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Blind restoration of turbulence degraded images based on two-channel alternating minimization algorithm 被引量:3
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作者 YANG Huizhen LI Songheng +3 位作者 LI Xin ZHANG Zhiguang YANG Haibo LIU Jinlong 《Optoelectronics Letters》 EI 2022年第2期122-128,共7页
Due to the atmospheric turbulence and the system noise, images are blurred in the astronomical or space object detection. Wavefront aberrations and system noise make the capability of detecting objects decrease greatl... Due to the atmospheric turbulence and the system noise, images are blurred in the astronomical or space object detection. Wavefront aberrations and system noise make the capability of detecting objects decrease greatly. A two-channel image restoration method based on alternating minimization is proposed to restore the turbulence degraded images. The images at different times are regarded as separate channels, then the object and the point spread function(PSF) are reconstructed in an alternative way. There are two optimization parameters in the algorithm: the object and the PSF. Each optimization step is transformed into a constraint problem by variable splitting and processed by the augmented Lagrangian method. The results of simulation and actual experiment verify that the two-channel image restoration method can always converge rapidly within five iterations, and values of normalized root mean square error(NRMSE) remain below 3% after five iterations. Standard deviation data show that optimized alternating minimization(OAM) has strong stability and adaptability to different turbulent levels and noise levels. Restored images are approximate to the ideal imaging by visual assessment, even though atmospheric turbulence and systemnoise have a strong impact on imaging. Additionally, the method can remove noise effectively during the process of image restoration. 展开更多
关键词 TURBULENCE minimization algorithm
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A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions 被引量:1
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作者 Anmol Gupta Sanjay Kumar 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2021年第3期370-389,共20页
Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization p... Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods. 展开更多
关键词 multiplicative calculus multiplicative least square method multiplicative Newton minimization multiplicative Gauss-Newton minimization non-linear exponential functions
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Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early
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作者 Karrar Alshaikhli Aws Alshaikhli 《Journal of Applied Mathematics and Physics》 2024年第2期661-682,共22页
This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V<sub>max</sub>), maximum tardy job, denote... This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V<sub>max</sub>), maximum tardy job, denoted by (T<sub>max</sub>), and maximum earliness (E<sub>max</sub>). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (V<sub>max</sub>, T<sub>max</sub>, E<sub>max</sub>) and 1//(V<sub>max</sub> + T<sub>max</sub> + E<sub>max</sub>). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time. 展开更多
关键词 Scheduling Single Machine Hierarchical Simultaneous minimization algorithmS Branch and Bound Local Search Heuristic Methods
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Harmonic Minimization in Seven-Level Cascaded Multilevel Inverter Using Evolutionary Algorithm 被引量:1
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作者 Jeyabharath Rajaiah Velmurugan Ramar Veena Parasunath 《Circuits and Systems》 2016年第9期2309-2322,共14页
