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Synthesis of thinned linear antenna array using genetic algorithm to lower peak sidelobe level and maintain half-power beamwidth
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作者 STEPANOV Maksim KARASEV Alexey 《Journal of Systems Engineering and Electronics》 2025年第5期1113-1121,共9页
Thinning of antenna arrays has been a popular topic for the last several decades.With increasing computational power,this optimization task acquired a new hue.This paper suggests a genetic algorithm as an instrument f... Thinning of antenna arrays has been a popular topic for the last several decades.With increasing computational power,this optimization task acquired a new hue.This paper suggests a genetic algorithm as an instrument for antenna array thinning.The algorithm with a deliberately chosen fitness function allows synthesizing thinned linear antenna arrays with low peak sidelobe level(SLL)while maintaining the half-power beamwidth(HPBW)of a full linear antenna array.Based on results from existing papers in the field and known approaches to antenna array thinning,a classification of thinning types is introduced.The optimal thinning type for a linear thinned antenna array is determined on the basis of a maximum attainable SLL.The effect of thinning coefficient on main directional pattern characteristics,such as peak SLL and HPBW,is discussed for a number of amplitude distributions. 展开更多
关键词 thinned antenna array genetic algorithm side lobe
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Research on Euclidean Algorithm and Reection on Its Teaching
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作者 ZHANG Shaohua 《应用数学》 北大核心 2025年第1期308-310,共3页
In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and t... In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and the greatest common divisor.We further provided several suggestions for teaching. 展开更多
关键词 Euclid's algorithm Division algorithm Bezout's equation
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An Algorithm for Cloud-based Web Service Combination Optimization Through Plant Growth Simulation
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作者 Li Qiang Qin Huawei +1 位作者 Qiao Bingqin Wu Ruifang 《系统仿真学报》 北大核心 2025年第2期462-473,共12页
In order to improve the efficiency of cloud-based web services,an improved plant growth simulation algorithm scheduling model.This model first used mathematical methods to describe the relationships between cloud-base... In order to improve the efficiency of cloud-based web services,an improved plant growth simulation algorithm scheduling model.This model first used mathematical methods to describe the relationships between cloud-based web services and the constraints of system resources.Then,a light-induced plant growth simulation algorithm was established.The performance of the algorithm was compared through several plant types,and the best plant model was selected as the setting for the system.Experimental results show that when the number of test cloud-based web services reaches 2048,the model being 2.14 times faster than PSO,2.8 times faster than the ant colony algorithm,2.9 times faster than the bee colony algorithm,and a remarkable 8.38 times faster than the genetic algorithm. 展开更多
关键词 cloud-based service scheduling algorithm resource constraint load optimization cloud computing plant growth simulation algorithm
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A Class of Parallel Algorithm for Solving Low-rank Tensor Completion
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作者 LIU Tingyan WEN Ruiping 《应用数学》 北大核心 2025年第4期1134-1144,共11页
In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice ... In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision. 展开更多
关键词 Tensor completion Low-rank CONVERGENCE Parallel algorithm
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Multi-QoS routing algorithm based on reinforcement learning for LEO satellite networks 被引量:1
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作者 ZHANG Yifan DONG Tao +1 位作者 LIU Zhihui JIN Shichao 《Journal of Systems Engineering and Electronics》 2025年第1期37-47,共11页
Low Earth orbit(LEO)satellite networks exhibit distinct characteristics,e.g.,limited resources of individual satellite nodes and dynamic network topology,which have brought many challenges for routing algorithms.To sa... Low Earth orbit(LEO)satellite networks exhibit distinct characteristics,e.g.,limited resources of individual satellite nodes and dynamic network topology,which have brought many challenges for routing algorithms.To satisfy quality of service(QoS)requirements of various users,it is critical to research efficient routing strategies to fully utilize satellite resources.This paper proposes a multi-QoS information optimized routing algorithm based on reinforcement learning for LEO satellite networks,which guarantees high level assurance demand services to be prioritized under limited satellite resources while considering the load balancing performance of the satellite networks for low level assurance demand services to ensure the full and effective utilization of satellite resources.An auxiliary path search algorithm is proposed to accelerate the convergence of satellite routing algorithm.Simulation results show that the generated routing strategy can timely process and fully meet the QoS demands of high assurance services while effectively improving the load balancing performance of the link. 展开更多
