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作者： Yarmolskyy, Oleksandr Brno University of Technology

Tato diplomová práce se zabývá problematikou distribuovaných a stochastických algoritmů včetně testování jejich konvergence v sítích. V teoretické části jso... 详细信息

Tato diplomová práce se zabývá problematikou distribuovaných a stochastických algoritmů včetně testování jejich konvergence v sítích. V teoretické části jsou výše uvedené algoritmy stručně popsané, včetně jejich dělení, problémů, výhod a nevýhod. Dále jsou vybrané dva distribuované algoritmy a dva stochastické algoritmy a následně jsou stručně popsané. V praktické části je provedeno jejich porovnání podle rychlosti konvergence na odlišných topologiích sítí v prostředí MATLAB.

关键词： distribuované algoritmy stochastické algoritmy konvergence MATLAB Bellmanův-Fordův algoritmus Dijkstrův algoritmus A* algoritmus Push-sum algoritmus distributed algorithms stochastic algorithms convergence MATLAB Bellman-Ford algorithm dijkst

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GLOBAL LINEAR CONVERGENCE OF EVOLUTION STRATEGIES ON MORE THAN SMOOTH STRONGLY CONVEX FUNCTIONS

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SIAM JOURNAL ON OPTIMIZATION 2022年第2期32卷 1402-1429页

作者： Akimoto, Youhei Auger, Anne Glasmachers, Tobias Morinaga, Daiki Univ Tsukuba Fac Engn Informat & Syst Tsukuba Ibaraki 3058571 Japan RIKEN AIP Tsukuba Ibaraki 3058571 Japan Ecole Polytech IP Paris INRIA F-91128 Paris France Ecole Polytech IP Paris CMAP F-91128 Paris France Ruhr Univ Bochum Inst Neural Computat D-44801 Bochum Germany Univ Tsukuba Dept Comp Sci Tsukuba Ibaraki 3058571 Japan

Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMAES is nowadays recognized as one of the state-of-the-art zeroth-order optimizers for difficult problems. Despite ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zeroth-order and also first-order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES family, namely, the (1+ 1)(kappa)-ES, which includes the (1+1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions.

关键词： evolution strategies randomized derivative free optimization black-box optimization linear convergence stochastic algorithms

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Modified LMS and NLMS algorithms with non-negative weights

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SIGNAL PROCESSING 2024年 223卷

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA USA Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil

Non -negative constraints arise in certain system identification problems when the systems to be identified have only positive coefficients. This paper studies the stochastic behavior of modified LMS and NLMS algorithms, modified so as to only allow adaptation with positive coefficients. The mean and second moment behavior of these algorithms are analyzed for Gaussian inputs. Excellent agreement is demonstrated between the theory and Monte Carlo simulations for the LMS algorithm.

关键词： Adaptive filters Analysis LMS algorithm stochastic algorithms

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A switched variable step size NLMS adaptive filter

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DIGITAL SIGNAL PROCESSING 2020年 101卷 102730-000页

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect & Comp Engn Irvine CA 92717 USA Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil Catholic Univ Pelotas UCPel Pelotas Grad Program Elect Engn & Comp Pelotas RS Brazil

This paper studies the statistical behavior of a switched variable step size Normalized Least Mean Square adaptive filter. The purpose of the switching is to obtain a Normalized Least Mean Square adaptive filter combination with fast convergence and small steady-state mean-square weight deviation (MSD). Previous works studied variable step-size Least Mean Square (LMS) and Normalized Mean Square (NLMS) adaptive filters using a measured quantity (say instantaneous squared error) in a nonlinear recursion for varying the step size. Here, it is proposed to avoid the nonlinear recursion in a novel way that is based upon a simple physical premise: For several practical applications, what is required is a faster initial convergence rate phase, followed by a slower convergence rate period that allows for a desired steady-state performance. The fast NLMS transient behavior is obtained with a fixed step size. After convergence, the step size is reduced to a smaller value to satisfy a desired tradeoff between the second transient and the desired steady-state MSD. Thus, during the first transient, the Switched VSS-NLMS adaptive weights will converge faster or as fast as any VSS-NLMS algorithm. Of course, during the second phase, some variable step size algorithms may eventually outperform the Switched VSS-NLMS algorithm. However, in many cases, this can be a small price to pay in exchange for the theoretical and computational simplicity. No new theory is needed to predict the behavior of the nonlinear recursion for the step size. Furthermore, the analytical theory for the MSD of the new scheme is well-known. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Adaptive filters Variable step-size NLMS algorithm stochastic algorithms

