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  • Solving non-smooth arc routing problems throughout biased-randomized heuristics

     González Martín, Sergio; Ferrer Biosca, Alberto; Juan-Pérez, Angel A.; Riera Terrén, Daniel
    Date of publication: 2014
    Book chapter

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    In non-smooth optimization problems the objective function to minimize or maximize is non-smooth and usually non-convex either, which is a frequent characteristic of real-life optimization problems. In this chapter we discuss the arc routing problem with a non-smooth cost function, and propose a randomized algorithm for solving it. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregulars solution space, for which the traditional optimization methods -both of exact and approximate nature- may fail to reach their full potential. The results obtained so far suggest that using biased probability distributions to randomize classical heuristics can be successfully applied in non-smooth optimization.

  • Solving DC programs using the cutting angle method

     Ferrer Biosca, Alberto; Bagirov, Adil; Beliakov, Gleb
    Journal of global optimization
    Date of publication: 2014-02
    Journal article

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    In this paper, we propose a new algorithm for global minimization of functions represented as a difference of two convex functions. The proposed method is a derivative free method and it is designed by adapting the extended cutting angle method. We present preliminary results of numerical experiments using test problems with difference of convex objective functions and box-constraints. We also compare the proposed algorithm with a classical one that uses prismatical subdivisions.

  • RPSALG algorithm for convex semi-infinite programming

     Ferrer Biosca, Alberto
    International Workshop on Simulation-Optimization for Logistics & Production
    Presentation's date: 2013-11-21
    Presentation of work at congresses

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    In this presentation we consider a partial implementation of RPSALG for solving ordinary convex semi-innite programming problems (CSIP). Each iteration of the algorithm involves two types of auxiliary optimization problems: the rst one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as the variable. The main computational diculties come from the non-convex optimization problem associated with the constraints, which must be solved eciently at each iteration. In this paper we use the so-called cutting angle method, a global optimization procedure for solving Lipschitz programming problems. We implement dierent variants of RPSALG and the results of a number of test problems are given and discussed.

  • Combining iterated local search and biased randomization for solving non-smooth flow-shop problems

     Ferrer Biosca, Alberto; Ramalhino Lourenço, Helena; Juan Perez, Angel Alejandro
    ICSO-HAROSA International Workshop on Simulation-Optimization & Internet Computing
    Presentation's date: 2012-06-15
    Presentation of work at congresses

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  • A global optimization algorithm for solving quasiconvex Location Programming Problems

     Ferrer Biosca, Alberto; Beliakov, Gleb
    CYTED-HAROSA Workshop and Meeting on Applied Optimization and Distributed Computing
    Presentation's date: 2011-07-18
    Presentation of work at congresses

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  • Deterministic and stochastic assessment of the harmonic currents consumed by discharge lamps

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    Electric power systems research
    Date of publication: 2011-01
    Journal article

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  • MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems

     Juan Perez, Angel Alejandro; Faulín, Javier; Ferrer Biosca, Alberto; Lourenço, Helena R.; Barrios, Barry
    TOP
    Date of publication: 2011
    Journal article

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    This paper discusses the use of probabilistic or randomized algorithms for solving vehicle routing problems with non-smooth objective functions. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods¿both of exact and approximate nature¿may fail to reach their full potential. The results obtained so far are promising enough to suggest that the idea of using biased probability distributions to randomize classical heuristics is a powerful one that can be successfully applied in a variety of cases.

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    A Parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics  Open access

     Ionescu, Dragos; Juan Perez, Angel Alejandro; Faulín, Javier; Ferrer Biosca, Alberto
    Date: 2011-01
    Report

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    This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases

  • A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

     Ionescu, Dragos; Juan Perez, Angel Alejandro; Faulín, Javier; Ferrer Biosca, Alberto
    Conference on Numerical Optimization and Applications in Engineering
    Presentation's date: 2010-10
    Presentation of work at congresses

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  • Bounded lower subdifferentiability optimization techniques: applications

     Beliakov, Gleb; Ferrer Biosca, Alberto
    Journal of global optimization
    Date of publication: 2010-06
    Journal article