Inverters are power electronic devices that change over DC to sinusoidal AC quantity. Be that as it may, in down to earth, these devices produce non-sinusoidal yield which contains harmonics, so as to blend a close si... Inverters are power electronic devices that change over DC to sinusoidal AC quantity. Be that as it may, in down to earth, these devices produce non-sinusoidal yield which contains harmonics, so as to blend a close sinusoidal component and to lessen the harmonic distortion multilevel inverters developed. Mathematical methods, which were developed, are derivative based and need initial considerations. To overcome this, evolutionary algorithms, which are derivative free and accurate, were developed for obtaining multi levels of output voltage. The proposed work uses two evolutionary algorithms, namely, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm. These algorithms are used to generate the switching angles by satisfying the non linear transcendental equations that govern the low order harmonic components. A seven level cascaded full bridge inverter is designed using MATLAB/Simulink and the results validate the results for switching angles. The Total Harmonic Distortion (THD) value obtained for GA and PSO is 11.81% and 10.84% respectively. The solution obtained from GA algorithm was implemented in hardware using dsPIC controller to validate the simulation results. The THD value obtained for cascaded seven-level multilevel inverter in the hardware prototype is 25.9%. 展开更多
关键词 Multilevel Inverter Selective Harmonic Elimination Genetic algorithm Particle Swarm Optimization Harmonic minimization
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An Optimized Test Case Minimization Technique Using Genetic Algorithm for Regression Testing
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作者 Rubab Sheikh Muhammad Imran Babar +2 位作者 Rawish Butt Abdelzahir Abdelmaboud Taiseer Abdalla Elfadil Eisa 《Computers, Materials & Continua》 SCIE EI 2023年第3期6789-6806,共18页
Regression testing is a widely used approach to confirm the correct functionality of the software in incremental development.The use of test cases makes it easier to test the ripple effect of changed requirements.Rigo... Regression testing is a widely used approach to confirm the correct functionality of the software in incremental development.The use of test cases makes it easier to test the ripple effect of changed requirements.Rigorous testingmay help in meeting the quality criteria that is based on the conformance to the requirements as given by the intended stakeholders.However,a minimized and prioritized set of test cases may reduce the efforts and time required for testingwhile focusing on the timely delivery of the software application.In this research,a technique named Test Reduce has been presented to get a minimal set of test cases based on high priority to ensure that the web applicationmeets the required quality criteria.A new technique TestReduce is proposed with a blend of genetic algorithm to find an optimized and minimal set of test cases.The ultimate objective associated with this study is to provide a technique that may solve the minimization problem of regression test cases in the case of linked requirements.In this research,the 100-Dollar prioritization approach is used to define the priority of the new requirements. 展开更多
关键词 Test case minimization regression testing testreduce genetic algorithm 100-dollar prioritization
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Improved hyper-spherical search algorithm for voltage total harmonic distortion minimization in 27-level inverter
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作者 A A KHODADOOST ARANI H KARAMI +1 位作者 B VAHIDI G B GHAREHPETIAN 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第10期2822-2832,共11页
Multi-level inverters(MLIs)have become popular in different applications such as industrial power control systems and distributed generations.There are different forms of MLIs.The cascaded MLIs(CMLIs)have some special... Multi-level inverters(MLIs)have become popular in different applications such as industrial power control systems and distributed generations.There are different forms of MLIs.The cascaded MLIs(CMLIs)have some special advantages among them such as more different output voltage levels using the same number of components and higher power quality.In this paper,a 27-level inverter switching algorithm considering total harmonic distortion(THD)minimization is investigated.Switching angles of the inverter switches are achieved by minimizing a THD-based objective function.In order to minimize the THD-based objective function,the hyper-spherical search(HSS)algorithm,as a novel optimization algorithm,is improved and the results of improved HSS(IHSS)are compared with HSS algorithm and other five evolutionary algorithms to show the advantages of IHSS algorithm. 展开更多
