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Multi-objective optimization of grinding process parameters for improving gear machining precision
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作者 YOU Tong-fei HAN Jiang +4 位作者 TIAN Xiao-qing TANG Jian-ping LU Yi-guo LI Guang-hui XIA Lian 《Journal of Central South University》 2025年第2期538-551,共14页
The gears of new energy vehicles are required to withstand higher rotational speeds and greater loads,which puts forward higher precision essentials for gear manufacturing.However,machining process parameters can caus... The gears of new energy vehicles are required to withstand higher rotational speeds and greater loads,which puts forward higher precision essentials for gear manufacturing.However,machining process parameters can cause changes in cutting force/heat,resulting in affecting gear machining precision.Therefore,this paper studies the effect of different process parameters on gear machining precision.A multi-objective optimization model is established for the relationship between process parameters and tooth surface deviations,tooth profile deviations,and tooth lead deviations through the cutting speed,feed rate,and cutting depth of the worm wheel gear grinding machine.The response surface method(RSM)is used for experimental design,and the corresponding experimental results and optimal process parameters are obtained.Subsequently,gray relational analysis-principal component analysis(GRA-PCA),particle swarm optimization(PSO),and genetic algorithm-particle swarm optimization(GA-PSO)methods are used to analyze the experimental results and obtain different optimal process parameters.The results show that optimal process parameters obtained by the GRA-PCA,PSO,and GA-PSO methods improve the gear machining precision.Moreover,the gear machining precision obtained by GA-PSO is superior to other methods. 展开更多
关键词 worm wheel gear grinding machine gear machining precision machining process parameters multi objective optimization
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Overview of multi-objective optimization methods 被引量:2
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作者 LeiXiujuan ShiZhongke 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2004年第2期142-146,共5页
To assist readers to have a comprehensive understanding, the classical and intelligent methods roundly based on precursory research achievements are summarized in this paper. First, basic conception and description ab... To assist readers to have a comprehensive understanding, the classical and intelligent methods roundly based on precursory research achievements are summarized in this paper. First, basic conception and description about multi-objective (MO) optimization are introduced. Then some definitions and related terminologies are given. Furthermore several MO optimization methods including classical and current intelligent methods are discussed one by one succinctly. Finally evaluations on advantages and disadvantages about these methods are made at the end of the paper. 展开更多
关键词 multi-objective optimization objective function Pareto optimality genetic algorithms simulated annealing fuzzy logical.
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Rotary unmanned aerial vehicles path planning in rough terrain based on multi-objective particle swarm optimization 被引量:25
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作者 XU Zhen ZHANG Enze CHEN Qingwei 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第1期130-141,共12页
This paper presents a path planning approach for rotary unmanned aerial vehicles(R-UAVs)in a known static rough terrain environment.This approach aims to find collision-free and feasible paths with minimum altitude,le... This paper presents a path planning approach for rotary unmanned aerial vehicles(R-UAVs)in a known static rough terrain environment.This approach aims to find collision-free and feasible paths with minimum altitude,length and angle variable rate.First,a three-dimensional(3D)modeling method is proposed to reduce the computation burden of the dynamic models of R-UAVs.Considering the length,height and tuning angle of a path,the path planning of R-UAVs is described as a tri-objective optimization problem.Then,an improved multi-objective particle swarm optimization algorithm is developed.To render the algorithm more effective in dealing with this problem,a vibration function is introduced into the collided solutions to improve the algorithm efficiency.Meanwhile,the selection of the global best position is taken into account by the reference point method.Finally,the experimental environment is built with the help of the Google map and the 3D terrain generator World Machine.Experimental results under two different rough terrains from Guilin and Lanzhou of China demonstrate the capabilities of the proposed algorithm in finding Pareto optimal paths. 展开更多
关键词 unmanned aerial vehicle(UAV) path planning multiobjective optimization particle swarm optimization
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A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making 被引量:3
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作者 LIANG Yan’gang QIN Zheng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2019年第3期535-544,共10页
A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the... A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform. 展开更多
关键词 layout optimization SATELLITE multi-objective optimization PARETO FRONT multi-ATTRIBUTE decision making
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Multi-objective workflow scheduling in cloud system based on cooperative multi-swarm optimization algorithm 被引量:2
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作者 YAO Guang-shun DING Yong-sheng HAO Kuang-rong 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第5期1050-1062,共13页
