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Multiple Global Peaks Big Bang-Big Crunch Algorithm for Multimodal optimization

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arXiv 2024年

作者： Stroppa, Fabio Astar, Ahmet Computer Engineering Department Kadir Has University Cibali Kadir Has Cd. Fatih Istanbul34083 Turkey

The main challenge of multimodal optimization problems is identifying multiple peaks with high accuracy in multidimensional search spaces with irregular landscapes. This work proposes the Multiple Global Peaks Big Bang-Big Crunch (MGP-BBBC) algorithm, which addresses the challenge of multimodal optimization problems by introducing a specialized mechanism for each operator. The algorithm expands the Big Bang-Big Crunch algorithm, a state-of-the-art metaheuristic inspired by the universe's evolution. Specifically, MGP-BBBC groups the best individuals of the population into cluster-based centers of mass and then expands them with a progressively lower disturbance to guarantee convergence. During this process, it (i) applies a distance-based filtering to remove unnecessary elites such that the ones on smaller peaks are not lost, (ii) promotes isolated individuals based on their niche count after clustering, and (iii) balances exploration and exploitation during offspring generation to target specific accuracy levels. Experimental results on twenty multimodal benchmark test functions show that MGP-BBBC generally performs better or competitively with respect to other state-of-the-art multimodal optimizers. © 2024, CC BY.

关键词： optimization algorithms

Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(ϵ−2) rather than O(ϵ−2)

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arXiv 2024年

作者： Gratton, Serge Sim, Chee-Khian Toint, Philippe L. Université de Toulouse INP IRIT Toulouse France University of Portsmouth Hampshire United Kingdom NAXYS University of Namur Namur Belgium

MSC Codes 49M37, 65K05, 68Q17, 68W40, 90C30We revisit the standard "telescoping sum" argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy ϵ. While bounds obtained using the standard argument typically are of the form O(ϵ−α) for some positive α, the refined results are of the form o(ϵ−α). We then explore to which known algorithms our refined bounds are applicable and finally describe an example showing how close the standard and refined bounds can be. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

AN optimization PROBLEM AND POINT-EVALUATION IN PALEY-WIENER SPACES

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arXiv 2024年

作者： Instanes, Sarah May TrondheimNO-7491 Norway

We study the constant Cp defined as the smallest constant C such that |f(0)|p ≤ Ckfkpp holds for every function f in the Paley-Wiener space PWp. Brevig, Chirre, Ortega-Cerdà, and Seip have recently shown that Cp... 详细信息

关键词： optimization algorithms

Fast FISTA Algorithm With New Backtracking Technique For Multiobjective optimization

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arXiv 2024年

作者： Chengzhi, Huang Jian, Chen Liping, Tang National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy addresses the limitation of existing algorithms that struggle to handle situations where the Lipschitz constant L(f) of the objective function’s gradient is still being determined. It mitigates the petite iteration step sizes caused by a significant value of L(f). Furthermore, the proposed strategy effectively avoids the limitation in convergence proofs arising from the non-negativity of the auxiliary sequence Wk(z):= mini=1,···,m[Fi(xk) - Fi(z)], thus providing a theoretical guarantee for its performance. We demonstrate that, under relatively mild assumptions, the algorithm achieves the convergence rate of O(1/k2). Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Dynamic Incremental optimization for Best Subset Selection

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arXiv 2024年

作者： Ren, Shaogang Qian, Xiaoning Department of Computer Science and Engineering University of Tennessee at Chattanooga United States Department of Electrical and Computer Engineering Texas A&M University United States

Best subset selection is considered the ‘gold standard’ for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of a family of 0-regularized problems. An efficient primal-dual algorithm is developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

DESIGN GUIDELINES FOR NOISE-TOLERANT optimization WITH APPLICATIONS IN ROBUST DESIGN

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arXiv 2024年

作者： Lou, Yuchen Sun, Shigeng Nocedal, Jorge Department of Industrial Engineering and Management Sciences Northwestern University United States Department of Engineering Sciences and Applied Mathematics Northwestern University United States

The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the problem. The application of our methodology is illustrated by the development of a line search gradient projection method, which is tested on an engineering design problem. It is shown that a new self-calibrated line search and noise-aware finite-difference techniques are effective even in the high noise regime. Numerical experiments investigate the resiliency of key algorithmic components. A convergence analysis of the line search gradient projection method establishes convergence to a neighborhood of *** Codes 90C30, 90C15, 93B51, 65K05 © 2024, CC BY.