关键词 low Earth orbit(LEO)satellite network reinforcement learning multi-quality of service(QoS) routing algorithm
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Temperature control for liquid-cooled fuel cells based on fuzzy logic and variable-gain generalized supertwisting algorithm
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作者 CHEN Lin JIA Zhi-huan +1 位作者 DING Tian-wei GAO Jin-wu 《控制理论与应用》 北大核心 2025年第8期1596-1605,共10页
The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade tempe... The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade temperature regulation performance.To address these challenges,we propose a composite control scheme combining fuzzy logic and a variable-gain generalized supertwisting algorithm(VG-GSTA).Firstly,a one-dimensional(1D)fuzzy logic controler(FLC)for the pump ensures stable coolant flow,while a two-dimensional(2D)FLC for the fan regulates the stack temperature near the reference value.The VG-GSTA is then introduced to eliminate steady-state errors,offering resistance to disturbances and minimizing control oscillations.The equilibrium optimizer is used to fine-tune VG-GSTA parameters.Co-simulation verifies the effectiveness of our method,demonstrating its advantages in terms of disturbance immunity,overshoot suppression,tracking accuracy and response speed. 展开更多
关键词 liquid-cooled fuel cell temperature control generalized supertwisting algorithm fuzzy control equilibrium optimizer
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Research on three-dimensional attack area based on improved backtracking and ALPS-GP algorithms of air-to-air missile
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作者 ZHANG Haodi WANG Yuhui HE Jiale 《Journal of Systems Engineering and Electronics》 2025年第1期292-310,共19页
In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of t... In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios,the limitations of existing research,including real-time calculation,accuracy efficiency trade-off,and the absence of the three-dimensional attack area model,restrict their practical applications.To address these issues,an improved backtracking algorithm is proposed to improve calculation efficiency.A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm.Furthermore,the age-layered population structure genetic programming(ALPS-GP)algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area,considering real-time requirements.The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm.The study reveals a remarkable combination of high accuracy and efficient real-time computation,with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10^(-4)s,thus meeting the requirements of real-time combat scenarios. 展开更多
关键词 air combat three-dimensional attack area improved backtracking algorithm age-layered population structure genetic programming(ALPS-GP) gradient descent algorithm
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A hybrid genetic algorithm to the program optimization model based on a heterogeneous network
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作者 CHEN Hang DOU Yajie +3 位作者 CHEN Ziyi JIA Qingyang ZHU Chen CHEN Haoxuan 《Journal of Systems Engineering and Electronics》 2025年第4期994-1005,共12页
Project construction and development are an impor-tant part of future army designs.In today’s world,intelligent war-fare and joint operations have become the dominant develop-ments in warfare,so the construction and ... Project construction and development are an impor-tant part of future army designs.In today’s world,intelligent war-fare and joint operations have become the dominant develop-ments in warfare,so the construction and development of the army need top-down,top-level design,and comprehensive plan-ning.The traditional project development model is no longer suf-ficient to meet the army’s complex capability requirements.Projects in various fields need to be developed and coordinated to form a joint force and improve the army’s combat effective-ness.At the same time,when a program consists of large-scale project data,the effectiveness of the traditional,precise mathe-matical planning method is greatly reduced because it is time-consuming,costly,and impractical.To solve above problems,this paper proposes a multi-stage program optimization model based on a heterogeneous network and hybrid genetic algo-rithm and verifies the effectiveness and feasibility of the model and algorithm through an example.The results show that the hybrid algorithm proposed in this paper is better than the exist-ing meta-heuristic algorithm. 展开更多
关键词 program optimization heterogeneous network genetic algorithm portfolio selection.