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  • Potential applications of discrete-event simulation and fuzzy rule-based systems to structural reliability and availability

     Juan Perez, Angel Alejandro; Ferrer Biosca, Alberto; Serrat Pie, Carles; Faulín, Javier; Beliakov, Gleb; Hester, J.
    Date of publication: 2010
    Book chapter

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    This chapter discusses and illustrates some potential applications of discrete-event simulation (DES) techniques in structural reliability and availability analysis, emphasizing the convenience of using probabilistic approaches in modern building and civil engineering practices. After reviewing existing literature on the topic, some advantages of probabilistic techniques over analytical ones are highlighted. Then, we introduce a general framework for performing structural reliability and availability analysis through DES. Our methodology proposes the use of statistical distributions and techniques ¿ such as survival analysis ¿ to model component-level reliability. Then, using failure- and repair-time distributions and information about the structural logical topology (which allows determination of the structural state from their components¿ state), structural reliability, and availability information can be inferred. Two numerical examples illustrate some potential applications of the proposed methodology to achieving more reliable and structural designs. Finally, an alternative approach to model uncertainty at component level is also introduced as ongoing work. This new approach is based on the use of fuzzy rule-based systems and it allows the introduction of experts¿ opinions and evaluations in our methodology.

  • Estudio y caracterización de cargas no lineales  Open access  awarded activity

     Mesas García, Juan José
    Defense's date: 2010-01-27
    Department of Electrical Engineering, Universitat Politècnica de Catalunya
    Theses

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    As a continuation of the work done by the QSE (Electrical Supply Quality) research group at the UPC (Polytechnic University of Catalonia) on non-linear load modelling to determine harmonic distortion in electrical power systems, this thesis consists of the carrying out of a series of studies of the most usual non-linear loads in the said systems (single-phase and three-phase rectifiers with capacitive filter, three-phase 6-pulse rectifiers and discharge lamps), basically aiming to characterize their behaviour and assess their influence on electrical power systems. The thesis was prepared in cooperation with the GNOM (Group of Numerical Optimization and Modelling) research group at the UPC in order to be able to analyse the numerical problem raised by the system of non-linear equations which characterizes each of the non-linear loads, as well as being able to approach optimization issues with some certainty of success. In summary, the aims of this thesis are as follows: -To analyse modelling of the most usual four non-linear loads in electrical power systems in order to incorporate the invariant concept in a justified way and establish ranges of values for the said invariants depending on their usual operating conditions. -To exploit the possibilities offered by invariants and, on the basis of the ranges of values obtained for each of them, to proceed to characterize the deterministic behaviour of the non-linear loads which are the object of the study and also to analyse the phenomena of harmonic cancellation and interaction. -To describe and study experimentally, also on the basis of invariants, the fundamental and harmonic currents (magnitude and angle) consumed by the non-linear loads considered in this thesis, whether by obtaining experimental models (databases) validated both experimentally and numerically, by validating the studied analytical models experimentally or by fitting the parameters of any of the previous models (parameter estimation) on the basis of experimental acquisitions. -To study the neutral conductor current in three-phase systems to which single-phase non-linear loads are connected (in particular, single-phase rectifiers with capacitive filter), by using invariants and validating the results of this experimentally.