关键词 27-level inverter cascade multi-level inverter improved hyper-spherical search(IHSS)algorithm total harmonic distortion(THD)minimization
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PARALLEL MINIMIZATION ALGORITHMS by GENERALIZED SUBDIFFERENTIABILITY
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作者 C. Sutti A. Peretti(Istituto di Matematica, Facolta di Economia e Commercio, Universita di Verona, Italy) 《Wuhan University Journal of Natural Sciences》 CAS 1996年第Z1期531-540,共10页
Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication resul... Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results. 展开更多
关键词 PARALLEL minimization algorithmS by GENERALIZED SUBDIFFERENTIABILITY
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AN ALGORITHM OF UNCONSTRAINED MINIMIZATION WITHOUT DERIVATIVE AND ITS CONVERGENCE
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作者 赖兰 《Acta Mathematica Scientia》 SCIE CSCD 1992年第2期139-143,共5页
In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we prese... In [1] the unconstrained minimization problem was considered and presented an algorithm without derivative. But the terminative conditions and convergence proof of the algorithm were not given. In this paper, we present a revised algorithm and prove its convergence. 展开更多
关键词 AN algorithm OF UNCONSTRAINED minimization WITHOUT DERIVATIVE AND ITS CONVERGENCE
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MARVEL:Multi-Agent Reinforcement Learning for VANET Delay Minimization 被引量:2
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作者 Chengyue Lu Zihan Wang +3 位作者 Wenbo Ding Gang Li Sicong Liu Ling Cheng 《China Communications》 SCIE CSCD 2021年第6期1-11,共11页
In urban Vehicular Ad hoc Networks(VANETs),high mobility of vehicular environment and frequently changed network topology call for a low delay end-to-end routing algorithm.In this paper,we propose a Multi-Agent Reinfo... In urban Vehicular Ad hoc Networks(VANETs),high mobility of vehicular environment and frequently changed network topology call for a low delay end-to-end routing algorithm.In this paper,we propose a Multi-Agent Reinforcement Learning(MARL)based decentralized routing scheme,where the inherent similarity between the routing problem in VANET and the MARL problem is exploited.The proposed routing scheme models the interaction between vehicles and the environment as a multi-agent problem in which each vehicle autonomously establishes the communication channel with a neighbor device regardless of the global information.Simulation performed in the 3GPP Manhattan mobility model demonstrates that our proposed decentralized routing algorithm achieves less than 45.8 ms average latency and high stability of 0.05%averaging failure rate with varying vehicle capacities. 展开更多
关键词 VANET multi-agent RL delay minimization routing algorithm
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Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks 被引量:1
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作者 李杰 钱摇琨 刘威 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2007年第1期21-28,共8页
In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm (MCRDA), is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the... In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm (MCRDA), is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation. 展开更多
关键词 minimal cut seismic reliability recursive decomposition algorithm large-scale lifeline system
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Algorithms for degree-constrained Euclidean Steiner minimal tree 被引量:1
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作者 Zhang Jin Ma Liang Zhang Liantang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第4期735-741,共7页
A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree... A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice. 展开更多
关键词 DEGREE-CONSTRAINED Euclidean Steiner minimal tree simulated annealing ant algorithm
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Two-stage robust power cost minimization in a natural gas compressor station
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作者 Yize Meng Ruoran Chen +1 位作者 Keren Zhang Tianhu Deng 《Petroleum Science》 SCIE CAS CSCD 2022年第1期409-428,共20页
