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Learning to select the recombination operator for derivative-free optimization

Science china Mathematics 2024年第6期67卷 1457-1480页

作者： Haotian zhang Jianyong Sun Thomas Back zongben {2. School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an710049China Leiden Institute of Advanced Computer Science Leiden UniversityLeiden2333 CANetherlands

Extensive studies on selecting recombination operators adaptively,namely,adaptive operator selection(AOS),during the search process of an evolutionary algorithm(EA),have shown that AOS is promising for improving EA's performance.A variety of heuristic mechanisms for AOS have been proposed in recent decades,which usually contain two main components:the feature extraction and the policy *** feature extraction refers to as extracting relevant features from the information collected during the search *** policy setting means to set a strategy(or policy)on how to select an operator from a pool of operators based on the extracted *** components are designed by hand in existing studies,which may not be efficient for adapting optimization *** this paper,a generalized framework is proposed for learning the components of AOS for one of the main streams of EAs,namely,differential evolution(DE).In the framework,the feature extraction is parameterized as a deep neural network(DNN),while a Dirichlet distribution is considered to be the policy.A reinforcement learning method,named policy gradient,is used to train the *** case studies,the proposed framework is applied to two DEs including the classic DE and a recently-proposed DE,which result in two new algorithms named PG-DE and PG-MPEDE,*** on the Congress of Evolutionary Computation(CEC)2.18 test suite show that the proposed new algorithms perform significantly better than their ***,we prove theoretically that the considered classic methods are the special cases of the proposed framework.

关键词： evolutionary algorithm differential evolution adaptive operator selection reinforcement learning deep learning

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Estimation of convergence rate for multi-regression learning algorithm

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Science china(information {2.) 2012年第3期55卷 701-713页

作者： xu zongben1,2. zhang {2. CAO feilong3.1.nstitute for information and system sciences, xi’an jiaotong university, xi’an 710049, china 2.OE Key Labratory for Intelligent Networks and Network Security, xi’an jiaotong university, xi’an 710049, china 3.epartment of information and Mathematics sciences, china Jiliang university, Hangzhou 3.0018, china 1. Institute for information and {2. {3. Xi’an Jiaotong University Xi’an 710049 China2. MOE Key Labratory for Intelligent Networks and Network Security Xi’an Jiaotong University Xi’an 710049 China3. Department of Information and Mathematics Sciences China Jiliang University Hangzhou 310018 China

In many applications, the pre-information on regression function is always unknown. Therefore, it is necessary to learn regression function by means of some valid tools. In this paper we investigate the regression problem in learning theory, i.e., convergence rate of regression learning algorithm with least square schemes in multi-dimensional polynomial space. Our main aim is to analyze the generalization error for multi-regression problems in learning theory. By using the famous Jackson operators in approximation theory, covering number, entropy number and relative probability inequalities, we obtain the estimates of upper and lower bounds for the convergence rate of learning algorithm. In particular, it is shown that for multi-variable smooth regression functions, the estimates are able to achieve almost optimal rate of convergence except for a logarithmic factor. Our results are significant for the research of convergence, stability and complexity of regression learning algorithm.

关键词： learning theory covering number rate of convergence entropy number

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The essential ability of sparse reconstruction of different compressive sensing strategies

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Science china(information {2.) 2012年第11期55卷 2582-2589页

作者： zhang Hai1,2.LIANG Yong3.GOU HaiLiang1 & xu zongben1 1 I{2. for information and system Science,xi'an jiaotong university,xi'an 710049,china 2.epartment of Mathematics,Northwest university,xi'an 710069,china 3.7} of Science and Technology,Macau 999078,china 1. Institute for information and {2. Science Xi’an Jiaotong University Xi’an 710049 China2. Department of Mathematics Northwest University Xi’an 710069 China3. University of Science and Technology Macau 999078 China

We show the essential ability of sparse signal reconstruction of different compressive sensing strategies,which include the L1 regularization,the L0 regularization(thresholding iteration algorithm and OMP algorithm),the Lq(0 1) regularizations,the Log regularization and the SCAD *** phase diagram as the basic tool for analysis,we find that(i) the solutions of the L0 regularization using hard thresholding algorithm and OMP algorithm are similar to those of the L1 regularization;(ii) the Lq regularization with the decreasing value of q,the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization;(iii) the L1/2.regularization can be taken as a representative of the Lq(0 1) *** 1/2.1,the L1/2.regularization always yields the sparsest solutions and when 0 1/2.the performance of the regularizations takes no significant *** results of this paper provide experimental evidence for our previous work.