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Topological optimization of metamaterial absorber based on improved estimation of distribution algorithm
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作者 TAO Shifei LIU Beichen +2 位作者 LIU Sixing WU Fan WANG Hao 《Journal of Systems Engineering and Electronics》 2025年第3期634-641,共8页
An improved estimation of distribution algorithm(IEDA)is proposed in this paper for efficient design of metamaterial absorbers.This algorithm establishes a probability model through the selected dominant groups and sa... An improved estimation of distribution algorithm(IEDA)is proposed in this paper for efficient design of metamaterial absorbers.This algorithm establishes a probability model through the selected dominant groups and samples from the model to obtain the next generation,avoiding the problem of building-blocks destruction caused by crossover and mutation.Neighboring search from artificial bee colony algorithm(ABCA)is introduced to enhance the local optimization ability and improved to raise the speed of convergence.The probability model is modified by boundary correction and loss correction to enhance the robustness of the algorithm.The proposed IEDA is compared with other intelligent algorithms in relevant references.The results show that the proposed IEDA has faster convergence speed and stronger optimization ability,proving the feasibility and effectiveness of the algorithm. 展开更多
关键词 METAMATERIAL topological optimization estimation of distribution algorithm
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Optimization model for performance-based warranty decision of degraded systems based on improved sparrow search algorithm
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作者 DONG Enzhi CHENG Zhonghua +3 位作者 LIU Zichang ZHU Xi WANG Rongcai BAI Yongsheng 《Journal of Systems Engineering and Electronics》 2025年第5期1259-1280,共22页
Performance-based warranties(PBWs)are widely used in industry and manufacturing.Given that PBW can impose financial burdens on manufacturers,rational maintenance decisions are essential for expanding profit margins.Th... Performance-based warranties(PBWs)are widely used in industry and manufacturing.Given that PBW can impose financial burdens on manufacturers,rational maintenance decisions are essential for expanding profit margins.This paper proposes an optimization model for PBW decisions for systems affected by Gamma degradation processes,incorporating periodic inspection.A system performance degradation model is established.Preventive maintenance probability and corrective renewal probability models are developed to calculate expected warranty costs and system availability.A benefits function,which includes incentives,is constructed to optimize the initial and subsequent inspection intervals and preventive maintenance thresholds,thereby maximizing warranty profit.An improved sparrow search algorithm is developed to optimize the model,with a case study on large steam turbine rotor shafts.The results suggest the optimal PBW strategy involves an initial inspection interval of approximately 20 months,with subsequent intervals of about four months,and a preventive maintenance threshold of approximately 37.39 mm wear.When compared to common cost-minimization-based condition maintenance strategies and PBW strategies that do not differentiate between initial and subsequent inspection intervals,the proposed PBW strategy increases the manufacturer’s profit by 1%and 18%,respectively.Sensitivity analyses provide managerial recommendations for PBW implementation.The PBW strategy proposed in this study significantly increases manufacturers’profits by optimizing inspection intervals and preventive maintenance thresholds,and manufacturers should focus on technological improvement in preventive maintenance and cost control to further enhance earnings. 展开更多
关键词 performance-based warranty gamma process periodic inspection intelligent optimization algorithm
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Bayesian-based ant colony optimization algorithm for edge detection
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作者 YU Yongbin ZHONG Yuanjingyang +6 位作者 FENG Xiao WANG Xiangxiang FAVOUR Ekong ZHOU Chen CHENG Man WANG Hao WANG Jingya 《Journal of Systems Engineering and Electronics》 2025年第4期892-902,共11页
Ant colony optimization(ACO)is a random search algorithm based on probability calculation.However,the uninformed search strategy has a slow convergence speed.The Bayesian algorithm uses the historical information of t... Ant colony optimization(ACO)is a random search algorithm based on probability calculation.However,the uninformed search strategy has a slow convergence speed.The Bayesian algorithm uses the historical information of the searched point to determine the next search point during the search process,reducing the uncertainty in the random search process.Due to the ability of the Bayesian algorithm to reduce uncertainty,a Bayesian ACO algorithm is proposed in this paper to increase the convergence speed of the conventional ACO algorithm for image edge detection.In addition,this paper has the following two innovations on the basis of the classical algorithm,one of which is to add random perturbations after completing the pheromone update.The second is the use of adaptive pheromone heuristics.Experimental results illustrate that the proposed Bayesian ACO algorithm has faster convergence and higher precision and recall than the traditional ant colony algorithm,due to the improvement of the pheromone utilization rate.Moreover,Bayesian ACO algorithm outperforms the other comparative methods in edge detection task. 展开更多
关键词 ant colony optimization(ACO) Bayesian algorithm edge detection transfer function.
