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Enhancing QUasi-Affine TRansformation Evolution (QUATRE) with adaptation scheme on numerical optimization

KNOWLEDGE-BASED SYSTEMS 2020年 197卷 105908-105908页

作者： Meng, Zhenyu Chen, Yuxin Li, Xiaoqing Yang, Cheng Zhong, Yuxin Fujian Univ Technol Inst Artificial Intelligence Fuzhou Peoples R China

Optimization problems exists extensively in real life, especially in science and engineering. Over the past decades, various optimization techniques have been developed to solve complex optimization problems in different areas especially that are unable to be solved by traditional methods. QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm is a new novel evolution structure for global optimization, which is a swarm based algorithm and use quasi-affine transformation approach for evolution. Nevertheless, there are still some weaknesses in these QUATRE variants. This paper presents a novel E-QUATRE algorithm in which an automatically generated evolution matrix with self-adaptive mechanism and an adaptive control parameter F are proposed for the enhancement of the QUATRE algorithm. Moreover, this paper also discusses the relationship between QUATRE algorithm, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm, all of which are also famous swarm based stochastic algorithms (SAs). algorithm validation is conducted under CEC2013 test suite on single-objective numerical optimization, and E-QUATRE algorithm is compared with several famous Particle Swarm Optimization (PSO) variants, Differential Evolution (DE) variants and QUATRE variants. The experiment results indicate that the proposed E-QUATRE algorithm has a better performance than these swarm based algorithms with fixed population. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Adaptation scheme stochastic algorithm Numerical optimization QUATRE structure

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Speeding up continuous GRASP

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期205卷 507-521页

作者： Hirsch, M. J. Pardalos, P. M. Resende, M. G. C. Raytheon Inc Network Centr Syst Largo FL 33773 USA Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA AT&T Labs Res Algorithms & Optimizat Res Dept Florham Pk NJ 07932 USA

Continuous GRASP (C-GRASP) is a stochastic local search metaheuristic for finding cost-efficient solutions to continuous global optimization problems subject to box constraints (Hirsch et al., 2007). Like a greedy randomized adaptive search procedure (GRASP), a C-GRASP is a multi-start procedure where a starting solution for local improvement is constructed in a greedy randomized fashion. In this paper, we describe several improvements that speed up the original C-GRASP and make it more robust. We compare the new C-GRASP with the original version as well as with other algorithms from the recent literature on a set of benchmark multimodal test functions whose global minima are known. Hart's sequential stopping rule (1998) is implemented and C-GRASP is shown to converge on all test problems. (C) 2010 Elsevier BM. All rights reserved.

关键词： GRASP Continuous GRASP Global optimization Multimodal functions Continuous optimization Heuristic stochastic algorithm stochastic local search Nonlinear programming

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Variance reduction for root-finding problems

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MATHEMATICAL PROGRAMMING 2023年第1期197卷 375-410页

作者： Davis, Damek Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 16850 USA

Minimizing finite sums of smooth and strongly convex functions is an important task in machine learning. Recent work has developed stochastic gradient methods that optimize these sums with less computation than methods that do not exploit the finite sum structure. This speedup results from using efficiently constructed stochastic gradient estimators, which have variance that diminishes as the algorithm progresses. In this work, we ask whether the benefits of variance reduction extend to fixed point and root-finding problems involving sums of nonlinear operators. Our main result shows that variance reduction offers a similar speedup when applied to a broad class of root-finding problems. We illustrate the result on three tasks involving sums of n nonlinear operators: averaged fixed point, monotone inclusions, and nonsmooth common minimizer problems. In certain "poorly conditioned regimes," the proposed method offers an n-fold speedup over standard methods.

关键词： stochastic algorithm Variance reduction Root-finding algorithm Operator splitting Monotone inclusions Saddle-point problems

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A Python/C library for bound-constrained global optimization with continuous GRASP

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OPTIMIZATION LETTERS 2013年第5期7卷 967-984页

作者： Silva, R. M. A. Resende, M. G. C. Pardalos, P. M. Hirsch, M. J. Univ Fed Pernambuco Ctr Informat CIn Recife PE Brazil AT&T Labs Res Algorithms & Optimizat Res Dept Florham Pk NJ 07932 USA Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Raytheon Co Intelligence & Informat Syst Annapolis Jct MD 20701 USA

This paper describes , a GNU-style dynamic shared Python/C library of the continuous greedy randomized adaptive search procedure (C-GRASP) for bound constrained global optimization. C-GRASP is an extension of the GRASP metaheuristic (Feo and Resende, 1989) and has been used to solve unstable and nondifferentiable problems, as well as hard global optimization problems, such as chemical equilibrium systems and robot kinematics applications (Hirsch et al. in Optim lett 1:201-212, 2007). After a brief introduction to C-GRASP, we show how to download, install, configure, and use the library through an illustrative example.

关键词： GRASP Continuous GRASP Global optimization Multimodal functions Continuous optimization Heuristic stochastic algorithm stochastic local search Nonlinear programming

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Multi-Scale Quantum Harmonic Oscillator algorithm With Truncated Mean Stabilization Strategy for Global Numerical Optimization Problems

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IEEE ACCESS 2019年 7卷 18926-18939页

作者： Ye, Xinggui Wang, Peng Xin, Gang Jin, Jin Huang, Yan Univ Chinese Acad Sci Beijing 100049 Peoples R China Chinese Acad Sci Chengdu Inst Comp Applicat Chengdu 610041 Sichuan Peoples R China China Unicom Cloud Comp & Big Data Ctr Fujian Branch Fuzhou 350007 Fujian Peoples R China Southwest Minzu Univ Sch Comp Sci & Technol Chengdu 610225 Sichuan Peoples R China Huaiyin Normal Univ Sch Comp Sci & Technol Huaian 223300 Peoples R China

A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimensionwise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations.

