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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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基于GA-Fuzzy-PID算法的棉田施肥灌溉系统研究 被引量:1
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作者 王昊 张立新 +2 位作者 胡雪 李文春 王晓瑛 《农机化研究》 北大核心 2025年第4期50-56,64,共8页
在水肥一体控制器中,PID控制算法易引起超调,产生振荡;Fuzzy-PID控制算法由于参数基于人为经验设定,控制欠细腻。针对上述问题,研究并设计了一种基于GA-Fuzzy-PID算法的控制器,以期实现施肥灌溉系统的精准控制。在不同目标EC设定值下,对... 在水肥一体控制器中,PID控制算法易引起超调,产生振荡;Fuzzy-PID控制算法由于参数基于人为经验设定,控制欠细腻。针对上述问题,研究并设计了一种基于GA-Fuzzy-PID算法的控制器,以期实现施肥灌溉系统的精准控制。在不同目标EC设定值下,对PID算法、Fuzzy-PID算法和GA-Fuzzy-PID算法进行仿真对比。结果表明:基于GA-Fuzzy-PID的控制器具有优异的控制效果,更能满足施肥灌溉系统精准控制的要求。 展开更多
关键词 棉田 灌溉施肥 精准控制 遗传优化 ga-fuzzy-PID
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Genetic algorithm and particle swarm optimization tuned fuzzy PID controller on direct torque control of dual star induction motor 被引量:16
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作者 BOUKHALFA Ghoulemallah BELKACEM Sebti +1 位作者 CHIKHI Abdesselem BENAGGOUNE Said 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第7期1886-1896,共11页
This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different he... This study presents analysis, control and comparison of three hybrid approaches for the direct torque control (DTC) of the dual star induction motor (DSIM) drive. Its objective consists of combining three different heuristic optimization techniques including PID-PSO, Fuzzy-PSO and GA-PSO to improve the DSIM speed controlled loop behavior. The GA and PSO algorithms are developed and implemented into MATLAB. As a result, fuzzy-PSO is the most appropriate scheme. The main performance of fuzzy-PSO is reducing high torque ripples, improving rise time and avoiding disturbances that affect the drive performance. 展开更多
关键词 dual star induction motor drive direct torque control particle swarm optimization (PSO) fuzzy logic control genetic algorithms
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Fuzzy adaptive genetic algorithm based on auto-regulating fuzzy rules 被引量:6
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作者 喻寿益 邝溯琼 《Journal of Central South University》 SCIE EI CAS 2010年第1期123-128,共6页
There are defects such as the low convergence rate and premature phenomenon on the performance of simple genetic algorithms (SGA) as the values of crossover probability (Pc) and mutation probability (Pro) are fi... There are defects such as the low convergence rate and premature phenomenon on the performance of simple genetic algorithms (SGA) as the values of crossover probability (Pc) and mutation probability (Pro) are fixed. To solve the problems, the fuzzy control method and the genetic algorithms were systematically integrated to create a kind of improved fuzzy adaptive genetic algorithm (FAGA) based on the auto-regulating fuzzy rules (ARFR-FAGA). By using the fuzzy control method, the values of Pc and Pm were adjusted according to the evolutional process, and the fuzzy rules were optimized by another genetic algorithm. Experimental results in solving the function optimization problems demonstrate that the convergence rate and solution quality of ARFR-FAGA exceed those of SGA, AGA and fuzzy adaptive genetic algorithm based on expertise (EFAGA) obviously in the global search. 展开更多
关键词 adaptive genetic algorithm fuzzy rules auto-regulating crossover probability adjustment
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2-D mini mumfuzzy entropy method of image thresholding based on genetic algorithm 被引量:1
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作者 张兴会 刘玲 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第3期557-560,共4页
A new image thresholding method is introduced, which is based on 2-D histgram and minimizing the measures of fuzziness of an input image. A new definition of fuzzy membership function is proposed, it denotes the chara... A new image thresholding method is introduced, which is based on 2-D histgram and minimizing the measures of fuzziness of an input image. A new definition of fuzzy membership function is proposed, it denotes the characteristic relationship between the gray level of each pixel and the average value of its neighborhood. When the threshold is not located at the obvious and deep valley of the histgram, genetic algorithm is devoted to the problem of selecting the appropriate threshold value. The experimental results indicate that the proposed method has good performance. 展开更多
关键词 image thresholding 2-D fuzzy entropy genetic algorithm.