Optimal operation of a compressor station is important since it accounts for 25%to 50%of a company’s total operating budget.In short-term management of a compressor station,handling demand uncertainty is important ye... Optimal operation of a compressor station is important since it accounts for 25%to 50%of a company’s total operating budget.In short-term management of a compressor station,handling demand uncertainty is important yet challenging.Previous studies either require precise information about the distribution of uncertain parameters or greatly simplify the compressor model.We build a two-stage robust optimization framework of power cost minimization in a natural gas compressor station with nonidentical compressors.In the first stage,decision variables are the ON/OFF state of each compressor and discharge pressure.The worst-case cost of the second stage is incorporated in the first stage.Firststage decision variables feasibility is discussed and proper feasibility cuts are also proposed for the first stage.We employ a piece-wise approximation and propose accelerate methods.Our numerical results highlight two advantages of robust approach when managing uncertainty in practical settings:(1)the feasibility of first-stage decision can be increased by up to 45%,and(2)the worst-case cost can be reduced by up to 25%compared with stochastic programming models.Furthermore,our numerical experiments show that the designed accelerate algorithm has time improvements of 1518.9%on average(3785.9%at maximum). 展开更多
关键词 Natural gas Single station power minimization Nonconvex robust optimization C&CG algorithm
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NON-LINEAR DYNAMIC MODEL RETRIEVAL OF SUBTROPICAL HIGH BASED ON EMPIRICAL ORTHOGONAL FUNCTION AND GENETIC ALGORITHM
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作者 张韧 洪梅 +4 位作者 孙照渤 牛生杰 朱伟军 闵锦忠 万齐林 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第12期1645-1653,共9页
Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF(empirica... Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF(empirical orthogonal function) temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results. A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high. 展开更多
关键词 genetic algorithm empirical orthogonal function non-linear model retrieval subtropical high
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THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
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作者 赵晓东 《Journal of Coal Science & Engineering(China)》 1998年第2期13-16,共4页
The non-linear inversion of rock mechanics parameters based on genetic algorithm is presented. The principIe and step of genetic algorithm is also given. A brief discussion of this method and an application example is... The non-linear inversion of rock mechanics parameters based on genetic algorithm is presented. The principIe and step of genetic algorithm is also given. A brief discussion of this method and an application example is presented at the end of this paper. From the satisfied result, quick, convenient and practical new approach is developed to solve this kind of problems. 展开更多
关键词 genetic algorithm rock mechanics parameters non-linear inversion
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The multi-motion-overlap algorithms for minimizing the time between successive scans of wafer stage
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作者 潘海鸿 Chen Lin +1 位作者 Li Xiaoqing Zhou Yunfei 《High Technology Letters》 EI CAS 2008年第3期282-288,共7页
In order to optimize the transitional time during the successive exposure scans for a step-and-scan lithography and improve the productivity in a wafer production process, an investigation of the motion trajectory pla... In order to optimize the transitional time during the successive exposure scans for a step-and-scan lithography and improve the productivity in a wafer production process, an investigation of the motion trajectory planning along the scanning direction for wafer stage was carried out. The motions of wafer stage were divided into two respective logical moves (i. e. step-move and scan-move) and the multi-motionoverlap algorithms (MMOA) were presented for optimizing the transitional