In order to improve the performance of multi-objective workflow scheduling in cloud system, a multi-swarm multiobjective optimization algorithm(MSMOOA) is proposed to satisfy multiple conflicting objectives. Inspired ... In order to improve the performance of multi-objective workflow scheduling in cloud system, a multi-swarm multiobjective optimization algorithm(MSMOOA) is proposed to satisfy multiple conflicting objectives. Inspired by division of the same species into multiple swarms for different objectives and information sharing among these swarms in nature, each physical machine in the data center is considered a swarm and employs improved multi-objective particle swarm optimization to find out non-dominated solutions with one objective in MSMOOA. The particles in each swarm are divided into two classes and adopt different strategies to evolve cooperatively. One class of particles can communicate with several swarms simultaneously to promote the information sharing among swarms and the other class of particles can only exchange information with the particles located in the same swarm. Furthermore, in order to avoid the influence by the elastic available resources, a manager server is adopted in the cloud data center to collect the available resources for scheduling. The quality of the proposed method with other related approaches is evaluated by using hybrid and parallel workflow applications. The experiment results highlight the better performance of the MSMOOA than that of compared algorithms. 展开更多
关键词 multi-objective WORKFLOW scheduling multi-swarm optimization particle SWARM optimization (PSO) CLOUD computing system
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Multi-objective evolutionary optimization for geostationary orbit satellite mission planning 被引量:4
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作者 Jiting Li Sheng Zhang +1 位作者 Xiaolu Liu Renjie He 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期934-945,共12页
In the past few decades, applications of geostationary orbit (GEO) satellites have attracted increasing attention, and with the development of optical technologies, GEO optical satellites have become popular worldwide... In the past few decades, applications of geostationary orbit (GEO) satellites have attracted increasing attention, and with the development of optical technologies, GEO optical satellites have become popular worldwide. This paper proposes a general working pattern for a GEO optical satellite, as well as a target observation mission planning model. After analyzing the requirements of users and satellite control agencies, two objectives are simultaneously considered: maximization of total profit and minimization of satellite attitude maneuver angle. An NSGA-II based multi-objective optimization algorithm is proposed, which contains some heuristic principles in the initialization phase and mutation operator, and is embedded with a traveling salesman problem (TSP) optimization. The validity and performance of the proposed method are verified by extensive numerical simulations that include several types of point target distributions. 展开更多
关键词 geostationary orbit (GEO) satellitemission planning multi-objective optimization evolutionary genetic
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Study on Multi-objective Optimization of Airbag Landing Attenuation System for Heavy Airdrop 被引量:1
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作者 Hong-yan WANG Huang-jie HONG +1 位作者 Jian-yang LI Qiang RUI 《Defence Technology(防务技术)》 SCIE EI CAS 2013年第4期237-241,共5页
A finite element model of vehicle and its airbag landing attenuation system is established and verified experimentally.Two design cases are selected to constrain the airbag design for extreme landing conditions,while ... A finite element model of vehicle and its airbag landing attenuation system is established and verified experimentally.Two design cases are selected to constrain the airbag design for extreme landing conditions,while the height and width of airbag and the area of vent hole are chosen as design variables.The optimization is forced to compromise the design variables between the conflicting requirements of the two extremes.In order to optimize the parameters of airbag,the multi-dimensional response surfaces based on extended Latin hypercube design and radial basis function are employed instead of the complex finite element model.Pareto optimal solution sets based on response surfaces are then obtained by multi-objective genetic algorithm.The results show the optimization method presented in this paper is a practical tool for the optimization of airbag landing attenuation system for heavy airdrop. 展开更多
关键词 多目标优化 系统 衰减 安全气囊 空投 着陆 PARETO最优解集 有限元模型
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Novel electromagnetism-like mechanism method for multiobjective optimization problems 被引量:1
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作者 Lixia Han Shujuan Jiang Shaojiang Lan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第1期182-189,共8页
As a new-style stochastic algorithm, the electromagnetism-like mechanism(EM) method gains more and more attention from many researchers in recent years. A novel model based on EM(NMEM) for multiobjective optimizat... As a new-style stochastic algorithm, the electromagnetism-like mechanism(EM) method gains more and more attention from many researchers in recent years. A novel model based on EM(NMEM) for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems. 展开更多
关键词 electromagnetism-like mechanism(EM) method multi-objective optimization problem PARTICLE Pareto optimal solutions
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Multi-objective fuzzy particle swarm optimization based on elite archiving and its convergence 被引量:1
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作者 Wei Jingxuan Wang Yuping 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期1035-1040,共6页
A fuzzy particle swarm optimization (PSO) on the basis of elite archiving is proposed for solving multi-objective optimization problems. First, a new perturbation operator is designed, and the concepts of fuzzy glob... A fuzzy particle swarm optimization (PSO) on the basis of elite archiving is proposed for solving multi-objective optimization problems. First, a new perturbation operator is designed, and the concepts of fuzzy global best and fuzzy personal best are given on basis of the new operator. After that, particle updating equations are revised on the basis of the two new concepts to discourage the premature convergence and enlarge the potential search space; second, the elite archiving technique is used during the process of evolution, namely, the elite particles are introduced into the swarm, whereas the inferior particles are deleted. Therefore, the quality of the swarm is ensured. Finally, the convergence of this swarm is proved. The experimental results show that the nondominated solutions found by the proposed algorithm are uniformly distributed and widely spread along the Pareto front. 展开更多
关键词 multi-objective optimization particle swarm optimization fuzzy personal best fuzzy global best elite archiving.