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Fuzzy-second order sliding mode control optimized by genetic algorithm applied in direct torque control of dual star induction motor 被引量:1
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作者 Ghoulemallah BOUKHALFA Sebti BELKACEM +1 位作者 Abdesselem CHIKHI Moufid BOUHENTALA 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第12期3974-3985,共12页
The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parame... The direct torque control of the dual star induction motor(DTC-DSIM) using conventional PI controllers is characterized by unsatisfactory performance, such as high ripples of torque and flux, and sensitivity to parametric variations. Among the most evoked control strategies adopted in this field to overcome these drawbacks presented in classical drive, it is worth mentioning the use of the second order sliding mode control(SOSMC) based on the super twisting algorithm(STA) combined with the fuzzy logic control(FSOSMC). In order to realize the optimal control performance, the FSOSMC parameters are adjusted using an optimization algorithm based on the genetic algorithm(GA). The performances of the envisaged control scheme, called G-FSOSMC, are investigated against G-SOSMC, G-PI and BBO-FSOSMC algorithms. The proposed controller scheme is efficient in reducing the torque and flux ripples, and successfully suppresses chattering. The effects of parametric uncertainties do not affect system performance. 展开更多
关键词 double star induction machine direct torque control fuzzy second order sliding mode control genetic algorithm biogeography based optimization algorithm
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Using genetic algorithm based fuzzy adaptive resonance theory for clustering analysis 被引量:3
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作者 LIU Bo WANG Yong WANG Hong-jian 《哈尔滨工程大学学报》 EI CAS CSCD 北大核心 2006年第B07期547-551,共5页
关键词 聚类分析 遗传算法 模糊自适应谐振理论 人工神经网络
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Hybrid Genetic Algorithms with Fuzzy Logic Controller
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作者 Zheng Dawei & Gen Mitsuo Department of Industrial and Systems Engineering, Ashikaga Institute of Technology, 326, Japan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2001年第3期9-15,共7页
In this paper, a new implementation of genetic algorithms (GAs) is developed for the machine scheduling problem, which is abundant among the modern manufacturing systems. The performance measure of early and tardy com... In this paper, a new implementation of genetic algorithms (GAs) is developed for the machine scheduling problem, which is abundant among the modern manufacturing systems. The performance measure of early and tardy completion of jobs is very natural as one's aim, which is usually to minimize simultaneously both earliness and tardiness of all jobs. As the problem is NP-hard and no effective algorithms exist, we propose a hybrid genetic algorithms approach to deal with it. We adjust the crossover and mutation probabilities by fuzzy logic controller whereas the hybrid genetic algorithm does not require preliminary experiments to determine probabilities for genetic operators. The experimental results show the effectiveness of the GAs method proposed in the paper. 展开更多
关键词 Machine scheduling problem Hybrid genetic algorithms fuzzy logic.
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Intelligent vehicle lateral controller design based on genetic algorithmand T-S fuzzy-neural network
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作者 RuanJiuhong FuMengyin LiYibin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第2期382-387,共6页
Non-linearity and parameter time-variety are inherent properties of lateral motions of a vehicle. How to effectively control intelligent vehicle (IV) lateral motions is a challenging task. Controller design can be reg... Non-linearity and parameter time-variety are inherent properties of lateral motions of a vehicle. How to effectively control intelligent vehicle (IV) lateral motions is a challenging task. Controller design can be regarded as a process of searching optimal structure from controller structure space and searching optimal parameters from parameter space. Based on this view, an intelligent vehicle lateral motions controller was designed. The controller structure was constructed by T-S fuzzy-neural network (FNN). Its parameters were searched and selected with genetic algorithm (GA). The simulation results indicate that the controller designed has strong robustness, high precision and good ride quality, and it can effectively resolve IV lateral motion non-linearity and time-variant parameters problem. 展开更多
关键词 intelligent vehicle genetic algorithm fuzzy-neural network lateral control robustness.