关键词： optimization algorithms

SPARKLE: A Unified Single-Loop Primal-Dual Framework for Decentralized Bilevel optimization

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arXiv 2024年

作者： Zhu, Shuchen Kong, Boao Lu, Songtao Huang, Xinmeng Yuan, Kun Peking University China IBM Research United States University of Pennsylvania United States National Engineering Labratory for Big Data Analytics and Applications AI for Science Institute Beijing China

This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient tracking to mitigate the influence of data heterogeneity, without exploring other well-known heterogeneity-correction techniques such as EXTRA or Exact Diffusion. Additionally, these studies often employ identical decentralized strategies for both upper- and lower-level problems, neglecting to leverage distinct mechanisms across different levels. To address these limitations, this paper proposes SPARKLE, a unified Single-loop Primal-dual AlgoRithm frameworK for decentraLized bilEvel optimization. SPARKLE offers the flexibility to incorporate various heterogeneity-correction strategies into the algorithm. Moreover, SPARKLE allows for different strategies to solve upper- and lower-level problems. We present a unified convergence analysis for SPARKLE, applicable to all its variants, with state-of-the-art convergence rates compared to existing decentralized bilevel algorithms. Our results further reveal that EXTRA and Exact Diffusion are more suitable for decentralized bilevel optimization, and using mixed strategies in bilevel algorithms brings more benefits than relying solely on gradient tracking. © 2024, CC BY.

关键词： optimization algorithms

Anisotropic Gaussian Smoothing for Gradient-based optimization

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arXiv 2024年

作者： Starnes, Andrew Zhang, Guannan Reshniak, Viktor Webster, Clayton Behavioral Research Learning Lab Lirio Inc. Computer Science and Mathematics Division Oak Ridge National Laboratory United States

This article introduces a novel family of optimization algorithms-Anisotropic Gaussian Smoothing Gradient Descent (AGS-GD), AGS-Stochastic Gradient Descent (AGS-SGD), and AGS-Adam-that employ anisotropic Gaussian smoothing to enhance traditional gradient-based methods, including GD, SGD, and Adam. The primary goal of these approaches is to address the challenge of optimization methods becoming trapped in suboptimal local minima by replacing the standard gradient with a non-local gradient derived from averaging function values using anisotropic Gaussian smoothing. Unlike isotropic Gaussian smoothing (IGS), AGS adapts the smoothing directionality based on the properties of the underlying function, aligning better with complex loss landscapes and improving convergence. The anisotropy is computed by adjusting the covariance matrix of the Gaussian distribution, allowing for directional smoothing tailored to the gradient's behavior. This technique mitigates the impact of minor fluctuations, enabling the algorithms to approach global minima more effectively. We provide detailed convergence analyses that extend the results from both the original (unsmoothed) methods and the IGS case to the more general anisotropic smoothing, applicable to both convex and non-convex, L-smooth functions. In the stochastic setting, these algorithms converge to a noisy ball, with its size determined by the smoothing parameters. The article also outlines the theoretical benefits of anisotropic smoothing and details its practical implementation using Monte Carlo estimation, aligning with established zero-order optimization *** Codes 90C26 © 2024, CC BY.

关键词： optimization algorithms

An Artificial Neural Network Based Strategy for Commutation Failure Forecasting in LCC-HVDC Transmission Networks

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An Artificial Neural Network Based Strategy for Commutation ...

2023 IEEE International Conference on Energy Technologies for Future Grids, ETFG 2023

作者： Mirsaeidi, Sohrab Shang, Fuxiang Ghaffari, Kimia He, Jinghan Said, Dalila Mat Muttaqi, Kashem M. Beijing Jiaotong University School of Electrical Engineering Beijing China Beijing Jiaotong University School of Economics and Management Beijing China School of Electrical Engineering Johor Malaysia University of Wollongong School of Electrical Computer and Telecommunications Engineering Wollongong Australia

ISBN: (纸本)9781665471640

Commutation failure (CF) is a major challenge associated with line-commutated converter high voltage dc (LCC-HVdc) systems. Faults at the inverter ac systems are regarded as main cause of commutation failure. The present study proposes a method for forecasting the commutation failure based on a feed-forward neural network (FFNN) combined with optimization algorithms and principal component analysis (PCA). To fulfill this, first, a two-terminal HVdc system is designed, and then, a large number of three-phase faults with different fault inductances are applied on the inverter ac side. In each fault case, 100 samples of the dc current signal in the interval between fault and commutation failure initial times are taken with the sampling frequency of 1 MHz. Subsequently, with the aim of dimensionality reduction, the samples are preprocessed by the PCA before serving as inputs of the neural network. Finally, various metaheuristic optimization methods, i.e. particle swarm optimization (PSO), grey wolf optimizer (GWO), simulated annealing (SA), and genetic algorithm (GA) are utilized to determine the most appropriate structure for the neural network in terms of the number of neurons in each hidden layer, and the type of transfer function (TF) in hidden layers and output layer. The simulation results indicate that the optimized artificial neural network can predict the commutation failure occurrence with an accuracy of roughly 90%. © 2023 IEEE.

关键词： artificial neural network Commutation failure forecasting optimization algorithms principal component analysis