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Analysis of the Least Mean Square algorithm with processing delays in the adaptive arm for Gaussian inputs for system identification

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SIGNAL PROCESSING 2024年 217卷

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil

This paper analyzes the effect of a processing delay on the Least Mean Squares (LMS) algorithm for a system identification problem when the processing delay is in the adaptive arm of the filter. Thus the sensing of the input signal is delayed. The input is assumed to be a zero mean stationary Gaussian process. The theoretical mean and mean square behavior of the adaptive weight vector is analyzed. The weight vector is shown to be biased and significantly affects the mean square deviation (MSD). Monte Carlo simulations are presented in support of the assumptions used to derive the theoretical model as a function of the delay, bandwidth and step-size for the LMS algorithm. The results suggest bias problems with other more complicated adaptive filtering algorithms such as Normalized LMS and Recursive Least Squares.

关键词： Adaptive filters Analysis LMS algorithm stochastic algorithms

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Block-wise primal-dual algorithms for large-scale doubly penalized ANOVA modeling

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2024年 194卷

作者： Fu, Penghui Tan, Zhiqiang Rutgers State Univ Dept Stat Piscataway NJ 08854 USA Chinese Univ Hong Kong Shenzhen Sch Data Sci Shenzhen 518172 Guangdong Peoples R China

For multivariate nonparametric regression, doubly penalized ANOVA modeling (DPAM) has recently been proposed, using hierarchical total variations (HTVs) and empirical norms as penalties on the component functions such as main effects and multi -way interactions in a functional ANOVA decomposition of the underlying regression function. The two penalties play complementary roles: the HTV penalty promotes sparsity in the selection of basis functions within each component function, whereas the empirical -norm penalty promotes sparsity in the selection of component functions. To facilitate large-scale training of DPAM using backfitting or block minimization, two suitable primal -dual algorithms are developed, including both batch and stochastic versions, for updating each component function in single -block optimization. Existing applications of primal -dual algorithms are intractable for DPAM with both HTV and empirical -norm penalties. The validity and advantage of the stochastic primal -dual algorithms are demonstrated through extensive numerical experiments, compared with their batch versions and a previous active -set algorithm, in large-scale scenarios.

关键词： ANOVA modeling Nonparametric regression Penalized estimation Primal-dual algorithms stochastic algorithms stochastic gradient methods Total variation

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A new optimization algorithm based on mimicking the voting process for leader selection

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PEERJ COMPUTER SCIENCE 2022年 8卷 e976页

作者： Trojovsky, Pavel Dehghani, Mohammad Univ Hradec Kralove Fac Sci Dept Math Hradec Kralove Czech Republic

stochastic-based optimization algorithms are effective approaches to addressing optimization challenges. In this article, a new optimization algorithm called the Election-Based Optimization Algorithm (EBOA) was developed that mimics the voting process to select the leader. The fundamental inspiration of EBOA was the voting process, the selection of the leader, and the impact of the public awareness level on the selection of the leader. The EBOA population is guided by the search space under the guidance of the elected leader. EBOA's process is mathematically modeled in two phases: exploration and exploitation. The efficiency of EBOA has been investigated in solving thirty-three objective functions of a variety of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and CEC 2019 types. The implementation results of the EBOA on the objective functions show its high exploration ability in global search, its exploitation ability in local search, as well as the ability to strike the proper balance between global search and local search, which has led to the effective efficiency of the proposed EBOA approach in optimizing and providing appropriate solutions. Our analysis shows that EBOA provides an appropriate balance between exploration and exploitation and, therefore, has better and more competitive performance than the ten other algorithms to which it was compared.