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Dynamic Bandwidth Allocation Technique in ATM Networks Based on Fuzzy Neural Networks and Genetic Algorithm
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作者 Zhang Liangjie Li Yanda Wang Pu (Dept of Automation Tsinghua University, Beijing 100084) 《通信学报》 EI CSCD 北大核心 1997年第3期10-17,共8页
DynamicBandwidthAlocationTechniqueinATMNetworksBasedonFuzyNeuralNetworksandGeneticAlgorithm①ZhangLiangjieLiY... DynamicBandwidthAlocationTechniqueinATMNetworksBasedonFuzyNeuralNetworksandGeneticAlgorithm①ZhangLiangjieLiYandaWangPu(Deptof... 展开更多
关键词 模糊神经网 动态带宽分配 异步传输网 基因算法
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基于GA-RELM多特征优选的烟叶多部位正反面识别方法 被引量:2
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作者 陈婷 赵晓琳 +5 位作者 张冀武 盖小雷 张晓伟 刘宇晨 王燕 龙杰 《湖南农业大学学报(自然科学版)》 北大核心 2025年第1期113-122,共10页
针对现有烟叶分级模型多基于平整烟叶的正面特征构建,分级模型准确率和实用性较低的问题,提出一种基于遗传算法-正则化极限学习机(GA-RELM)多特征优选的烟叶多部位正反面识别方法。首先,对自然状态下的烟叶进行多尺度正反面特征提取,构... 针对现有烟叶分级模型多基于平整烟叶的正面特征构建,分级模型准确率和实用性较低的问题,提出一种基于遗传算法-正则化极限学习机(GA-RELM)多特征优选的烟叶多部位正反面识别方法。首先,对自然状态下的烟叶进行多尺度正反面特征提取,构建正反面数据集,根据特征重要性和特征间的潜在关系,实现特征降维并构建新特征组合。其次,对正则化极限学习机(RELM)进行隐藏层偏置寻优,以提高模型实际应用性和分类精度。结果表明:与原极限学习机(ELM)相比,GA-RELM对自然状态下的烟叶正反面和多部位正反面的分类精度分别提高了0.84%和7.88%,运算时间分别减少2.56 s和5.72 s;与其他烟叶分级算法相比,GA-RELM在准确率、精确率、召回率、F1评分等多个指标上表现出明显优势。 展开更多
关键词 烤烟 烟叶分级 多特征优选 遗传算法 正则化极限学习机
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基于自适应分组GA-FLC的电池组均衡控制策略研究
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作者 吴铁洲 杜亨昱 刘珉诺 《电源技术》 北大核心 2025年第7期1482-1492,共11页
在实际应用中将多个电池单体通过串并联成组使用会存在电池不一致性问题,影响电池组使用寿命。集中式电感均衡是广泛使用的均衡技术之一,但传统极值法集中式电感电路在均衡过程中存在频繁切换均衡目标导致开关频繁通断、速度慢的问题。... 在实际应用中将多个电池单体通过串并联成组使用会存在电池不一致性问题,影响电池组使用寿命。集中式电感均衡是广泛使用的均衡技术之一,但传统极值法集中式电感电路在均衡过程中存在频繁切换均衡目标导致开关频繁通断、速度慢的问题。在集中式电感均衡拓扑结构的基础上,提出了一种基于自适应分组GA-FLC策略的集中式电感均衡电路控制方法,在均衡开启前,使用基于滑动窗口法的自适应分组策略对相邻且SOC值接近的电池合并成组,再结合遗传算法对自适应分组后的电池组进行最优路径选择,利用FLC控制均衡电流大小。以6个电池串联的电池组为例,设计静置、充电、放电三种工况下的电池组均衡实验,结果表明,与对极值法、自适应分组GA法均衡相比,提出的均衡策略显著降低了开关的通断次数,相较极值法、自适应分组GA法分别提升69%、30%的均衡速度,有助于电池组的整体性能提升和延长使用寿命。 展开更多
关键词 主动均衡 自适应分组 遗传算法 模糊逻辑控制 均衡速度
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Improved genetic algorithm for nonlinear programming problems 被引量:8
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作者 Kezong Tang Jingyu Yang +1 位作者 Haiyan Chen Shang Gao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第3期540-546,共7页
An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w... An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms. 展开更多
关键词 genetic algorithm(ga) nonlinear programming problem constraint handling non-dominated solution optimization problem.