    Como continuación de los trabajos realizados por el grupo de investigación QSE (Calidad del Suministro Eléctrico) de la UPC (Universidad Politécnica de Cataluña) sobre modelización de cargas no lineales para la determinación de la distorsión armónica en los sistemas eléctricos de potencia, se ha realizado como tesis una serie de estudios sobre las cargas no lineales más habituales en dichos sistemas (rectificadores monofásicos y trifásicos con filtro capacitivo, rectificadores trifásicos de 6 pulsos y lámparas de descarga) encaminados básicamente a la caracterización de su comportamiento y al análisis de su influencia en los sistemas eléctricos de potencia. La tesis se ha desarrollado en colaboración con el grupo de investigación GNOM (Grupo de Optimización Numérica y Modelización) de la UPC para poder analizar el problema numérico planteado por el sistema de ecuaciones no lineales que caracteriza cada una de las cargas no lineales, así como poder abordar con garantías problemas de optimización. Resumidamente, los objetivos de esta tesis son: -Analizar la modelización de las cuatro cargas no lineales más habituales en los sistemas eléctricos de potencia con el objetivo de introducir de forma justificada el concepto de invariante y establecer rangos de valores para dichos invariantes de acuerdo a sus condiciones habituales de funcionamiento. -Aprovechar las posibilidades que ofrecen los invariantes y, a partir de los rangos de valores obtenidos para cada uno de ellos, proceder a caracterizar el comportamiento determinístico de las cargas no lineales objeto de estudio y también a analizar los fenómenos de la cancelación y la interacción armónica. -Caracterizar y estudiar experimentalmente, también a partir de los invariantes, las intensidades fundamental y armónicas (módulo y ángulo) que consumen las cargas no lineales consideradas en esta tesis, ya sea mediante la obtención de modelos experimentales (bases de datos) validados tanto experimental como numéricamente, la validación experimental de los modelos analíticos estudiados o bien el ajuste de los parámetros de cualquiera de los anteriores modelos (estimación de parámetros) a partir de adquisiciones experimentales. -Estudiar la intensidad del neutro en sistemas trifásicos en los que hay conectadas cargas no lineales monofásicas (en particular, rectificadores monofásicos con filtro capacitivo), utilizando los invariantes y validando experimentalmente los resultados que se obtengan.

  • Using discrete-event simulation to design reliable and cost-efficient civil engineering structures

     Ferrer Biosca, Alberto; Serrat Pie, Carles; Faulín, Javier; Hester, Josh; Juan Pérez, Ángel Alejandro; López Brosa, Pere
    Date of publication: 2009
    Book chapter

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    In this paper the topic of Structural Reliability Analysis and its importance in modern Civil Engineering is introduced. Throughout the paper, some advantages that simulation-based approaches offer with respect to other classical approaches are discussed. After a review of the most relevant literature on the subject, a simulation-based approach is described. Our methodology makes use of discrete-event simulation techniques to help the civil engineer design more reliable and cost-efficient structures. A numerical example illustrates some potential applications of the proposed methodology. Finally, potential research and academic applications of this approach are also discussed.

  • Deterministic and stochastic study of the three-phase non-linear load behavior

     Ferrer Biosca, Alberto; Mesas García, Juan José; Sainz Sapera, Luis
    Date of publication: 2009
    Book chapter

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    The paper examines the deterministic and stochastic behavior of three-phase uncontrolled rectifiers and three-phase 6-pulse rectifiers from extensive simulations performed by a MATLAB customized program. The study is based on non-linear load invariants and analyzes the harmonic current magnitudes and phase angles of these loads. Invariants are the minimum number of parameters characterizing non-linear loads univocally. Two practical laboratory examples are presented to illustrate the numerical study.

  • Applications of discrete-event simulation to reliability and availability assessment in civil engineering structures

     Juan-Pérez, Angel A.; Monteforte, Arai; Ferrer Biosca, Alberto; Serrat Pie, Carles; Faulín, Javier
    Date of publication: 2009
    Book chapter

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    Welcome to the 2009 Winter Simulation Conference (WSC), recognized as the premiere international conference for simulation professionals in discrete and combined discrete-continuous simulation. WSC is always located in exciting and dynamic locations and in 2009 we are delighted to hold the conference in Austin, Texas. This is the first time that WSC has been held in Texas. The conference theme, Energy Alternatives, encourages attendees to examine the issues of energy supply, technology development and deployment, and climate change and invites practitioners to share their contributions to solving these pressing global challenges through the use of modeling and simulation. These efforts are highlighted in the new Energy and Material Flow Simulation track. WSC '09 offers a comprehensive program ranging from introductory tutorials to state-of-the-art research and practice. Following its unbridled success last year, WSC '09 will again incorporate the MASM (Modeling and Analysis for Semiconductor Manufacturing) Conference, the leading modeling and analysis conference for global semiconductor manufacturing and supply chain operations. WSC '09 also continues the popular pre-conference workshop Simulation 101 and expands the training offerings with a full week of training sessions running in parallel to the main conference tracks.