关键词： compressive sensing regularization sparsity L1/2.regularization

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L1/2.regularization

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Science china(information {2.) 2010年第6期53卷 1159-1169页

作者： xu zongben 1 , {2. Hai 1,2., WANG Yao 1 , CHANG xiangYu 1 & LIANG Yong 3.1 Institute of information and system Science, xi'an jiaotong university, xi'an 710049, china 2.Department of Mathematics, Northwest university, xi'an 710069, china 3.university of Science and Technology, Macau 999078, china 1. Institute of information and {2. Science Xi’an Jiaotong University Xi’an 710049 China2. Department of Mathematics Northwest University Xi’an 710069 China3. University of Science and Technology Macau 999078 China

In this paper we propose an L1 /2.regularizer which has a nonconvex *** L 1/2.regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties.A reweighed iterative algorithm is proposed so that the solution of the L 1/2.regularizer can be solved through transforming it into the solution of a series of L 1 *** solution of the L 1/2.regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2.regularizer is much simpler than solving the L 0 *** experiments show that the L 1/2.regularizer is very useful and efficient, and can be taken as a representative of the Lp(0 1) regularizer.

关键词： machine learning variable selection regularizer compressed sensing

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Sparse SAR imaging based on L1/2.regularization

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Science china(information {2.) 2012年第8期55卷 1755-1775页

作者： ZENG JinShan,FANG Jian&xu zongben I{2. for {3. and system sciences&Ministry of Education Key Lab for Intelligent Networks and Network Security,xi’an jiaotong university,xi’an 710049,china 1. Institute for information and {2. {3. & Ministry of Education Key Lab for Intelligent Networks and Network Security Xi’an Jiaotong University Xi’an 710049 China

In this paper,a novel method for synthetic aperture radar(SAR)imaging is *** approach is based on L1/2.regularization to reconstruct the scattering field,which optimizes a quadratic error term of the SAR observation process subject to the interested scene *** to the conventional SAR imaging technique,the new method implements SAR imaging effectively at much lower sampling rate than the Nyquist rate,and produces high-quality images with reduced sidelobes and increased ***,over the prevalent greedy pursuit and L1 regularization based SAR imaging methods,there are remarkable performance improvements of the new *** one hand,the new method significantly reduces the number of measurements needed for reconstruction,as supported by a phase transition diagram *** the other hand,the new method is more robust to the observation *** fundamental properties of the new method are supported and demonstrated both by simulations and real SAR data experiments.

关键词： synthetic aperture radar matched filtering compressed sensing L1/2.regularization L1 regularization

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Lower estimation of approximation rate for neural networks

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Science in china(Series F) 2009年第8期52卷 1321-1327页

作者： CAO feilong zhang {2. {3. zongben College of Science China Jiliang University Hangzhou 310018 China Institute of information and {2. {3. Xi'an Jiaotong University Xi'an 710049 China

Let SFd and ∏φ,n,d ={∑j^n=1bjφ（wj.x＋θj）：bj,θj∈R,wj∈R^d} be the set of periodic and Lebesgue＇s square-integrable functions and the set of feedforward neural network （FNN） functions, respectively. Denote by dist （SFd , ∏φ,n,d） the deviation of the set SFd from the set ∏φ,n,d. A main purpose of this paper is to estimate the deviation. In particular, based on the Fourier transforms and the theory of approximation, a lower estimation for dist （SFd and ∏φ,n,d） is proved. That is, dist（SFd and ∏φ,n,d） ≥C/（nlog2.）1/2. The obtained estimation depends only on the number of neuron in the hidden layer, and is independent of the approximated target functions and dimensional number of input. This estimation also reveals the relationship between the approximation rate of FNNs and the topology structure of hidden layer.

关键词： feedforward neural networks approximation topology structure of hidden layer rate lower

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A New Method Based on the Non-isothermal Kinetic Equation to Estimate the Critical Temperature of Thermal Explosion for Energetic Materials Using Non-isothermal DSC

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Journal of Shanghai jiaotong university(Science) 2011年第2期16卷 247-251页

作者：张海胡俊英胡荣祖赵凤起高红旭 Department of Mathematics Northwest University Institute of system and {2. Science Xi'an Jiaotong University xi'an Modern Chemistry Research Institute

A method for estimating the critical temperature of thermal explosion for energetic materials using differential scanning calorimetry (DSC) measurement is derived from the Semenov's thermal explosion theory and the non-isothermal kinetic equation based on Harcourt-Esson's kinetic *** result obtained from this method coincides completely with that of the Hu-Yang-Liang-Wu method.