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Multi-objective reentry trajectory optimization method via GVD for hypersonic vehicles 被引量:1
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作者 Chaofang Hu Yue Xin Hao Feng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第4期732-744,共13页
In the constrained reentry trajectory design of hypersonic vehicles, multiple objectives with priorities bring about more difficulties to find the optimal solution. Therefore, a multi-objective reentry trajectory opti... In the constrained reentry trajectory design of hypersonic vehicles, multiple objectives with priorities bring about more difficulties to find the optimal solution. Therefore, a multi-objective reentry trajectory optimization (MORTO) approach via generalized varying domain (GVD) is proposed. Using the direct collocation approach, the trajectory optimization problem involving multiple objectives is discretized into a nonlinear multi-objective programming with priorities. In terms of fuzzy sets, the objectives are fuzzified into three types of fuzzy goals, and their constant tolerances are substituted by the varying domains. According to the principle that the objective with higher priority has higher satisfactory degree, the priority requirement is modeled as the order constraints of the varying domains. The corresponding two-side, single-side, and hybrid-side varying domain models are formulated for three fuzzy relations respectively. By regulating the parameter, the optimal reentry trajectory satisfying priorities can be achieved. Moreover, the performance about the parameter is analyzed, and the algorithm to find its specific value for maximum priority difference is proposed. The simulations demonstrate the effectiveness of the proposed method for hypersonic vehicles, and the comparisons with the traditional methods and sensitivity analysis are presented. 展开更多
关键词 hypersonic vehicle reentry trajectory design multi-objective optimization generalized varying domain direct collocation method
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Evolutionary many objective optimization based on bidirectional decomposition 被引量:1
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作者 LYU Chengzhong LI Weimin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2019年第2期319-326,共8页
The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot sprea... The decomposition based approach decomposes a multi-objective problem into a series of single objective subproblems, which are optimized along contours towards the ideal point. But non-dominated solutions cannot spread uniformly, since the Pareto front shows different features, such as concave and convex. To improve the distribution uniformity of non-dominated solutions, a bidirectional decomposition based approach that constructs two search directions is proposed to provide a uniform distribution no matter what features problems have. Since two populations along two search directions show differently on diversity and convergence, an adaptive neighborhood selection approach is presented to choose suitable parents for the offspring generation. In order to avoid the problem of the shrinking search region caused by the close distance of the ideal and nadir points, a reference point update approach is presented. The performance of the proposed algorithm is validated with four state-of-the-art algorithms. Experimental results demonstrate the superiority of the proposed algorithm on all considered test problems. 展开更多
关键词 MANY objective optimization BIDIRECTIONAL DECOMPOSITION REFERENCE UPDATE EVOLUTIONARY algorithm
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Multi-objective Optimal Generation Dispatch With Consideration of Operation Risk 被引量:4
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作者 QIU Wei ZHANG Jianhua +2 位作者 LIU Nian ZHU Xingyang LIU Lihua 《中国电机工程学报》 EI CSCD 北大核心 2012年第22期I0009-I0009,共1页
关键词 多目标优化 发电调度 操作 风险 经济调度 经济发展 燃料成本 安全约束
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Optimal setting and placement of FACTS devices using strength Pareto multi-objective evolutionary algorithm 被引量:2
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作者 Amin Safari Hossein Shayeghi Mojtaba Bagheri 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第4期829-839,共11页
This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for... This work proposes a novel approach for multi-type optimal placement of flexible AC transmission system(FACTS) devices so as to optimize multi-objective voltage stability problem. The current study discusses a way for locating and setting of thyristor controlled series capacitor(TCSC) and static var compensator(SVC) using the multi-objective optimization approach named strength pareto multi-objective evolutionary algorithm(SPMOEA). Maximization of the static voltage stability margin(SVSM) and minimizations of real power losses(RPL) and load voltage deviation(LVD) are taken as the goals or three objective functions, when optimally locating multi-type FACTS devices. The performance and effectiveness of the proposed approach has been validated by the simulation results of the IEEE 30-bus and IEEE 118-bus test systems. The proposed approach is compared with non-dominated sorting particle swarm optimization(NSPSO) algorithm. This comparison confirms the usefulness of the multi-objective proposed technique that makes it promising for determination of combinatorial problems of FACTS devices location and setting in large scale power systems. 展开更多
