量子智能优化算法及其在电机优化应用中的研究
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摘要
量子计算是结合了信息科学和量子力学的新兴交叉科学，而以量子算法为代表的量子计算理论，由于其高度的并行性、指数级存储容量和对经典启发式算法的指数级加速作用，因而具有极大的优越性并且蕴涵着强大的生命力，现在已经成为世界各国相关学者研究的前沿热点领域。而将量子计算理论引入传统智能优化算法，改变了传统智能优化算法的迭代寻优方式，提高了传统智能优化算法的迭代收敛速度和全局寻优能力等性能。因此，研究量子智能优化算法及其在电机优化中的应用有着重要的理论和现实意义。本论文主要研究连续量子蚁群优化、连续量子粒子群优化、连续量子免疫克隆优化，以及量子智能优化算法在电机优化应用中的研究。具体可归纳如下。
1．将量子计算原理和蚁群优化相融合，提出连续量子蚁群优化算法，数值仿真结果表明连续量子蚁群优化算法的迭代收敛速度和全局寻优能力明显优于蚁群优化算法。以一台117kW高速永磁发电机为例，通过温度场计算分析和量子智能优化算法对其冷却结构进行了优化设计研究。使电机内温度分布趋于均匀，并研究了流道高度和通道截面变化位置对电机内温度分布的综合作用影响。建立了双目标函数双维度变量的流道优化设计的连续量子蚁群优化数学模型，通过优化算法得到了定子绕组最高温度和轴向温差均为最小的流道结构方案。得出的规律性结论可为高速永磁发电机冷却系统的改进设计与研究提供参考。
2．将量子计算原理和粒子群优化相融合，提出连续量子粒子群优化算法，仿真结果表明引入量子计算的相关理论，可明显提高算法的优化效率。建立了多优化目标的流道优化设计连续量子粒子群优化数学模型，以降低电机定子绕组最高温度和定子铁心轴向最高温度，减小定子绕组轴向温差和定子铁心轴向温差为目标。根据连续量子粒子群优化确定的流道优化最优方案，电机不同位置轴向最高温度和温差均显著减小，为高速永磁发电机内冷却结构的优化设计提供一种新的优化方法。
3．将量子计算理论和免疫克隆算法相融合，提出连续量子免疫克隆优化，仿真结果表明连续量子免疫克隆优化的优化性能明显优于免疫克隆算法。深入研究了高速永磁发电机冷却结构双维度多目标优化。以降低电机定子绕组最高温度、转子最高温度和定子铁心轴向最高温度，减小定子绕组轴向温差、转子轴向温差和定子铁心轴向温差为目标，对流道dh和dl参数优化进行了研究。根据连续量子免疫克隆优化确定的流道优化最优方案，使得电机内轴向温度分布更趋均匀。
Quantum computation is an emerging interdisciplinary science whichcombines information science and quantum mechanics. And quantumcomputation theory, represented by quantum algorithm, has great superiority andstrong vitality because it has a high degree of parallelism, the index level ofstorage capacity, and can speed up the classic heuristic algorithms, so it hasbecome the frontier research field for many relevant scholars around the word.The integration of traditional intelligent optimization algorithms and quantumcomputation theory changes iterative optimization method of traditionalintelligent optimization algorithms, improve iterative convergence rate andglobal search capability. Hence, the research on quantum intelligent optimizationalgorithm and its application to motor optimization has important theoretical andpractical significance. This dissertation mainly studied the continuous quantumant colony optimization、continuous quantum particle swarm optimization、continuous quantum immune clonal optimization、and the applications to motoroptimization, the specific content of the paper can be summarized as follows.
1．Through integration of the quantum computation theory and the antcolony optimization, the continuous quantum ant colony optimization is proposed,the simulation results show that its convergence speed and approximation abilityare evidently superior to the ant colony optimization. The optimal design of a117kW level high speed permanent magnetic generator (HSPMG) cooingstructure is studied through thermal analysis and the quantum intelligentoptimization algorithm. The new cooling systems can make temperaturedistribute more evenly in HSPMG, and the influences of groove height and theaxial variation position on HSPMG temperature distributions are studied. Basedon the continuous quantum ant colony optimization, a mathematical optimizationmodel with dual objective functions and two dimensional variables for statorslots grooves optimal design is proposed, and a groove structure which could make both the windings axial largest temperature and the axial temperaturedifference to be the minimum ones is obtained by optimization algorithm. Theobtained conclusions may provide useful reference for the design and research ofcooling structure in HSPMG.