  • Discharge lamp harmonic interaction study by Monte Carlo simulation and experimental measurements

     Ferrer Biosca, Alberto; Mesas García, Juan José; Sainz Sapera, Luis
    Date of publication: 2009
    Book chapter

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    Applications of discrete-event simulation to reliability and availability assesment in civil engineering structures  Open access

     Ferrer Biosca, Alberto; Serrat Pie, Carles; Faulín, Javier; Juan-Pérez, Angel A.; Monteforte, Arai
    Winter Simulation Conference
    Presentation's date: 2009
    Presentation of work at congresses

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    This paper discusses the convenience of predicting, quantitatively, time-dependent reliability and availability levels asso-ciated with most building or civil engineering structures. Then, the paper reviews different approaches to these problems and proposes the use of discrete-event simulation as the most realistic way to deal with them, specially during the design stage. The paper also reviews previous work on the use of both Monte Carlo simulation and discrete-event simulation in this area and shows how discrete-event simulation, in particular, could be employed to solve uncertainty in time-dependent structural reliability problems. Finally, a case study is developed to illustrate some of the concepts previously covered in the paper.

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    Using discrete-event simulation to design reliable and cost-efficient civil engineering structures  Open access

     Juan Perez, Angel Alejandro; Ferrer Biosca, Alberto; Serrat Pie, Carles; Faulín, Javier; Lopez Brosa, Pere; Hester, Josh
    European Modeling and Simulation Symposium
    Presentation's date: 2009
    Presentation of work at congresses

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    In this paper the topic of Structural Reliability Analysis and its importance in modern Civil Engineering is introduced. Throughout the paper, some advantages that simulation-based approaches offer with respect to other classical approaches are discussed. After a review of the most relevant literature on the subject, a simulation-based approach is described. Our methodology makes use of discrete-event simulation techniques to help the civil engineer design more reliable and cost-efficient structures. A numerical example illustrates some potential applications of the proposed methodology. Finally, potential research and academic applications of this approach are also discussed.

    In this paper the topic of Structural Reliability Analysis and its importance in modern Civil Engineering is introduced. Throughout the paper, some advantages that simulation-based approaches offer with respect to other classical approaches are discussed. After a review of the most relevant literature on the subject, a simulation-based approach is described. Our methodology makes use of discrete-event simulation techniques to help the civil engineer design more reliable and cost-efficient structures. A numerical example illustrates some potential applications of the proposed methodology. Finally, potential research and academic applications of this approach are also discussed.

  • Discrete event simulation and fuzzy sets in structural reliability and availability in building construction

     Ferrer Biosca, Alberto; Juan Perez, Angel Alejandro; Serrat Pie, Carles; Lopez, P.; Faulín, Javier; Beliakov, Gleb
    International Conference on Construction and Building Research
    Presentation's date: 2009-06-24
    Presentation of work at congresses

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  • Estimation of single-phase uncontrolled recitifier parameters

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    IASTED International Conference on Power and Energy Systems
    Presentation of work at congresses

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  • GNOM: GROUP OF NUMERICAL OPTIMIZATION AND MODELLING

     Gonzalez Alastrue, Jose Antonio; Heredia Cervera, Fco. Javier; Ferrer Biosca, Alberto; Corchero García, Cristina; Nabona Francisco, Narcis; Nasini, Stefano; Mari Tomas, Laura; Castro Perez, Jordi
    Participation in a competitive project

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  • PLANIFICACIÓN ÓPTIMA DE LA GENERACIÓN ELÉCTRICA A CORTO Y MEDIO PLAZO EN ENTORNOS DE MERCADOS MÚLTIPLES CON RESTRICCIONES DE RIESGO

     Nabona Francisco, Narcis; Corchero García, Cristina; Ferrer Biosca, Alberto; Marí, Laura; Heredia Cervera, Fco. Javier
    Participation in a competitive project

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  • Deterministic and stochastic study of the three-phase non-linear load behavior

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    IEEE International Conference on Power Engineering, Energy and Electrical Drives
    Presentation's date: 2009
    Presentation of work at congresses

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    The paper examines the deterministic and stochastic behavior of three-phase uncontrolled rectifiers and three-phase 6-pulse rectifiers from extensive simulations performed by a MATLAB customized program. The study is based on non-linear load invariants and analyzes the harmonic current magnitudes and phase angles of these loads. Invariants are the minimum number of parameters characterizing non-linear loads univocally. Two practical laboratory examples are presented to illustrate the numerical study.