关键词 STRENGTH PARETO multi-objective evolutionary algorithm STATIC var COMPENSATOR (SVC) THYRISTOR controlled series capacitor (TCSC) STATIC voltage stability margin optimal location
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A ε-indicator-based shuffled frog leaping algorithm for many-objective optimization problems
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作者 WANG Na SU Yuchao +2 位作者 CHEN Xiaohong LI Xia LIU Dui 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第1期142-155,共14页
Many-objective optimization problems take challenges to multi-objective evolutionary algorithms.A number of nondominated solutions in population cause a difficult selection towards the Pareto front.To tackle this issu... Many-objective optimization problems take challenges to multi-objective evolutionary algorithms.A number of nondominated solutions in population cause a difficult selection towards the Pareto front.To tackle this issue,a series of indicatorbased multi-objective evolutionary algorithms(MOEAs)have been proposed to guide the evolution progress and shown promising performance.This paper proposes an indicator-based manyobjective evolutionary algorithm calledε-indicator-based shuffled frog leaping algorithm(ε-MaOSFLA),which adopts the shuffled frog leaping algorithm as an evolutionary strategy and a simple and effectiveε-indicator as a fitness assignment scheme to press the population towards the Pareto front.Compared with four stateof-the-art MOEAs on several standard test problems with up to 50 objectives,the experimental results show thatε-MaOSFLA outperforms the competitors. 展开更多
关键词 evolutionary algorithm many-objective optimization shuffled frog leaping algorithm(SFLA) ε-indicator
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Real-time object segmentation based on convolutional neural network with saliency optimization for picking 被引量:1
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作者 CHEN Jinbo WANG Zhiheng LI Hengyu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第6期1300-1307,共8页
This paper concerns the problem of object segmentation in real-time for picking system. A region proposal method inspired by human glance based on the convolutional neural network is proposed to select promising regio... This paper concerns the problem of object segmentation in real-time for picking system. A region proposal method inspired by human glance based on the convolutional neural network is proposed to select promising regions, allowing more processing is reserved only for these regions. The speed of object segmentation is significantly improved by the region proposal method.By the combination of the region proposal method based on the convolutional neural network and superpixel method, the category and location information can be used to segment objects and image redundancy is significantly reduced. The processing time is reduced considerably by this to achieve the real time. Experiments show that the proposed method can segment the interested target object in real time on an ordinary laptop. 展开更多
关键词 convolutional neural network object detection object segmentation superpixel saliency optimization
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Multi-optimizationofasphericalmechanismforminimallyinvasivesurgery 被引量:2
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作者 NIU Guo-jun PAN Bo +2 位作者 ZHANG Fu-hai FENG Hai-bo FU Yi-li 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第6期1406-1417,共12页
In order to obtain the remote center motion(RCM) mechanism with better performance indexes and avoid the collision of multi-manipulators in minimally invasive surgery(MIS), a novel multi-objective optimization model w... In order to obtain the remote center motion(RCM) mechanism with better performance indexes and avoid the collision of multi-manipulators in minimally invasive surgery(MIS), a novel multi-objective optimization model was presented. There were two optimization objectives: a global kinematic performance index and a comprehensive stiffness index. Other indexes to characterize the design requirements such as collision probability, workspace, mechanism parameter, mass, and wall thickness were considered as constraints. Angles between two adjacent joints and cross-section dimensions of links were chosen as the design variables. The non-dominated sorting genetic algorithm II(NSGA-II) was adopted to solve the complex multi-objective optimization problem. Then, a 3-degree of freedom(DoF) MIS robotic prototype based on optimization results has been built up. The experiments to test the spatial position change of the remote center point and to test the absolute position accuracy and repetitive position accuracy of the MIS robot were achieved, and the experimental results meet the requirements of MIS. 展开更多