2．Through integration of the quantum computation theory and the particleswarm optimization, continuous quantum particle swarm optimization isproposed, the simulation results show that the induction of quantum computationtheory can significantly improve the optimization efficiency of algorithm. Amathematical optimization model with multi-objective optimization for statorslots grooves optimal design is proposed based on the continuous quantum antcolony optimization, which could make the stator windings axial largesttemperature, the stator core axial largest temperature, the stator windings axialtemperature difference and the stator core axial temperature difference to be theminimum ones. According to the optimal solution of stator slots groovesdetermined by continuous quantum ant colony optimization, the motor axiallargest temperature and axial temperature difference in motor different positionsare decreased significantly, a new kind of optimization method is proposed forHSPMG cooling structure.
3．Through integration of the quantum computation theory and the immuneclonal algorithm, the continuous quantum immune clonal optimization isproposed, and the simulation results show the optimization ability of continuousquantum immune clonal optimization is evidently superior to the immune clonalalgorithm. Multi-objective optimization with two dimensional variables forcooling structure in HSPMG is studied in depth. The stator windings axial largesttemperature, the stator core axial largest temperature, the rotor axial largesttemperature, the stator windings axial temperature difference, the rotor axialtemperature difference and the stator core axial temperature difference areselected as optimization goals, the stator slots grooves parameters dh and dloptimization are studied. The stator slots grooves optimal solution based on thecontinuous quantum immune clonal optimization make the motor axialtemperature distribution more uniform.
1．将量子计算原理和蚁群优化相融合，提出连续量子蚁群优化算法，数值仿真结果表明连续量子蚁群优化算法的迭代收敛速度和全局寻优能力明显优于蚁群优化算法。以一台117kW高速永磁发电机为例，通过温度场计算分析和量子智能优化算法对其冷却结构进行了优化设计研究。使电机内温度分布趋于均匀，并研究了流道高度和通道截面变化位置对电机内温度分布的综合作用影响。建立了双目标函数双维度变量的流道优化设计的连续量子蚁群优化数学模型，通过优化算法得到了定子绕组最高温度和轴向温差均为最小的流道结构方案。得出的规律性结论可为高速永磁发电机冷却系统的改进设计与研究提供参考。
2．将量子计算原理和粒子群优化相融合，提出连续量子粒子群优化算法，仿真结果表明引入量子计算的相关理论，可明显提高算法的优化效率。建立了多优化目标的流道优化设计连续量子粒子群优化数学模型，以降低电机定子绕组最高温度和定子铁心轴向最高温度，减小定子绕组轴向温差和定子铁心轴向温差为目标。根据连续量子粒子群优化确定的流道优化最优方案，电机不同位置轴向最高温度和温差均显著减小，为高速永磁发电机内冷却结构的优化设计提供一种新的优化方法。
3．将量子计算理论和免疫克隆算法相融合，提出连续量子免疫克隆优化，仿真结果表明连续量子免疫克隆优化的优化性能明显优于免疫克隆算法。深入研究了高速永磁发电机冷却结构双维度多目标优化。以降低电机定子绕组最高温度、转子最高温度和定子铁心轴向最高温度，减小定子绕组轴向温差、转子轴向温差和定子铁心轴向温差为目标，对流道dh和dl参数优化进行了研究。根据连续量子免疫克隆优化确定的流道优化最优方案，使得电机内轴向温度分布更趋均匀。
Quantum computation is an emerging interdisciplinary science whichcombines information science and quantum mechanics. And quantumcomputation theory, represented by quantum algorithm, has great superiority andstrong vitality because it has a high degree of parallelism, the index level ofstorage capacity, and can speed up the classic heuristic algorithms, so it hasbecome the frontier research field for many relevant scholars around the word.The integration of traditional intelligent optimization algorithms and quantumcomputation theory changes iterative optimization method of traditionalintelligent optimization algorithms, improve iterative convergence rate andglobal search capability. Hence, the research on quantum intelligent optimizationalgorithm and its application to motor optimization has important theoretical andpractical significance. This dissertation mainly studied the continuous quantumant colony optimization、continuous quantum particle swarm optimization、continuous quantum immune clonal optimization、and the applications to motoroptimization, the specific content of the paper can be summarized as follows.
