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Optimizing algorithms and decision making problems through novel distance techniques with complex fermatean fuzzy numbers

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Partial Differential Equations in Applied Mathematics 2024年

作者： Ziad Khan Fawad Hussain Ikhtesham Ullah Tariq Rahim Madad Khan Rashid Jan Ibrahim Mekawy Department of Mathematics Abbottabad University of Science and Technology Abbottabad 22500 Pakistan Department of Mathematics COMSATS University Islamabad Abbottabad Campus Abbottabad 22060 Pakistan Institute of Energy Infrastructure (IEI) Department of Civil Engineering College of Engineering Universiti Tenaga Nasional (UNITEN) Putrajaya Campus Jalan IKRAM-UNITEN 43000 Kajang Selangor Malaysia Department of Mathematics College of Science Qassim University Buraydah 51452 Saudi Arabia

The concept of C F FSs offers a more comprehensive on CFSs, C I FSs, and C PY FSs, with greater potential for practical applications due to their flexible structure, larger space, adjustable parameters, and influential design compared to other generalization of FSs. The striking framework of C F FSs is keen to provide a larger preference range for the modeling of uncertain information. This article sets out a decision-making analysis for the interaction between complex-valued membership and complex-valued non-membership degrees with the help of C F FNs. Some of the unique operational laws and their fundamental properties for C F FNs are studied. Distance measures have been extensively used in many areas as an essential approach that may successfully disclose the difference between CFSs and their generalizations. Some of the well-known distance measures for C F FNs has been studied in the literature, so on the basis of these distances, some novel distance measures for C F FNs have been analyzed. The applications of the proposed C F FDMs are demonstrated in scenarios including telecommunication and medical diagnostic problems. A comparative analysis of the obtained novel C F FDMs with similar existing distances is conducted through numerical examples. All the observations and results are presented graphically. The present novel C F FDMs are fantastically designated for the classification of the most favorable alternatives by examining the closeness of all available choices from a particular ideal solution.

关键词： Decision-making problems Novel distance measures Complex fermatean fuzzy numbers algorithms for CFFNs optimization algorithms Diagnosis

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Improving Metaheuristic algorithms With Information Feedback Models

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IEEE TRANSACTIONS ON CYBERNETICS 2019年第2期49卷 542-555页

作者： Wang, Gai-Ge Tan, Ying Ocean Univ China Dept Comp Sci & Technol Qingdao 266100 Peoples R China Jiangsu Normal Univ Sch Comp Xuzhou 221116 Jiangsu Peoples R China Northeast Normal Univ Inst Algorithm & Big Data Anal Changchun 130117 Jilin Peoples R China Northeast Normal Univ Sch Comp Sci & Informat Technol Changchun 130117 Jilin Peoples R China Peking Univ Sch Elect Engn & Comp Sci Key Lab Machine Percept Beijing 100871 Peoples R China Peking Univ Sch Elect Engn & Comp Sci Dept Machine Intelligence Beijing 100871 Peoples R China

In most metaheuristic algorithms, the updating process fails to make use of information available from individuals in previous iterations. If this useful information could be exploited fully and used in the later optimization process, the quality of the succeeding solutions would be improved significantly. This paper presents our method for reusing the valuable information available from previous individuals to guide later search. In our approach, previous useful information was fed back to the updating process. We proposed six information feedback models. In these models, individuals from previous iterations were selected in either a fixed or random manner. Their useful information was incorporated into the updating process. Accordingly, an individual at the current iteration was updated based on the basic algorithm plus some selected previous individuals by using a simple fitness weighting method. By incorporating six different information feedback models into ten metaheuristic algorithms, this approach provided a number of variants of the basic algorithms. We demonstrated experimentally that the variants outperformed the basic algorithms significantly on 14 standard test functions and 10 CEC 2011 real world problems, thereby, establishing the value of the information feedback models.