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An improved genetic algorithm for causal discovery
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作者 MAO Tengjiao BU Xianjin +2 位作者 CAI Chunxiao LU Yue DU Jing 《Journal of Systems Engineering and Electronics》 2025年第3期768-777,共10页
The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms(GA).The score-based algorithms are prone to searching space explosion.Classical GA is slow to converge,and prone to... The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms(GA).The score-based algorithms are prone to searching space explosion.Classical GA is slow to converge,and prone to falling into local optima.To address these issues,an improved GA with domain knowledge(IGADK)is proposed.Firstly,domain knowledge is incorporated into the learning process of causality to construct a new fitness function.Secondly,a dynamical mutation operator is introduced in the algorithm to accelerate the convergence rate.Finally,an experiment is conducted on simulation data,which compares the classical GA with IGADK with domain knowledge of varying accuracy.The IGADK can greatly reduce the number of iterations,populations,and samples required for learning,which illustrates the efficiency and effectiveness of the proposed algorithm. 展开更多
关键词 genetic algorithm(GA) causal discovery convergence rate fitness function mutation operator
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Functional cartography of heterogeneous combat networks using operational chain-based label propagation algorithm
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作者 CHEN Kebin JIANG Xuping +2 位作者 ZENG Guangjun YANG Wenjing ZHENG Xue 《Journal of Systems Engineering and Electronics》 2025年第5期1202-1215,共14页
To extract and display the significant information of combat systems,this paper introduces the methodology of functional cartography into combat networks and proposes an integrated framework named“functional cartogra... To extract and display the significant information of combat systems,this paper introduces the methodology of functional cartography into combat networks and proposes an integrated framework named“functional cartography of heterogeneous combat networks based on the operational chain”(FCBOC).In this framework,a functional module detection algorithm named operational chain-based label propagation algorithm(OCLPA),which considers the cooperation and interactions among combat entities and can thus naturally tackle network heterogeneity,is proposed to identify the functional modules of the network.Then,the nodes and their modules are classified into different roles according to their properties.A case study shows that FCBOC can provide a simplified description of disorderly information of combat networks and enable us to identify their functional and structural network characteristics.The results provide useful information to help commanders make precise and accurate decisions regarding the protection,disintegration or optimization of combat networks.Three algorithms are also compared with OCLPA to show that FCBOC can most effectively find functional modules with practical meaning. 展开更多
关键词 functional cartography heterogeneous combat network functional module label propagation algorithm operational chain
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Multi-platform collaborative MRC-PSO algorithm for anti-ship missile path planning
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作者 LIU Gang GUO Xinyuan +2 位作者 HUANG Dong CHEN Kezhong LI Wu 《Journal of Systems Engineering and Electronics》 2025年第2期494-509,共16页
To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO al... To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper pro-posed multi-operator real-time constraints particle swarm opti-mization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and inte-grates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evo-lution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection opti-mization of paths, gradually reducing algorithmic space, accele-rating convergence, and enhances path cooperativity. Simula-tion experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demon-strate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. More-over it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collabora-tive path planning. The experiments are conducted in three col-laborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality. 展开更多
关键词 anti-ship missiles multi-platform collaborative path planning particle swarm optimization(PSO)algorithm
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A tracking algorithm based on adaptive Kalman filter with carrier-to-noise ratio estimation under solar radio bursts interference
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作者 ZHU Xuefen LI Ang +2 位作者 LUO Yimei LIN Mengying TU Gangyi 《Journal of Systems Engineering and Electronics》 2025年第4期880-891,共12页
Solar radio burst(SRB)is one of the main natural interference sources of Global Positioning System(GPS)signals and can reduce the signal-to-noise ratio(SNR),directly affecting the tracking performance of GPS receivers... Solar radio burst(SRB)is one of the main natural interference sources of Global Positioning System(GPS)signals and can reduce the signal-to-noise ratio(SNR),directly affecting the tracking performance of GPS receivers.In this paper,a tracking algorithm based on the adaptive Kalman filter(AKF)with carrier-to-noise ratio estimation is proposed and compared with the conventional second-order phase-locked loop tracking algo-rithms and the improved Sage-Husa adaptive Kalman filter(SHAKF)algorithm.It is discovered that when the SRBs occur,the improved SHAKF and the AKF with carrier-to-noise ratio estimation enable stable tracking to loop signals.The conven-tional second-order phase-locked loop tracking algorithms fail to track the receiver signal.The standard deviation of the carrier phase error of the AKF with carrier-to-noise ratio estimation out-performs 50.51%of the improved SHAKF algorithm,showing less fluctuation and better stability.The proposed algorithm is proven to show more excellent adaptability in the severe envi-ronment caused by the SRB occurrence and has better tracking performance. 展开更多
关键词 solar radio burst(SRB) global positioning system(GPS) adaptive Kalman filter(AKF) tracking algorithm.