1．Through integration of the quantum computation theory and the antcolony optimization, the continuous quantum ant colony optimization is proposed,the simulation results show that its convergence speed and approximation abilityare evidently superior to the ant colony optimization. The optimal design of a117kW level high speed permanent magnetic generator (HSPMG) cooingstructure is studied through thermal analysis and the quantum intelligentoptimization algorithm. The new cooling systems can make temperaturedistribute more evenly in HSPMG, and the influences of groove height and theaxial variation position on HSPMG temperature distributions are studied. Basedon the continuous quantum ant colony optimization, a mathematical optimizationmodel with dual objective functions and two dimensional variables for statorslots grooves optimal design is proposed, and a groove structure which could make both the windings axial largest temperature and the axial temperaturedifference to be the minimum ones is obtained by optimization algorithm. Theobtained conclusions may provide useful reference for the design and research ofcooling structure in HSPMG.
2．Through integration of the quantum computation theory and the particleswarm optimization, continuous quantum particle swarm optimization isproposed, the simulation results show that the induction of quantum computationtheory can significantly improve the optimization efficiency of algorithm. Amathematical optimization model with multi-objective optimization for statorslots grooves optimal design is proposed based on the continuous quantum antcolony optimization, which could make the stator windings axial largesttemperature, the stator core axial largest temperature, the stator windings axialtemperature difference and the stator core axial temperature difference to be theminimum ones. According to the optimal solution of stator slots groovesdetermined by continuous quantum ant colony optimization, the motor axiallargest temperature and axial temperature difference in motor different positionsare decreased significantly, a new kind of optimization method is proposed forHSPMG cooling structure.
3．Through integration of the quantum computation theory and the immuneclonal algorithm, the continuous quantum immune clonal optimization isproposed, and the simulation results show the optimization ability of continuousquantum immune clonal optimization is evidently superior to the immune clonalalgorithm. Multi-objective optimization with two dimensional variables forcooling structure in HSPMG is studied in depth. The stator windings axial largesttemperature, the stator core axial largest temperature, the rotor axial largesttemperature, the stator windings axial temperature difference, the rotor axialtemperature difference and the stator core axial temperature difference areselected as optimization goals, the stator slots grooves parameters dh and dloptimization are studied. The stator slots grooves optimal solution based on thecontinuous quantum immune clonal optimization make the motor axialtemperature distribution more uniform.
引文
[1] P W Shor．Algorithms for quantum computation：Discrete logarithmsandfactoring[C]．Proc．of the35th Annual Symp．on Foundations ofComputer Science, New York, USA, IEEE Computer Society Press,1994：124-134．
[2] L K Grover． A fast quantum mechanical algorithm for databasesearch[C]． Proc． of the28th Annual ACM symp． on theory ofcomputing, New York, USA, ACM Press,1996：212-219．
[3] M A N, I L Chuang． Quantum computation and quantuminformation[M]．London：Cambridge University Press,2000：38~65．
[4] A N, M Moore． Quantum-inspired genetic algorithms[C]． Proc． ofIEEE International conference on evolutionary computation, Nagoya, Japan,1996：61-66．
[5] K H Han, J H Kim．Genetic quantum algorithm and its applicationto combinational optimization problem[C]． Proc． of the Internationalcongress on evolutionary computation, IEEE Press, San Diego, CA,2000：1354-1360．
[6] K H Han, K H Park, C H Lee, J H Kim．Parallel quantum-inspired geneticalgorithm for combinatorial optimization problem[C]．Proceedings of theinternational congress on evolutionary computation, Seoul, Korea,2001：1422-1429．
[7] K H Han, J H Kim．Quantum-inspired evolutionary algorithm for aclass of combinatorial optimization[J]．IEEE Transactions on evolutionarycomputation,2002,6(6)：580-593.