关键词： Benchmark evolutionary algorithms (EAs) evolutionary computation information feedback metaheuristic algorithms optimization algorithms swarm intelligence

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Effective methodology based on neural network optimizer for extracting model parameters of PEM fuel cells

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 2019年第14期43卷 8136-8147页

作者： Fawzi, Mohamed El-Fergany, Attia A. Hasanien, Hany M. Mansoura Univ Fac Engn Dept Elect Engn Mansoura Egypt Zagazig Univ Fac Engn Elect Power & Machines Dept Zagazig 44519 Egypt Ain Shams Univ Fac Engn Elect Power & Machines Dept Cairo 11517 Egypt

I/V polarization curves of proton-exchange membrane fuel cells (PEMFCs) are used to characterize the performance of single cells and stacks. Numerous semi-empirical models are presented to predict such polarization curves by determining the unknown parameters of mathematical model of the PEMFCs stack. In this paper, a novel optimization approach, namely neural network algorithm (NNA) is applied for an estimation of the unknown PEMFC model parameters. The NNA is employed to minimize adopted objective function, which is formulated as the sum of squared deviations (SSD) between the actual data and estimated voltage points subjects to set of inequality constraints are satisfied. Three commercial types of PEMFCs stack namely Ballard Mark V, BCS-500 W, and Nedstack PS6 are numerically simulated to show the effectiveness of the proposed NNA-based tool for parameter identification. The minimum values of SSD are 0.8536 V-2 for Ballard Mark V, 0.011698 V-2 for BCS-500 W stack, and 2.14487 V-2 for Nedstack PS6, respectively. The obtained results of the NNA are compared with other optimizers recently published in the literature such as flower pollination algorithm, slap swarm optimizer, grey wolf algorithm, grasshopper optimization algorithm, and shark smell algorithm under the same conditions. The comparisons and other performance tests indicate the robustness and the competition of the adopted NNA-based method for producing accurate I/V polarization curves under different operating scenarios.

关键词： optimization algorithms parameter extraction polymer electrolyte membrane fuel cells steady-state modeling

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Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2019年第6期64卷 2442-2456页

作者： Umenberger, Jack Manchester, Ian R. Univ Sydney Australian Ctr Field Robot Sch Aerosp Mech & Mechatron Engn Sydney NSW 2006 Australia Uppsala Univ Dept Informat Technol S-75237 Uppsala Sweden

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and nonconvexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP);however, the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper, we develop a path-following interior-point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the dataset. The new algorithm enables empirical comparisons to established methods including nonlinear autoregressive models with exogenous inputs, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.

关键词： Nonlinear system identification optimization algorithms stability of nonlinear systems

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Bounds for the tracking error of first-order online optimization methods

arXiv

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arXiv 2020年

作者： Madden, Liam Becker, Stephen Dall'Anese, Emiliano Dept. of Applied Mathematics University of Colorado Boulder United States Dept. of Electrical Computer and Energy Engineering University of Colorado Boulder United States

This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking iterate error (the limit supremum of the norm of the difference between the optimal solution and the iterates) for online gradient descent are derived. The paper then considers a general first-order framework, where a universal lower bound on the tracking iterate error is established. Furthermore, a method using "long-steps" is proposed and shown to achieve the lower bound up to a fixed constant. This method is then compared with online gradient descent for specific examples. Finally, the paper analyzes the effect of regularization when the cost is not strongly convex. With regularization, it is possible to achieve a non-regret bound. The paper ends by testing the accelerated and regularized methods on synthetic time-varying least-squares and logistic regression problems, respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： optimization algorithms

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Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying optimization Approach

Implicit Trajectory Planning for Feedback Linearizable Syste...

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American Control Conference

作者： Tianqi Zheng John Simpson-Porco Enrique Mallada Department of Electrical and Computer Engineering Johns Hopkins University Baltimore MD USA Department of Electrical and Computer Engineering University of Waterloo Waterloo ON Canada

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to, e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-object or multi-agent tracking problems with constraints.

关键词： Time-varying optimization motion planning feedback linearization motion planning optimization algorithms control law trajectory trajectory planning Feedback time varying

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Statistical optimization for High Dimensional Machine Learning with Privacy and Sparsity Constraints

Statistical Optimization for High Dimensional Machine Learni...

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作者： Ge, Jason Princeton University

学位级别：Ph.D.