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Job shop scheduling problem with alternative machines using genetic algorithms 被引量:10
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作者 I.A.Chaudhry 《Journal of Central South University》 SCIE EI CAS 2012年第5期1322-1333,共12页
The classical job shop scheduling problem(JSP) is the most popular machine scheduling model in practice and is known as NP-hard.The formulation of the JSP is based on the assumption that for each part type or job ther... The classical job shop scheduling problem(JSP) is the most popular machine scheduling model in practice and is known as NP-hard.The formulation of the JSP is based on the assumption that for each part type or job there is only one process plan that prescribes the sequence of operations and the machine on which each operation has to be performed.However,JSP with alternative machines for various operations is an extension of the classical JSP,which allows an operation to be processed by any machine from a given set of machines.Since this problem requires an additional decision of machine allocation during scheduling,it is much more complex than JSP.We present a domain independent genetic algorithm(GA) approach for the job shop scheduling problem with alternative machines.The GA is implemented in a spreadsheet environment.The performance of the proposed GA is analyzed by comparing with various problem instances taken from the literatures.The result shows that the proposed GA is competitive with the existing approaches.A simplified approach that would be beneficial to both practitioners and researchers is presented for solving scheduling problems with alternative machines. 展开更多
关键词 alternative machine genetic algorithm (ga job shop scheduling SPREADSHEET
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Memristive network-based genetic algorithm and its application to image edge detection 被引量:7
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作者 YU Yongbin YANG Chenyu +3 位作者 DENG Quanxin NYIMA Tashi LIANG Shouyi ZHOU Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2021年第5期1062-1070,共9页
This paper proposes a mem-computing model of memristive network-based genetic algorithm(MNGA)by building up the relationship between the memristive network(MN)and the genetic algorithm(GA),and a new edge detection alg... This paper proposes a mem-computing model of memristive network-based genetic algorithm(MNGA)by building up the relationship between the memristive network(MN)and the genetic algorithm(GA),and a new edge detection algorithm where image pixels are defined as individuals of population.First,the computing model of MNGA is designed to perform mem-computing,which brings new possibility of the hardware implementation of GA.Secondly,MNGA-based edge detection integrating image filter and GA operator deployed by MN is proposed.Finally,simulation results demonstrate that the figure of merit(FoM)of our model is better than the latest memristor-based swarm intelligence.In summary,a new way is found to build proper matching of memristor to GA and aid image edge detection. 展开更多
关键词 memristive network(MN) genetic algorithm(ga) edge detection mem-computing
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Worst-case tolerance analysis on array antenna based on chaos-genetic algorithm 被引量:2
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作者 Hao Yuan Dan Songt +1 位作者 Qiangfeng Zhou Huaping Xu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第6期824-830,共7页
This paper studies the effect of amplitude-phase errors on the antenna performance. Via builting on a worst-case error tolerance model, a simple and practical worst error tolerance analysis based on the chaos-genetic ... This paper studies the effect of amplitude-phase errors on the antenna performance. Via builting on a worst-case error tolerance model, a simple and practical worst error tolerance analysis based on the chaos-genetic algorithm (CGA) is proposed. The proposed method utilizes chaos to optimize initial population for the genetic algorithm (GA) and introduces chaotic disturbance into the genetic mutation, thereby improving the ability of the GA to search for the global optimum. Numerical simulations demonstrate that the accuracy and stability of the worst-case analysis of the proposed approach are superior to the GA. And the proposed algorithm can be used easily for the error tolerant design of antenna arrays. 展开更多
关键词 genetic algorithm (ga array antenna tolerance anal-ysis chaos disturbance logistic map
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Space-borne antenna adaptive anti-jamming method based on gradient-genetic algorithm 被引量:2
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作者 Tao Haihong Liao Guisheng Yu Jiang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第3期469-475,共7页
A novel space-borne antenna adaptive anti-jamming method based on the genetic algorithm (GA), which is combined with gradient-like reproduction operators is presented, to search for the best weight for pattern synth... A novel space-borne antenna adaptive anti-jamming method based on the genetic algorithm (GA), which is combined with gradient-like reproduction operators is presented, to search for the best weight for pattern synthesis in radio frequency (RF). Combined, the GA's the capability of the whole searching is, but not limited by selection of the initial parameter, with the gradient algorithm's advantage of fast searching. The proposed method requires a smaller sized initial population and lower computational complexity. Therefore, it is flexible to implement this method in the real-time systems. By using the proposed algorithm, the designer can efficiently control both main-lobe shaping and side-lobe level. Simulation results based on the spot survey data show that the algorithm proposed is efficient and feasible. 展开更多
关键词 space-borne antenna genetic algorithm (ga gradient-like ANTI-JAMMING pattern synthesis.