  • Discharge lamp harmonic interaction study by Monte Carlo simulation and experimental measurements

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    IEEE International Conference on Power Engineering, Energy and Electrical Drives
    Presentation's date: 2009
    Presentation of work at congresses

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    The growing presence of discharge lamps in power distribution systems has increased the harmonic distortion in these systems. The paper studies the magnetic ballast discharge lamp modelization with and without harmonic interaction. The supply harmonic voltage influence on lamp behavior is analyzed by Monte Carlo simulation. The results are validated with experimental measurements.

  • Deterministic and experimental study on three-phase 6-pulse rectifiers

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    IASTED International Conference on Power and Energy Systems
    Presentation of work at congresses

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  • Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

     Ferrer Biosca, Alberto; Martínez-Legaz, Juan Enrique
    Journal of global optimization
    Date of publication: 2009-04
    Journal article

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  • Three-phase full-wave rectifier study with experimental measurements

     Sainz Sapera, Luis; Mesas García, Juan José; Ferrer Biosca, Alberto
    Electric power systems research
    Date of publication: 2009-04
    Journal article

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  • Deterministic and stochastic study of the single-phase non-linear load behavior

     Mesas García, Juan José; Sainz Sapera, Luis; Ferrer Biosca, Alberto
    IASTED International Conference on Power and Energy Systems
    Presentation of work at congresses

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  • A simulation-based algorithm to predict time-dependent structural reability

     Juan Perez, Angel Alejandro; Serrat Pie, Carles; Ferrer Biosca, Alberto; Faulín, Javier; Sorroche Montellano, Mateo
    Date of publication: 2008
    Book chapter

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  • Modelos del análisis convexo, optimización moderada y aplicaciones.

     Ferrer Biosca, Alberto
    Participation in a competitive project

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  • Journal of mathematical analysis and applications

     Ferrer Biosca, Alberto
    Collaboration in journals

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  • Characterization of non-linear load behavior

     Sainz Sapera, Luis; Mesas García, Juan José; Ferrer Biosca, Alberto
    Electric power systems research
    Date of publication: 2008-10
    Journal article

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  • Joint solution to the long-term power generation planning and maintenance scheduling

     Pages Bernaus, Adela; Nabona Francisco, Narcis; Ferrer Biosca, Alberto
    23rd IFIP TC 7 Conference on System Modelling and Optimization
    Presentation of work at congresses

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  • e-Learning de las matemáticas en las universidades españolas: tendencias, tecnologías emergentes y adaptación

     Ferrer Biosca, Alberto; Antonia Huertas Sánchez, Mª
    Participation in a competitive project

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  • "aCTeX": Autoaprenentatge científico-tècnic en xarxa

     Guillamon Grabolosa, Antoni; Ferrer Biosca, Alberto
    Date: 2007-01
    Report

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  • European journal of operational research

     Ferrer Biosca, Alberto
    Collaboration in journals

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  • IEEE transactions on fuzzy systems

     Ferrer Biosca, Alberto
    Collaboration in journals

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  • Applying global optimization to a problem in short-term hydrothermal scheduling

     Ferrer Biosca, Alberto
    Date of publication: 2005
    Book chapter

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    A method for modeling a real constrained optimization problem as a reverse convex programming problem has been developed from a new procedure of representation of a polynomial function as a difference of convex polynomials. An adapted algorithm, which uses a combined method of outer approximation and prismatical subdivisions, has been implemented to solve this problem. The solution obtained with a local optimization package is also included and their results are compared

  • Planificación de la generación eléctrica a corto y largo plazo en un mercado liberizado con contratos bilaterales

     Ferrer Biosca, Alberto; Nabona Francisco, Narcis
    Participation in a competitive project