High-dimensionality and privacy sensitive data in modern machine learning problems poses computational challenges that ask for novel optimization algorithms. This thesis presents optimization algorithms that achieve superior theoretical and empirical performance by leveraging structure of the statistical model in machine learning problems. Chapter 2 of the thesis proposes a distributed privacy-preserving sparse PCA (DPS-PCA) algorithm that generates a minimax-optimal sparse PCA estimator under differential privacy constraints. Data providers can use this algorithm to collaboratively analyze the union of their datasets while limiting the disclosure of their private information. DPS-PCA can recover the leading eigen-space of the population covariance at a geometric convergence rate, and simultaneously achieves the optimal minimax statistical error for high-dimensional data. In Chapter 3, we present a pathwise Active Set Proximal Newton algorithm for estimating L1 regularized sparse generalized linear models in high dimensions. With an efficient active set strategy and a pathwise optimization scheme, our algorithm leverages the restricted strong convexity of the loss function (i.e., the negative log-likelihood) and achieves an asymptotic quadratic rate of convergence, even if the loss function itself is not strongly convex. Chapter 4 presents a DC proximal Newton algorithm for solving high-dimensional sparse learning problems under non-convex penalties such as MCP and SCAD. We prove in theory that the proposed algorithm can achieve local quadratic convergence within each stage of convex relaxation, and it takes only a few convex relaxations to obtain a sparse approximate local optimum. Finally in Chapter 5 we present an R and Python package that implements the sparse learning algorithms. Our package achieves state-of-the-art performance among all the available sparse learning solvers that handles L1 and nonconvex penalties.

关键词： High dimensional statistics Machine Learning optimization algorithms Privacy-preserving data analysis Sparse Learning

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Multiphase Equilibrium Calculation Framework for Compositional Simulation of CO2 Injection in Low-Temperature Reservoirs

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2019年第5期58卷 2052-2070页

作者： Pan, Huanquan Connolly, Michael Tchelepi, Hamdi Stanford Univ Dept Energy Resources Engn Stanford CA 94305 USA

CO2 injection into an oil reservoir at low temperature can lead to the formation of three hydrocarbon phases. Key challenges persist in the development of phase equilibrium calculations for three-phase hydrocarbon-CO2 systems. One challenge is the identification of a third equilibrium phase via stability testing of a two-phase mixture. Stability testing requires initial estimates of phase equilibrium ratios (K-values). Existing methods for estimating K-values for the identification of three-phase behavior are unable to detect the whole three-phase region. In addition, many of the initial K-value estimates are redundant, wherein convergence is to the same composition. In this work, we present systematic procedures for single-phase and two-phase stability testing using optimized sets of initial K-value estimates. We show that two-phase stability testing requires one to test both of the equilibrium phases in the system. We reveal that three-phase hydrocarbon-CO2 behavior cannot be resolved across the pressure-composition parameter space with existing methods for the estimates of the initial K-value. We introduce a new initial K-value estimate for two-phase stability testing to resolve three-phase behavior. Our approach significantly improves the reliability and reduces the cost of phase stability testing. Reservoir simulation requires fast and reliable algorithms for stability testing and flash calculations. Failure of the phase equilibrium kernel leads to time-step cuts and the potential cessation of the simulator. We have implemented a combined successive substitution, Newton, and trust-region optimization algorithm for both stability testing and multiphase flash calculations. We have also developed a novel optimization algorithm to solve the multiphase Rachford-Rice equations. We present the performance of our phase equilibrium framework using nine characterized fluid systems from the literature. Rigorous testing across a wide parameter space demonstrates the robust

关键词： PHASE BEHAVIOR FLASH CALCULATION CARBON DIOXIDE INJECTION MULTI-PHASE stability study phase equilibria optimization algorithms parameter space methods

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Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval

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MATHEMATICAL PROGRAMMING 2019年第1-2期176卷 5-37页

作者： Chen, Yuxin Chi, Yuejie Fan, Jianqing Ma, Cong Princeton Univ Dept Elect Engn Princeton NJ 08544 USA Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA

This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest x?Rn from m quadratic equations/samples yi=(ai?x?)2,1im. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficacy of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descentwhen randomly initializedyields an E-accurate solution in O(logn+log(1/E)) iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain statistical dependency between the gradient descent iterates and the data.

关键词： initialization optimization algorithms descent Physical science DECOUPLING Gauss Gradient retrieval global convergence

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Itakura-Saito Divergence as an Element of the Information Theory of Speech Perception

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2019年第6期64卷 590-596页

作者： Savchenko, V. V. Linguist Univ Nizhny Novgorod Nizhnii Novgorod 603155 Russia

On the basis of the information theory of speech perception, a substantiation of the symmetric form of the Itakura-Saito divergence as the minimum decision-making statistics of the asymptotically optimal algorithm for recognition of speech signals at the basic, phonetic level of their processing is given. The conclusions of the theoretical study are confirmed by the results of an experiment. It is shown that the use of the synthesized algorithm can significantly improve the accuracy and reliability of the automatic recognition of the most problematic phonetic units.

关键词： Speech Perception Information Theory Theoretical Study phonetics Speech optimization algorithms

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