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基于改进RRT与GA的多目标路径规划——以无人机林区巡检为例 被引量:1
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作者 张彪 康峰 许舒婷 《北京林业大学学报》 北大核心 2025年第4期129-141,共13页
【目的】为解决无人机在人工林区巡检任务(如病虫害监测、火灾预防等)中的路径规划问题,即求解巡检点的最优遍历序列以及生成避障飞行轨迹,本文通过融合改进快速随机扩展树(RRT)算法和遗传算法(GA),提出一种多目标路径规划算法。【方法... 【目的】为解决无人机在人工林区巡检任务(如病虫害监测、火灾预防等)中的路径规划问题,即求解巡检点的最优遍历序列以及生成避障飞行轨迹,本文通过融合改进快速随机扩展树(RRT)算法和遗传算法(GA),提出一种多目标路径规划算法。【方法】首先改进传统GA,使其能够在三维空间中遍历所有巡检点并求解最优序列。其次,依据该序列进行路径搜索,改进RRT算法的随机采样原理,通过靶心和绕树策略实现避障效果,并采用连续选择父节点策略,取消因避障产生的多余转折点。最后,通过3次B样条曲线优化,生成最终路径。【结果】仿真结果表明,本算法能够在复杂林区环境中遍历所有巡检点,并在短时间内规划出高质量、无碰撞的路径。与粒子群算法(PSO)、蚁群算法(ACO)和RRT算法相比,当巡检点从3个增加到9个时,PSO、ACO、RRT算法搜索时间分别增加了221.77%、332.42%、184.78%,而本算法仅增加了102.35%。在9个巡检点的复杂环境中,本算法的路径耗散分别比PSO、ACO和RRT算法降低了14.46%、30.28%、24.76%,且路径质量显著提高,消除了路径交叉重合现象。此外,通过ROS平台,利用无人机在林区点云上进行模拟飞行并验证成功,证明本算法适用于林区巡检的多目标路径规划。【结论】针对人工林区无人机巡检任务中的飞行路线规划问题,本文通过改进RRT与GA,成功规划出一条遍历所有巡检点且避开林区障碍物的无碰撞路径。相较于PSO、ACO和RRT算法,本算法在路径质量、路径耗散和搜索时间上均表现出显著优势。 展开更多
关键词 多目标优化 路径规划 快速随机扩展树(RRT) 遗传算法(ga) 无人机 粒子群算法(PSO) 蚁群算法(ACO)
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PHUI-GA: GPU-based efficiency evolutionary algorithm for mining high utility itemsets
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作者 JIANG Haipeng WU Guoqing +3 位作者 SUN Mengdan LI Feng SUN Yunfei FANG Wei 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第4期965-975,共11页
Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining perform... Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining performance,but they still require huge computational resource and may miss many HUIs.Due to the good combination of EA and graphics processing unit(GPU),we propose a parallel genetic algorithm(GA)based on the platform of GPU for mining HUIM(PHUI-GA).The evolution steps with improvements are performed in central processing unit(CPU)and the CPU intensive steps are sent to GPU to eva-luate with multi-threaded processors.Experiments show that the mining performance of PHUI-GA outperforms the existing EAs.When mining 90%HUIs,the PHUI-GA is up to 188 times better than the existing EAs and up to 36 times better than the CPU parallel approach. 展开更多
关键词 high utility itemset mining(HUIM) graphics process-ing unit(GPU)parallel genetic algorithm(ga) mining perfor-mance
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Method for electromagnetic detection satellites scheduling based on genetic algorithm with alterable penalty coefficient 被引量:1
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作者 Jun Li Hao Chen +2 位作者 Zhinong Zhong Ning Jing Jiangjiang Wu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第5期822-832,共11页
The electromagnetic detection satellite (EDS) is a type of earth observation satellites (EOSs). The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The... The electromagnetic detection satellite (EDS) is a type of earth observation satellites (EOSs). The Information collected by EDSs plays an important role in some fields, such as industry, science and military. The scheduling of EDSs is a complex combinatorial optimization problem. Current research mainly focuses on the scheduling of imaging satellites and SAR satellites, but little work has been done on the scheduling of EDSs for its specific characteristics. A multi-satellite scheduling model is established, in which the specific constrains of EDSs are considered, then a scheduling algorithm based on the genetic algorithm (GA) is proposed. To deal with the specific constrains of EDSs, a penalty function method is introduced. However, it is hard to determine the appropriate penalty coefficient in the penalty function. Therefore, an adaptive adjustment mechanism of the penalty coefficient is designed to solve the problem, as well as improve the scheduling results. Experimental results are used to demonstrate the correctness and practicability of the proposed scheduling algorithm. 展开更多
关键词 electromagnetic detection satellite (EDS) scheduling genetic algorithm (ga constraint handling penalty function method alterable penalty coefficient.
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