关键词： Multi-scale quantum harmonic oscillator algorithm swarm intelligence population-based algorithm stochastic algorithm truncated mean stabilization strategy

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ET-DASG: An Efficient Decentralized algorithm for Convex Optimization Over Networks

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2022年第3期9卷 1789-1801页

作者： Lu, Qingguo Liao, Xiaofeng Deng, Shaojiang Li, Huaqing Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China Minist Educ Key Lab Ind Internet Things & Networked Control Chongqing 400065 Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China

This article studies the problem of decentralized optimization to minimize a finite-sum of convex cost functions over the nodes of a network where each cost function is further considered as the average of several constituent functions. Recalling the existing work, decentralized accelerated methods that consider improving both communication and computation efficiency have not yet been investigated. Based on this, we present an effective event-triggering decentralized accelerated stochastic gradient algorithm, namely, ET-DASG. ET-DASG leverages the event-triggering strategy for improving communication efficiency, the variance-reduction technique of SAGA for promoting computation efficiency, and the Nesterov's acceleration mechanism for the accelerated convergence. We provide a convergence analysis and show that ET-DASG with well-selected constant step-size can converge in the mean to the exact optimal solution. At the same time, linear convergence rate is achieved if each constituent function is strongly convex and smooth due to the adoption of gradient-tracking scheme. Under certain conditions, we prove that for each node the time interval between two successive triggering instants is larger than the iteration interval. Finally, simulation results also confirm the appealing performance of ET-DASG.

关键词： Convergence Machine learning Task analysis Training Cost function stochastic processes Simulation Decentralized optimization stochastic algorithm event-triggering variance-reduction Nesterov's acceleration

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A sum-over-paths impulse-response moment-extraction algorithm for RLC IC-interconnect networks

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SOLID-STATE ELECTRONICS 2005年第10期49卷 1604-1616页

作者： Le Coz, YL Krishna, D Hariharan, G Petranovic, DM Rensselaer Polytech Inst ECSE Dept Troy NY 12180 USA Mentor Graphics Corp Wilsonville OR 97070 USA

We have created a new impulse-response (IR) moment-extraction algorithm for RLC circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RLC lines furnished promising results: 5% and 10% approximate 1-sigma error for first- and second-order IR moments, respectively, after only 100 sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RLC-interconnect networks, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR-moment extraction algorithm may find useful application in a massively coupled electrical system, such as that encountered in high-end digital-IC interconnects. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： Feynman sum-over-paths IC-interconnect modeling impulse response moment extraction RLC circuit networks stochastic algorithm

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Genetic algorithm for optimal weapon allocation in multilayer defence scenario

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DEFENCE SCIENCE JOURNAL 2001年第3期51卷 285-293页

作者： Malhotra, A Jain, RK Inst Syst Studies & Anal Delhi 110054 India

Several heuristic optimisation techniques have been studied in the past to determine the most effective mix of weapons and their allocation to enemy targets in a multilayer defence scenario. This paper discusses a genetic algorithm approach to arrive at improved solutions with reduced computational time. The most important aspect of the new approach is the mapping of the nonlinear optimisation problem into a discrete 0-1 problem. The results demonstrate that if the problem mapping is correct, even a primitive algorithm can yield high quality results to a complex optimisation problem.

关键词： heuristic optimisation technique genetic algorithm stochastic algorithm neural network weapon deployment

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Recursive estimators of integrated squared density derivatives

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STATISTICS & PROBABILITY LETTERS 2020年 157卷 108609-000页

作者： Mokkadem, Abdelkader Pelletier, Mariane Univ Paris Saclay Lab Math Versailles UVSQ CNRS F-78035 Versailles France

Hall and Marron (1987) introduced kernel estimators of integrals of various squared derivatives of a probability density. The aim of this paper is the study of recursive versions of their estimators. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987), the recursive estimators may achieve the parametric rate n(-1);the striking fact is that their MSE are then equivalent to those of their nonrecursive versions, whereas the recursive nonparametric estimators are known for usually having larger MSE than their nonrecursive version. We also provide recursive estimators of the optimal bandwidth in the framework of density estimation. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Recursive estimation Kernel estimators of integrals stochastic algorithm Mean squared error Rate of convergence

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Construction of main effects plans orthogonal through the block factor based on level permutation

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2015年第4期44卷 538-545页

作者： Chen, Xue-Ping Lin, Jin-Guan Huang, Xing-Fang Southeast Univ Dept Math Nanjing 211189 Jiangsu Peoples R China Jiangsu Univ Technol Dept Math Changzhou 213001 Peoples R China

In this paper, We first demonstrate that the orthogonal property of main effects plans orthogonal through the block factor (Bagchi, 2010) remains unchanged under level permutation. However, level permutation of factors could alter their geometrical structures and statistical properties. Hence uniformity is used to further distinguish main effects plans orthogonal through the block factor (POTB). A modified optimization algorithm is proposed to search uniform or nearly uniform POTBs and many new optimal POTBs with lower-discrepancy are obtained. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Uniformity Level permutation stochastic algorithm Centered L-2-discrepancy Block factor

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