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  • Planificación de la generación eléctrica a corto y largo plazo en un mercado liberalizado con contratos bilaterales (DPI2005-09117-C02-01)

     Nabona Francisco, Narcis; Ferrer Biosca, Alberto; Heredia Cervera, Fco. Javier; Corchero García, Cristina
    Participation in a competitive project

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  • Applicability of deterministic global optimization to the short-term hydrothermal coordination problem  Open access

     Ferrer Biosca, Alberto
    Defense's date: 2004-03-30
    Department of Statistics and Operations Research, Universitat Politècnica de Catalunya
    Theses

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    Esta Tesis esta motivada por el interés en aplicar procedimientos de optimización global a problemas del mundo real. Para ello, nos hemos centrado en el problema de Coordinación Hidrotérmica de la Generación Eléctrica a Corto Plazo (llamado Problema de Generación en esta Tesis) donde la función objetivo y las restricciones no lineales son polinomios de grado como máximo cuatro. En el Problema de Generación no tenemos disponible una representación en diferencia convexa de las funciones involucradas ni tampoco es posible utilizar la estructura del problema para simplificarlo. No obstante, cuando disponemos de una función continua f(x) definida en un conjunto cerrado y no vacío S el problema puede transformarse en otro equivalente expresado mediante minimize l(z) subject to z 2 D n int. (programa d.c. canónico), donde l(z) es una función convexa (en general suele ser una función lineal) con D y C conjuntos convexos y cerrados. Una estructura matemática tal como Dnint C no resulta siempre aparente y aunque lo fuera siempre queda por realizar una gran cantidad de cálculos para expresarla de manera que se pueda resolver el problema de una manera eficiente desde un punto de vista computacional.La característica más importante de esta estructura es que aparecen conjuntos convexos y complementarios de conjuntos convexos. Por este motivo en tales problemas se pueden usar herramientas analíticas tales como subdifernciales y hiperplanos soporte. Por otro lado, como aparecen conjuntos complementarios de conjuntos convexos, estas herramientas analíticas se deben usar de una manera determinada y combinándolas con herramientas combinatorias tales como cortes por planos, Branco and bound y aproximación interior.En esta tesis se pone de manifiesto la estructura matemática subyacente en el Problema de Generación utilizando el hecho de que los polinomios son expresables como diferencia de funciones convexas. Utilizando esta propiedad describimos el problema como un programa d.c. canónico equivalente. Pero aun mas, partiendo de la estructura de las funciones del Problema de Generación es posible rescribirlo de una manera mas conveniente y obtener de este modo ventajas numéricas desde elpunto de vista de la implementación.Basándonos en la propiedad de que los polinomios homogéneos de grado 1 son un conjunto de generadores del espacio vectorial de los polinomios homogéneos de grado m hemos desarrollamos los conceptos y propiedades necesarios que nos permiten expresar un polinomio cualquiera como diferencia de polinomios convexos, También, se ha desarrollado y demostrado la convergencia de un nuevo algoritmo de optimización global (llamado Algoritmo Adaptado) que permite resolver el Problema de Generación. Como el programa equivalente no esta acotado se ha introducido una técnica de subdivisión mediante prismas en lugar de la habitual subdivisión mediante conos.Para obtener una descomposición óptima de un polinomio en diferencia de polinomios convexos, se ha enunciado el Problema de Norma Mínima mediante la introducción del concepto de Descomposición con Mínima Desviación, con lo cual obtenemos implementaciones m´as eficientes, al reducir el n´umero de iteraciones del Algoritmo Adaptado. Para resolver el problema de Norma Mínima hemos implementado un algoritmo de programación cuadrática semi-infinita utilizando una estrategia de build-up and build-down, introducida por Den Hertog (1997) para resolver programas lineales semi-infinitos, la cual usa un procedimiento de barrera logarítmica.Finalmente, se describen los resultados obtenidos por la implementación de los algoritmos anteriormente mencionados y se dan las conclusiones.