关键词 MINIMALLY INVASIVE SURGERY medical robot multi-objective optimization remote CENTRE motion
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System optimization-oriented spare parts dynamic configuration model for multi-echelon multi-indenture system 被引量:9
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作者 Minzhi Ruan Hua Li Jian Fu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期923-933,共11页
In order to optimize the spares configuration project at different stages during the life cycle, the factor of time is considered to relax the assumption of the spares steady demand in multi-echelon technique for reco... In order to optimize the spares configuration project at different stages during the life cycle, the factor of time is considered to relax the assumption of the spares steady demand in multi-echelon technique for recoverable item control (METRIC) theory. According to the method of systems analysis, the dynamic palm theorem is introduced to establish the prediction model of the spares demand rate, and its main influence factors are analyzed, based on which, the spares support effectiveness evaluation index system is studied, and the system optimization-oriented spares dynamic configuration method for multi-echelon multi-indenture system is proposed. Through the analysis of the optimization algorithm, the layered marginal algorithm is designed to improve the model calculation efficiency. In a given example, the multi-stage spares configuration project during its life cycle is gotten, the research result conforms to the actual status, and it can provide a new way for the spares dynamic optimization. 展开更多
关键词 system optimization spare parts dynamic demand support effectiveness multi-echelon multi-indenture layered marginal algorithm
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Improved particle swarm optimization algorithm for fuzzy multi-class SVM 被引量:18
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作者 Ying Li Bendu Bai Yanning Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第3期509-513,共5页
An improved particle swarm optimization(PSO) algorithm is proposed to train the fuzzy support vector machine(FSVM) for pattern multi-classification.In the improved algorithm,the particles studies not only from its... An improved particle swarm optimization(PSO) algorithm is proposed to train the fuzzy support vector machine(FSVM) for pattern multi-classification.In the improved algorithm,the particles studies not only from itself and the best one but also from the mean value of some other particles.In addition,adaptive mutation was introduced to reduce the rate of premature convergence.The experimental results on the synthetic aperture radar(SAR) target recognition of moving and stationary target acquisition and recognition(MSTAR) dataset and character recognition of MNIST database show that the improved algorithm is feasible and effective for fuzzy multi-class SVM training. 展开更多
关键词 particle swarm optimization(PSO) fuzzy support vector machine(FSVM) adaptive mutation multi-classification.
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Multi-objective Transmission Expansion Planning Considering Life Cycle Cost 被引量:31
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作者 LIU Lu CHENG Haozhong MA Zeliang YAO Liangzhong BAZARGAN Masoud 《中国电机工程学报》 EI CSCD 北大核心 2012年第22期I0007-I0007,19,共1页
为克服目前全寿命周期成本(life cycle cost,LCC)技术的应用局限于设备运行或维护阶段的不足,针对输电网整体建立一个3维LCC层级模型,包括时间维度、元件维度和费用维度。费用维度进一步分解为设备级、系统级、外部环境成本。研究了... 为克服目前全寿命周期成本(life cycle cost,LCC)技术的应用局限于设备运行或维护阶段的不足,针对输电网整体建立一个3维LCC层级模型,包括时间维度、元件维度和费用维度。费用维度进一步分解为设备级、系统级、外部环境成本。研究了以可靠性为中心的维护手段的应用对维护成本的影响,利用电量不足期望值计算故障成本。在此基础上,对风电等4种不确定因素进行建模,建立以LCC成本最小和切负荷量最小为多目标的输电网机会约束规划模型。采用正态边界交点算法联合改进小生境遗传算法,对模型有效求解。最后,分别对18节点系统和77节点系统进行算例分析。研究结果给出了帕累托解集及推荐的最优规划方案;此外,LCC费用分解图表明了各费用的比重和影响,有利于指导未来资产管理。 展开更多
关键词 生命周期成本 输电网规划 多目标 扩展规划 输电网络 最低成本 维护成本 成本管理
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Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion 被引量:2
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作者 MENG Xiangfei WANG Ying +2 位作者 LI Chao WANG Xiaoyang LYU Maolong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第6期1197-1208,共12页
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia... An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach. 展开更多
关键词 uncertainty theory uncertain multi-objective programming expected-variance value criterion
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