关键词： critical temperature thermal explosion differential scanning calorimetry (DSC) non-isothermal

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Cubature Formula for Spherical Basis Function Networks

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Chinese Annals of Mathematics,Series B 2012年第6期33卷 807-814页

作者： Shaobo LIN feilong CAO zongben {2. xiaofei GUO Institute of information and {2. {3. Xi'an Jiaotong University Institute of Metrology and Computational Science China Jiliang University

Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the *** cubature formula plays an important role in computing these spherical *** paper is devoted to establishing an exact positive cubature formula for spherical basis function *** authors give an existence proof of the exact positive cubature formula for spherical basis function networks,and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data.

关键词： Cubature formula Spherical basis function Scattered data

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Learning rates of regularized regression on the unit sphere

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Science china Mathematics 2013年第4期56卷 861-876页

作者： CAO feilong LIN ShaoBo CHANG xiangYu xu {2. Institute of Metrology and Computational Science China Jiliang University Institute for information and {2. {3. Xi'an Jiaotong University

This paper addresses the learning algorithm on the unit *** main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics *** excess error can be estimated by the sum of sample errors and regularization *** study shows that by introducing a suitable spherical harmonics kernel,the regularization parameter can decrease arbitrarily fast with the sample size.

关键词： sphere regularized regression spherical harmonics kernel rate of convergence

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The In-Flight Realtime Trigger and Localization Software of GECAM

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Research in Astronomy and Astrophysics 2024年第10期24卷 11-24页

作者： xiao-Yun Zhao Shao-Lin xiong xiang-Yang Wen xin-Qiao Li Ce Cai Shuo xiao Qi Luo Wen-xi Peng Dong-Ya Guo Zheng-Hua An Ke Gong Jin-Yuan Liao Yan-Qiu zhang Yue Huang Lu Li xing Wen Fei zhang Jing Duan Chen-Wei Wang Dong-Li Shi Peng zhang Qi-Bin Yi Chao-Yang Li Yan-Bing {3. xiao-Hua Liang Ya-Qing Liu Da-Li zhang xi-Lei Sun Fan zhang Gang Chen Huan-Yu Wang Sheng Yang xiao-Jing Liu Min Gao Mao-Shun Li Jin-Zhou Wang xing Zhou Yi Zhao Wang-Chen {3.e Chao Zheng Jia-Cong Liu xing-Bo Han Jin-Ling Qi Jia Huang Ke-Ke zhang Can Chen xiong-Tao Yang Dong-Jie Hou Yu-Sa Wang Rui Qiao xiang Ma xiao-Bo Li Ping Wang xin-Ying Song Li-Ming Song Shi-Jie Zheng Bing Li Hong-Mei zhang Yue Zhu Wei Chen Jian-Jian He Zhen zhang Jin Hou Hong-Jun Wang Yan-Chao Hao xiang-Yu Wang Zong-Yuan Yang Zhi-Long Wen Zhi Chang Yuan-Yuan Du Rui Gao xiao-Fei Lan Yan-Guo Li Gang Li {3.-Fang Li Fang-Jun Lu Hong Lu Bin Meng Feng Shi Hui Wang Hui-Zhen Wang Yu-Peng {3. Jia-Wei Yang {3.e-Juan Yang Shuang-Nan zhang Chao-Yue zhang Cheng-Mo zhang Zhi-Cheng Tang Cheng Cheng Key Laboratory of Particle Astrophysics Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China university of Chinese Academy of sciences Chinese Academy of SciencesBeijing 100049China School of information Science and Technology Southwest Jiaotong UniversityChengdu 611756China Key Laboratory of Stellar and Interstellar Physics and Department of Physics Xiangtan UniversityXiangtan 411105China Physics and Space Science College China West Normal UniversityNanchong 637002China Department of Astronomy Beijing Normal UniversityBeijing 100875China Innovation Academy for Microsatellites of CAS Shanghai 201203China Changchun university of Science and Technology Changchun 130022China Chinese Academy of sciences South America Center for Astronomy National Astronomical ObservatoriesCASBeijing 100101China

Realtime trigger and localization of bursts are the key functions of GECAM,an all-sky gamma-ray monitor launched on 2.2. December *** developed a multifunctional trigger and localization software operating in the CPU of the GECAM Electronic *** onboard software has the following features:high trigger efficiency for real celestial bursts with a suppression of false triggers caused by charged particle bursts and background fluctuation,dedicated localization algorithm optimized for both short and long bursts,and low time latency of the trigger information which is downlinked through the Global Short Message Communication service of the global BeiDou navigation *** paper provides a detailed description of the design and development of the trigger and localization software {3. for *** covers the general design,workflow,the main functions,and the algorithms used in the *** paper also includes on-ground trigger tests using simulated gamma-ray bursts generated by a dedicated X-ray tube,as well as an overview of the performance for real celestial bursts during its in-orbit operation.

关键词： telescopes instrumentation:detectors methods:observational

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