    This Thesis has been motivated by the interest in applying deterministic global optimization procedures to problems in the real world with no special structures. We have focused on the Short-Term Hydrothermal Coordination of Electricity Generation Problem (also named Generation Problem in this Thesis) where the objective function and the nonlinear constraints are polynomials of degree up to four. In the Generation Problem there is no available d.c. representation of the involved functions and we cannot take advantage of any special structure of the problem either. Hence, a very general problem, such as the above-mentioned, does not seem to have any mathematical structure conducive to computational implementations. Nevertheless, when f(x) is a continuous function and S is a nonempty closed set the problem can be transformed into an equivalent problem expressed by minimize l(z) subject to z 2 D n intC (canonical d.c. program), where l(z) is a convex function (which is usually a linear function) and D and C are closed convex sets. A mathematical complementary convex structure such as D n int C is not always apparent and even when it is explicit, a lot of work still remains to be done to bring it into a form amenable to efficient computational implementations. The attractive feature of the mathematicalcomplementary convex structure is that it involves convexity. Thus, we can use analytical tools from convex analysis like sub differential and supporting hyper plane.On the other hand, since convexity is involved in a reverse sense, these tools must be used in some specific way and combined with combinatorial tools like cutting planes, branch and bound and outer approximation.We introduce the common general mathematical complementary convex structure underlying in global optimization problems and describe the Generation Problem, whose functions are d.c. functions because they are polynomials. Thus, by using the properties of the d.c. functions, we describe the Generation Problem as an equivalent canonical d.c. programming problem. From the structure of its functions the Generation Problem can be rewritten as a more suitable equivalent reverse convex program in order to obtain an adaptation for advantageous numerical implementations.Concepts and properties are introduced which allow us to obtain an explicit representation of a polynomial as a deference of convex polynomials, based on the fact that the set of mth powers of homogeneous polynomials of degree 1 is a generating set for the vector space of homogeneous polynomials of degree m.We also describe a new global optimization algorithm (adapted algorithm) in order to solve the Generation Problem. Since the equivalent reverse convex program is unbounded we use prismatical subdivisions instead of conical ones. Moreover, we prove the convergence of the adapted algorithm by using a prismatical subdivision process together with an outer approximation procedure.We enounce the Minimal Norm Problem by using the concept of Least Deviation Decomposition in order to obtain the optimal d.c. representation of a polynomial function, which allows a more efficient implementation, by reducing the number of iterations of the adapted algorithm.A quadratic semi-infinite algorithm is described. We propose a build-up and down strategy, introduced by Den Hertog (1997) for standard linear programs that uses a logarithmic barrier method.Finally, computational results are given and conclusions are explained.

  • Ajuts per a projectes de millora de la docència

     Bruguera Padro, Maria Montserrat; Ferrer Biosca, Alberto; Guillamon Grabolosa, Antoni; Mitjana Riera, Margarida; Pañella Brustenga, Francisco de Asis; Rodriguez Jordana, Juan; Serrat Pie, Carles; Panyella, F; Pérez, R
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  • Coordinación hidrotérmica a corto y largo plazo de la generación eléctrica en un mercado competitivo (DPI2002-03330)

     Nabona Francisco, Narcis; Ferrer Biosca, Alberto; Heredia Cervera, Fco. Javier; Corchero García, Cristina
    Participation in a competitive project

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  • Coordinación hidrotérmica a corto y largo plazo de la generación eléctrica en un mercado competitivo

     Ferrer Biosca, Alberto; Nabona Francisco, Narcis
    Participation in a competitive project

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  • L'aprenentatge via la realització de "Projectes integrats"

     Ferrer Biosca, Alberto; Serrat Pie, Carles
    I Jornada de reflexió sobre la docència i la recerca a la Universitat. El cas de l'EUPB
    Presentation of work at congresses

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  • Appliying global optimization to a problem in short-term hydrothermal scheduling

     Ferrer Biosca, Alberto
    7th International Symposium on Generalized Convexity and Generalized Monotonicity
    Presentation of work at congresses

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  • Planificación óptima de gran dimensión de la producción hidrotérmica de energía eléctrica (TAP99-1075-C02-01 )

     Ferrer Biosca, Alberto; Nabona Francisco, Narcis; Heredia Cervera, Fco. Javier
    Participation in a competitive project

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