time between the successive exposure scans. The conventional motion planning method, the Hazelton method and the MMOA were analyzed theoretically and simulated using MATLAB under four different exposure field sizes. The results show that the total time between two successive scans consumed by MMOA is reduced by 4.82%, 2.62%, 3.06% and 3.96%, compared with those of the conventional motion planning method; and reduced by 2.58%, 0.76%, 1.63% and 2.92%, compared with those of the Hazehon method respectively. The theoretical analyses and simulation results illuminate that the MMOA can effectively minimize the transitional step time between successive exposure scans and therefore increase the wafer fabricating productivity. 展开更多
关键词 multi-motion-overlap algorithm minimizing time successive exposure scans wafer stage step-and-scan lithography
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An Innovative Genetic Algorithms-Based Inexact Non-Linear Programming Problem Solving Method
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作者 Weihua Jin Zhiying Hu Christine Chan 《Journal of Environmental Protection》 2017年第3期231-249,共19页
In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact infor... In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact information (inexact non-linear operation programming). GAINLP was developed based on a GA-based inexact quadratic solving method. The Genetic Algorithm Solver of the Global Optimization Toolbox (GASGOT) developed by MATLABTM was adopted as the implementation environment of this study. GAINLP was applied to a municipality solid waste management case. The results from different scenarios indicated that the proposed GA-based heuristic optimization approach was able to generate a solution for a complicated nonlinear problem, which also involved uncertainty. 展开更多
关键词 GENETIC algorithms INEXACT non-linear PROGRAMMING (INLP) ECONOMY of Scale Numeric Optimization Solid Waste Management
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一类新的无参数的填充打洞函数法
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作者 袁柳洋 汤梦瑶 迟晓妮 《运筹学学报(中英文)》 北大核心 2025年第2期214-220,共7页
自填充函数算法被提出以来,参数被视为制约算法效率的主要因素,因此构造无参数的填充函数显得极为重要。为了提高算法效率,本文构造了一类新的无参数的填充打洞函数,分析并讨论了该函数的性质。基于新的填充打洞函数,提出了一个新的全... 自填充函数算法被提出以来,参数被视为制约算法效率的主要因素,因此构造无参数的填充函数显得极为重要。为了提高算法效率,本文构造了一类新的无参数的填充打洞函数,分析并讨论了该函数的性质。基于新的填充打洞函数,提出了一个新的全局优化算法,并对算法进行了数值实验,数值实验结果表明该算法可行且有效。 展开更多
关键词 填充函数法 打洞函数法 全局优化算法 局部极小点 全局极小点
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手术机器人路径规划方法研究
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作者 张吉焱 阎科承 +4 位作者 高明亮 薛瑞丹 曹远航 师为礼 李飞 《计量科学与技术》 2025年第11期3-10,33,共9页
在腹腔镜手术过程中,手术机器人的振动或抖动会直接影响手术器械的定位精度,进而降低手术效果。同时,为提高伺服控制效率并减少手术时间,还需对手术机器人的运动轨迹进行优化处理。为提升手术机器人的运动精度与稳定性,对其关节空间进... 在腹腔镜手术过程中,手术机器人的振动或抖动会直接影响手术器械的定位精度,进而降低手术效果。同时,为提高伺服控制效率并减少手术时间,还需对手术机器人的运动轨迹进行优化处理。为提升手术机器人的运动精度与稳定性,对其关节空间进行了轨迹规划,采用3-5-3多项式插值法进行轨迹插值,确保轨迹在位置、速度和加速度上具备连续性。针对传统麻雀算法在寻优效果上的不足,进行了以下改进,首先引入二维Logistic混沌映射优化种群初始分布,改善算法的初始化条件;其次在跟随者更新过程中采用螺旋黏菌搜索策略,增强算法的全局探索能力;最后增加柯西-高斯变异策略,避免算法陷入局部最优解。基于改进后的麻雀算法,对3-5-3多项式插值轨迹进行时间最优轨迹规划。实验结果表明,所提出的手术机器人轨迹规划算法在性能提升方面具有可行性和有效性。 展开更多
关键词 计量学 手术机器人 微创手术 路径规划 麻雀算法 腹腔镜
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广义约束CX=D条件下矩阵方程AX=E的极小最小二乘解的迭代算法
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作者 杨家稳 宋园 张太阳 《滁州学院学报》 2025年第2期21-28,共8页
为解决在广义约束CX=D条件下矩阵方程AX=E的极小最小二乘解,提出了基于搜索方向正交与梯度投影相结合的一种迭代算法。算法的总体思路是将目标函数F(X)=‖E-AX‖^(2)在矩阵X处的负梯度投影到约束集S={X|CX=D}中获得g,然后,根据共轭梯度... 为解决在广义约束CX=D条件下矩阵方程AX=E的极小最小二乘解,提出了基于搜索方向正交与梯度投影相结合的一种迭代算法。算法的总体思路是将目标函数F(X)=‖E-AX‖^(2)在矩阵X处的负梯度投影到约束集S={X|CX=D}中获得g,然后,根据共轭梯度法的原理,通过g在可行域上构造搜索方向d,要求所有搜索方向的拉直算子vec(d)两两相互正交。定理证明了该算法对于任意一个满足一定条件的初始矩阵X 1,经过有限次迭代能够求得约束条件下方程的极小最小二乘解。数值例子验证了该算法的有效性,同时还表明算法能解决特殊约束下矩阵方程AX=E的极小最小二乘解。 展开更多
关键词 矩阵方程 极小最小二乘解 梯度投影 迭代算法
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广义约束条件下矩阵方程AXB+CX^(T)D=E最佳逼近解的迭代算法
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作者 杨家稳 万鹏 梁金荣 《吉首大学学报(自然科学版)》 2025年第1期1-11,共11页
为了计算广义约束条件GX=H下矩阵方程AXB+CX^(T)D=E的最佳逼近解,设计了一种基于梯度投影与搜索方向正交的迭代算法.证明了任意给定一个满足广义约束条件的特殊初始矩阵,通过有限次迭代算法,能够获得广义约束条件下矩阵方程的极小范数... 为了计算广义约束条件GX=H下矩阵方程AXB+CX^(T)D=E的最佳逼近解,设计了一种基于梯度投影与搜索方向正交的迭代算法.证明了任意给定一个满足广义约束条件的特殊初始矩阵,通过有限次迭代算法,能够获得广义约束条件下矩阵方程的极小范数最小二乘解,并利用该极小范数最小二乘解计算出最佳逼近解. 展开更多
关键词 极小范数最小二乘解 最佳逼近解 迭代算法 梯度投影
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