used: square coverage antennas, omnidirectional antennas that cover a circular area, etc. In this work we use omnidirectional antennas. On the other hand, RND is an NP-hard problem; therefore its solution by means of evolutionary algorithms is appropriate. In this work we study different evolutionary approaches to tackle this problem. PBIL (Population-Based Incremental Learning) is based on genetic algorithms and competitive learning (typical in neural networks). DE (Differential Evolution) is a very simple population-based stochastic function minimizer used in a wide range of optimization problems, including multi-objective optimization. SA (Simulated Annealing) is a classic trajectory descent optimization technique. Finally, CHC is a particular class of evolutionary algorithm which does not use mutation and relies instead on incest prevention and disruptive crossover. Due to the complexity of such a large analysis including so many techniques, we have used not only sequential algorithms, but also grid computing with BOINC in order to execute thousands of experiments in only several days using around 100 computers.

Journal ArticleDOI
TL;DR: The results indicate that a hybridization of a GA with a local search algorithm (simulated annealing) is beneficial and that the use of parallelism not only introduces a speedup in the algorithms compared (as expected) but also allows us to improve the quality of the solutions found.
Abstract: In this article, we perform a comparative study of different heuristics used to design combinational logic circuits This study mainly emphasizes the use of local search hybridized with a genetic algorithm (GA) and the impact of introducing parallelism Our results indicate that a hybridization of a GA with a local search algorithm (simulated annealing) is beneficial and that the use of parallelism not only introduces a speedup in the algorithms compared (as expected) but also allows us to improve the quality of the solutions found

Book ChapterDOI
12 Feb 2007
TL;DR: Results show that the SPEA2 algorithm is the most accurate metaheuristic for solving the broadcasting problem in metropolitan MANETs with up to seven different advanced multiobjective metaheuristics.
Abstract: Mobile Ad-hoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any pre-existing infrastructure In such scenario, broadcasting becomes an operation of tremendous importance for the own existence and operation of the network Optimizing a broadcasting strategy in MANETs is a multiobjective problem accounting for three goals: reaching as many stations as possible, minimizing the network utilization, and reducing the duration of the operation itself This research, which has been developed within the OPLINK project (http://oplinklccumaes), faces a wide study about this problem in metropolitan MANETs with up to seven different advanced multiobjective metaheuristics They all compute Pareto fronts of solutions which empower a human designer with the ability of choosing the preferred configuration for the network The quality of these fronts is evaluated by using the hypervolume metric The obtained results show that the SPEA2 algorithm is the most accurate metaheuristic for solving the broadcasting problem

Posted Content
TL;DR: In this article, two genetic algorithms (generational and steady-state) are used to optimize three instances of this topology control problem and present results that show initial evidence of their capacity to solve it.
Abstract: This work aims at optimizing injection networks, which consist in adding a set of long-range links (called bypass links) in mobile multi-hop ad hoc networks so as to improve connectivity and overcome network partitioning. To this end, we rely on small-world network properties, that comprise a high clustering coefficient and a low characteristic path length. We investigate the use of two genetic algorithms (generational and steady-state) to optimize three instances of this topology control problem and present results that show initial evidence of their capacity to solve it.

Book ChapterDOI
12 Feb 2007
TL;DR: The differences in performance among different implementations, in Java, of the data structures used in an evolutionary algorithm (EA) are studied.
Abstract: In this paper we study the differences in performance among different implementations, in Java, of the data structures used in an evolutionary algorithm (EA). Typical studies on EAs performance deal only with different abstract representations of the data and pay no attention to the fact that each data representation has to be implemented in a concrete programming language which, in general, offers several possibilities, with differences in time consumed, that may be worthy of consideration.


01 Jan 2007
TL;DR: This paper investigates the use of a distributed Cooperative Coevolutionary Genetic Algorithm (CCGA) and compares its performance to a generational and a steady state genetic algorithm for optimizing one instance of this topology control problem and presents initial evidence of its use.
Abstract: Multi-hop ad-hoc networks allow establishing local groups of communicating devices in a selforganizing way. However, in a global setting such networks fail to work properly due to network partitioning. This means that users locally interacting could eventually spread and move away from each other and consequently loose their connections. Considering that devices are capable of communicating both locally (e.g. using Wi-Fi or Bluetooth) and additionally with remote devices (e.g. using GSM/UMTS links) the objective of our work is to optimize the way of inter-linking multiple network partitions. To this end we rely on smallworld network properties, that consist in using special attributes like the clustering coefficient and the characteristic path length. In this paper we investigate the use of a distributed Cooperative Coevolutionary Genetic Algorithm (CCGA) and compare its performance to a generational and a steady state genetic algorithm (genGa and ssGA) for optimizing one instance of this topology control problem and present initial evidence of its ca-

Journal ArticleDOI
TL;DR: In this paper, the authors proposed two parallel versions of an estimation of distribution algorithm (EDA) that represent the probability distribution by means of a single connected graphical model based on a polytree structure (PADA).
Abstract: This paper proposes two parallel versions of an Estimation of Distribution Algorithm (EDA) that represents the probability distribution by means of a single connected graphical model based on a polytree structure (PADA). The main goal is to design a new and more efficient EDA. Our algorithm (pPADA) is based on the master/slave model which allows to perform the estimation of the probability distribution (the most time-consuming phase in EDAs) in a parallel way. The aim of our experimental studies is manifold. Firstly, we show that our parallel versions achieve a notable reduction of the total execution time with respect to existing algorithms. Secondly, we study the behavior of the algorithm from the numerical point of view, analyzing the different versions. Finally, our methods are evaluated over three interconnection networks (Fast Ethernet, Gigabit Ethernet, and Myrinet) and a study on the influence of the parallel platform in the communication is performed.