关键词： Optimization Optimization problem Human-based metahurestic algorithm stochastic algorithms Population-based algorithms Applied mathematics Voting process Leader selection Population matrix Recurring process

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A new sine cosine algorithm for economic and emission dispatch problems with price penalty factors

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2019年第3期40卷 679-697页

作者： Gonidakis, Dimitrios Vlachos, Aristidis Univ Piraeus Dept Informat 80M Karaoli & A Dimitriou St Piraeus 18534 Greece Acad Merchant Marine Aspropyrgos Deptartment Mech Engn Aspropyrgos 19300 Greece

Combined economic and emission dispatch (CEED) is the process of determining the outputs of generating units in a power system in order to minimise the fuel cost and pollutants emissions at the same time. This multi-objective mathematical problem can be transformed into a single-objective with the insertion of a price penalty factor. In this study, a newly developed sine and cosine algorithm (SCA) is employed to solve CEED. The proposed method is described by a trigonometric-based model and applied to three test systems with different characteristics. The numerical results indicate that SCA provides high quality solutions and outperforms other recently reported optimisation methods.

关键词： Combined economic and emission dispatch Economic load dispatch Sine cosine algorithm Multi-objective optimisation Price penalty factor stochastic algorithms

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Meta-heuristics for the deterministic hybrid flow shop problem

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Journal Europeen des Systemes Automatises 2000年第9期34卷 1107-1135页

作者： Gourgand, Michel Grangeon, Nathalie Norre, Sylvie Univ. Blaise Pascal Clermont-F. LIMOS - CNRS FRE 2239 Complexe Sci. des Cézeaux F-63177 Aubière Cedex France

This article deals with the hybrid flow shop problem : scheduling of input jobs and resource assignment are both studied. We propose a predictive approach using metaheuristics : stochastic algorithms based on simulated annealing. These algorithms allow to study many types of hybrid flow shop problems (limited or unlimited storage, no storage, no wait, ...) and many types of criteria. We propose neighbouring systems and present results for literature problems, generated problems with identical, uniform or unrelated parallel machines (up to 500 jobs and 20 machines) and an industrial problem with 7000 jobs and 4 stages. We obtain good results, closed to lower bound or optimal solution in a short processing time.

关键词： Hybrid Flow Shop Metaheuristics Neighbouring systems Predictive approach Resource assignment Scheduling stochastic algorithms

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Identification of Mechanical Parameters in Flexible Drive Systems Using Hybrid Particle Swarm Optimization Based on the Quasi-Newton Method

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algorithms 2023年第8期16卷 371-371页

作者： Hafez, Ishaq Dhaouadi, Rached Amer Univ Sharjah Coll Engn Mechatron Grad Program Sharjah 26666 U Arab Emirates Amer Univ Sharjah Coll Engn Dept Elect Engn Sharjah 26666 U Arab Emirates

This study presents hybrid particle swarm optimization with quasi-Newton (HPSO-QN), a hybrid optimization method for accurately identifying mechanical parameters in two-mass model (2MM) systems. These systems are commonly used to model and control high-performance electric drive systems with elastic joints, which are prevalent in modern industrial production. The proposed method combines the global exploration capabilities of particle swarm optimization (PSO) with the local exploitation abilities of the quasi-Newton (QN) method to precisely estimate the motor and load inertias, shaft stiffness, and friction coefficients of the 2MM system. By integrating these two optimization techniques, the HPSO-QN method exhibits superior accuracy and performance compared to standard PSO algorithms. Experimental validation using a 2MM system demonstrates the effectiveness of the proposed method in accurately identifying and improving the mechanical parameters of these complex systems. The HPSO-QN method offers significant implications for enhancing the modeling, performance, and stability of 2MM systems and can be extended to other systems with flexible shafts and couplings. This study contributes to the development of accurate and effective parameter identification methods for complex systems, emphasizing the crucial role of precise parameter estimation in achieving optimal control performance and stability.

关键词： parameter identification two-mass model electric drive systems particle swarm optimization quasi-Newton method hybrid optimization stochastic algorithms mechanical parameters optimal control performance elastic joints

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