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On Fourier transforms of distribution semigroups

JOURNAL OF FUNCTIONAL ANALYSIS 2007年第2期242卷 400-441页

作者： Kisynski, Jan Polish Acad Sci Inst Math PL-00956 Warsaw Poland

A one-to-one correspondence is established between Fourier transforms of ultradistribution semigroups in the sense of Beurling and some class of pseudoresolvents characterized by conditions concerning their domains of... 详细信息

关键词： test functions ultradistributions of Beurling distribution semigroups Fourier and Laplace transformations implicit differential equations

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Designing an Integral LQR Controller for DC-DC X-Converter based on Enhanced Shuffled Frog-Leaping Optimization Algorithm

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JOURNAL OF ELECTRICAL SYSTEMS 2020年第2期16卷 152-170页

作者： Abbas, Nizar Hadi Algamluoli, Ammar Falah Univ Baghdad Dept Elect Engn Coll Engn Baghdad Iraq

Power Electronics DC-DC converter plays an important role in different applications, for example, electric vehicles, wind generation and PV systems. This paper addresses the design of DC-DC X-converter with optimal LQR controller combined with integral gain action. Therefore, the proposed controlling scheme for DC-DC converter is very important to make the system stable under different conditions. In order to achieve high performance for DC-DC converter system, the current controller was made first as an inner loop and then an output voltage controller was designed as an outer loop. The behavior of an LQR controller design with integral action is characterized by two parameters: state and control weighting matrices. The problem of finding the semi-optimum weighting matrices has been formulated as an optimization problem. Standard Shuffled Frog-Leaping (SSFL) optimization algorithm is introduced to optimize the selection of the controller s weighting matrices. Furthermore, an Enhanced SFL Optimization Algorithm (ESFLA) is proposed to improve the stability performance of the considered system. The performances of both SSFLA and ESFLA are evaluated in terms of speed of convergence to the global optimum and algorithm accuracy, based on a set of ten benchmark test functions. The simulation results demonstrate that the DC-DC X-converter based on LQR with integral gain timed by ESFLA outperforms other designs incorporating SSFLA in terms of control effort, stability performance as well as transient response specifications.

关键词： DC-DC X converter LQR SSFLA ESFLA test functions

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Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy

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EVOLUTIONARY COMPUTATION 2000年第2期8卷 149-172页

作者： Knowles, Joshua D. Corne, David W. Univ Reading Sch Comp Sci Cybernet & Elect Engn Reading RG6 6AY Berks England

We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1 + 1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1 + 1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1 + lambda) and (mu + lambda) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

关键词： Genetic algorithms evolution strategies multiobjective optimization test functions multiobjective performance assessment

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Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

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EVOLUTIONARY COMPUTATION 2000年第2期8卷 173-195页

作者： Zitzler, Eckart Deb, Kalyanmoy Thiele, Lothar Swiss Fed Inst Technol Dept Elect Engn CH-8092 Zurich Switzerland Indian Inst Technol Dept Mech Engn Kanpur 208016 Uttar Pradesh India

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e. g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

关键词： Evolutionary algorithms multiobjective optimization Pareto optimality test functions elitism

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The reproducing kernel thesis for lower bounds of weighted composition operators

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ARCHIV DER MATHEMATIK 2019年第2期113卷 179-187页

作者： Chalendar, I. Partington, J. R. Univ Paris Est LAMA UMR 8050 UPEMUPECCNRS F-77454 Marne La Vallee France Univ Leeds Sch Math Leeds LS2 9JT W Yorkshire England

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including repro... 详细信息

关键词： Reproducing kernel Weighted composition operator Reverse Carleson measure Hardy space Bergman space test functions

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A modified Secant method for unconstrained optimization

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期186卷 1000-1004页

作者： Kahya, Emin Chen, Jinhai Eskisehir Osmangazi Univ Dept Ind Engn TR-26030 Eskisehir Turkey City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China

In this study, a modification of the classical Secant method for solving nonlinear, univariate and unconstrained optimization problems based on the development of the cubic approximation is presented. The iteration formula including an approximation of the third derivative of f(x) by using the Taylor series expansion is derived. The performance of the new method is analyzed in terms of the number of iterations in comparison with the Secant methods using six test functions. (c) 2006 Elsevier Inc. All rights reserved.

关键词： unconstrained optimization univariate optimization Secant method test functions

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Compact difference scheme for parabolic and Schrodinger-type equations with variable coefficients

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JOURNAL OF COMPUTATIONAL PHYSICS 2018年 375卷 1451-1468页

作者： Gordin, Vladimir A. Tsymbalov, Evgenii A. Natl Res Univ Higher Sch Econ Hydrometeorol Ctr Russia Moscow 123242 Russia Natl Res Univ Higher Sch Econ Skolkovo Inst Sci & Technol Moscow Russia

We develop a new compact scheme for the second-order PDE (parabolic and Schrodinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Compact difference scheme Parabolic equation Implicit scheme test functions Self-adjointness Neumann boundary conditions

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Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

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BULLETIN OF MATHEMATICAL BIOLOGY 2023年第11期85卷 1-36页

作者： Bortz, David M. Messenger, Daniel A. Dukic, Vanja Univ Colorado Dept Appl Math Boulder CO 80309 USA

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support *** demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://***/MathBioCU/WENDy.

关键词： Data-driven modeling Parameter estimation Parameter inference Weak Form test functions

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A Novel Quantum Firefly Algorithm for Global Optimization

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2021年第9期46卷 8741-8759页

作者： Zitouni, Farouq Harous, Saad Maamri, Ramdane Kasdi Merbah Univ Dept Comp Sci Ouargla Algeria Abdelhamid Mehri Univ LIRE Lab Constantine Algeria UAE Univ Abu Dhabi Dept Comp Sci & Software Engn Al Ain U Arab Emirates Abdelhamid Mehri Univ Dept Comp Sci Constantine Algeria

A novel nature-inspired metaheuristic optimization algorithm, called the quantum firefly algorithm, is proposed in this paper. The algorithm imitates (a) the social behaviour of fireflies mating in nature, (b) laws of quantum physics, and (c) laws of natural evolution. The algorithm combines the powers of two well-known algorithms: the firefly algorithm and the quantum genetic algorithm. The proposed quantum firefly algorithm's performance is tested on 15 mathematical test functions and one structural design problem. The obtained results show that the quantum firefly algorithm is very competitive compared to the firefly algorithm and the quantum genetic algorithm.

关键词： Firefly algorithm Quantum genetic algorithm Global optimization Metaheuristics test functions

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Evolutionary Algorithms for Constrained Parameter Optimization Problems

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EVOLUTIONARY COMPUTATION 1996年第1期4卷 1-32页

作者： Michalewicz, Zbigniew Schoenauer, Marc Univ N Carolina Dept Comp Sci Charlotte NC 28223 USA Polish Acad Sci Inst Comp Sci PL-01237 Warsaw Poland Ecole Polytech CMAP URA CNRS 756 F-91128 Palaiseau France

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems;however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem;(2) survey several approaches that have emerged in the evolutionary computation community;and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

关键词： Parametric optimization constraint handling test functions

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