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科学实践能力测评——新加坡O-level生物学考试的经验与启示
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作者 刘雨田 朱方舟 王俊民 《生物学教学》 北大核心 2025年第4期63-65,共3页
科学实践是新加坡科学素养的三大构件之一,现已融入O-level生物学考试,成为其重点测评对象。通过分析新加坡O-level生物学考试对科学实践的概念界定和能力测评,发现其概念内涵既深受美国科学教育的影响,也体现新加坡重视培养科学思维的... 科学实践是新加坡科学素养的三大构件之一,现已融入O-level生物学考试,成为其重点测评对象。通过分析新加坡O-level生物学考试对科学实践的概念界定和能力测评,发现其概念内涵既深受美国科学教育的影响,也体现新加坡重视培养科学思维的底层逻辑、主张科学教育“为生活和社会服务”等本国特色。其科学实践能力测评同生物学和其他学科的知识测评相结合,强调立足实证和情境进行考查,注重考查实验技能和调查过程,测评题型丰富、方式灵活,对我国生物学学科情境下培养和测评学生的科学实践能力具有重要启示。 展开更多
关键词 科学实践 O-level生物学考试 新加坡
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学科核心素养下A-level生物学实验课程评析
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作者 陈博雅 夏玉娇 《生物学教学》 北大核心 2025年第2期45-48,共4页
基于生物学学科核心素养的角度,采用文献法、教材分析法和图表统计法对英国A-Level(英国普通中等教育证书考试高级水平课程)生物学实验课程从课程标准(大纲)、教学内容、评价方式等方面进行了分析。研究得出,A-Level生物学实验课程标准... 基于生物学学科核心素养的角度,采用文献法、教材分析法和图表统计法对英国A-Level(英国普通中等教育证书考试高级水平课程)生物学实验课程从课程标准(大纲)、教学内容、评价方式等方面进行了分析。研究得出,A-Level生物学实验课程标准从操作能力、情感态度和价值观等方面对实验培养目标进行了全面的界定。研究期望对我国中学生物学教师的教育教学提供一定的参考或启发。 展开更多
关键词 学科核心素养 A-level课程 生物学实验 评析
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Improvement and performance of parallel multilevel fast multipole algorithm 被引量:16
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作者 Zhanhe Liu Peilin Huang +1 位作者 Zhe Wu Xu Gao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第1期164-169,共6页
The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm(PMLFMA).Considering the main complements of multilevel fast multipole algorithm(M... The method of establishing data structures plays an important role in the efficiency of parallel multilevel fast multipole algorithm(PMLFMA).Considering the main complements of multilevel fast multipole algorithm(MLFMA) memory,a new parallelization strategy and a modified data octree construction scheme are proposed to further reduce communication in order to improve parallel efficiency.For far interaction,a new scheme called dynamic memory allocation is developed.To analyze the workload balancing performance of a parallel implementation,the original concept of workload balancing factor is introduced and verified by numerical examples.Numerical results show that the above measures improve the parallel efficiency and are suitable for the analysis of electrical large-scale scattering objects. 展开更多
关键词 multilevel fast multipole algorithm(MLFMA) electromagnetic scattering PARALLELIZATION radar cross section(RCS).
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Solution for integer linear bilevel programming problems using orthogonal genetic algorithm 被引量:10
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期443-451,共9页
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith... An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm. 展开更多
关键词 integer linear bilevel programming problem integer optimization genetic algorithm orthogonal experiment design
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Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems 被引量:4
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作者 Li Hecheng Wang Yuping 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第6期1157-1164,共8页
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower's functions are separable with respect to the follower's variables, and the other is that the follower's f... Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower's functions are separable with respect to the follower's variables, and the other is that the follower's functions are convex if the follower's variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader's variable x, it is proved that the optimal solution y of the follower's mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower's programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust. 展开更多
关键词 mixed-integer nonlinear bilevel programming genetic algorithm exponential distribution optimalsolutions
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