[8] H Talbi, A D, M B．A new quantum-inspired genetic algorithm forsolvingthe travelling salesman problem[C]． Proceedings of the internationalconference on industrial technology, Hammamet, Tunisia,2004：1192-1197．
[9] A R Khorsand, M R Akbarzadeh．Quantum gate optimization in a meta-level genetic quantum algorithm[C]．2005IEEE international conferenceon systems, man and cybernetics, Hawaii, USA,2005：3055-3062．
[10] P Moore, G K V．Evolving combinational logic circuits using a hybridquantum evolution and particle swarm inspired algorithm[C]．Proc．of theNASA/DoD conference on evolvable hardware, Washington DC,2005：97-102．
[11] S M Mikki, A A Kishk． Quantum particle swarm optimization forelectromagnetics[J]． IEEE Transactions on antennas and propagation,2006,54(10)：2764-2775．
[12] G X Zhang, W D Jin, L Z Hu． A novel parallel quantum geneticalgorithm[C]． Proceedings of the fourth international conference onparallel and distributed computing, applications and technologies, Chengdu,China,2003：693-697．
[13] J A Yang, B Li, Q Zhuang．Multi-universe parallel quantum geneticalgorithmand its application to blind-source separation[C]．Proceedings ofthe international conference on neural networks and signal processing,Nanjing, China,2003：393-398．
[14] H Chen, J H Zhang, C Zhang．Chaos updating rotated gates quantum-inspired genetic algorithm[C]．Proceedings of the international conferenceon communications, cuircuits and systems, Tainan, Taiwan,2004：1108-1112．
[15] S Y Yang, M Wang, L C Jiao．A genetic algorithm based on quantumchromosome[C]．Proceedings of the7th international conference on signalprocessing, Beijing, China,2004：1622-1625．
[16] L Wang, F Tang, H Wu．Hybrid genetic algorithm based on quantumcomputing for numerical optimization and parameter estimation[J]．Applied mathematics and computation,2005,171(2)：1141-1156．
[17] J Sun, W B Xu, B Feng．A global search strategy of quantum-behavedparticle swarm optimization[C]．Proceedings of the IEEE conference oncybernetics and intelligent systems, Singapore,2004：111-116．
[18] W Fang, J Sun, W B Xu．Analysis of adaptive IIR filters design based onquantum-behaved particle swarm optimization[C]．Proceedings of the6thworld congress on intelligent control and automation, Dalian, China,2006：3396-3400．
[19] W Fang, J Sun, W B Xu．Design of two-dimensional recursive filters byusing quantum-behaved particle swarm optimization[C]．Proceedings ofthe international conference on intelligent information hiding andmultimedia signal processing, California, USA,2006：240-243．
[20]冯斌，王璋，孙俊．基于混沌变异算子的小生境量子粒子群算法[J]．计算机应用与软件，2009，26(1)：50-52．
[21] W Fang, J Sun, W B Xu, J Liu．FIR digital filters design based onquantum-behaved particle swarm optimization[C]．Proceedings of the firstinternational conference on innovative computing, information and control,2006：615-619．
[22] B Feng, W B Xu． Quantum oscillator model of particle swarmsystem[C]．Proceedings of the8th international conference on control,automation, robotics and vision．Kunming, China,2004：1454-1459．
[23] J Liu, W B Xu, J Sun．Quantum-behaved particle swarm optimization withmutation operator[C]． Proceedings of the17th IEEE internationalconference on tools with artificial intelligence, Hong Kong, China,2005：1-4．
[24] B Feng, W B Xu. Adaptive particle swarm optimization based on quantumoscillator model[C]．Proceedings of the IEEE conference on cybemeticsand intelligent systems, Singapore,2004：291-294．
[25] Licheng Jiao, Yangyang Li, Maoguo Gong, Xiangrong Zhang．Quantum-inspired immune clonal algorithm for global optimization[J]． IEEETransactions on systems, man, and cybernetics, part B：cybernetics,2008,38(5)：1234-1253．
[26]杨佳，许强，张金荣，曹长修．一种新的量子蚁群优化算法[J]．中山大学学报：自然科学版，2009，48(3)：22-27．
[27]李盼池，杨雨，张巧翠．相位编码量子蚁群算法及在连续优化中的应用[J]．计算机应用研究，2010，27(12)：4450-4453．
[28]高炜欣，罗先觉．基于蚂蚁算法的配电网网络规划[J]．中国电机工程学报，2004，24(9)：110-114．
[29]孙雅明，王晨力，张智晟，刘尚伟．基于蚁群优化算法的电力系统负荷序列的聚类分析[J]．中国电机工程学报，2005，25(18)：40-45．
[30]孙昌志，曲春雨，陈冬阳．改进蚁群算法及其在永磁同步电机设计中的应用[J]．沈阳工业大学学报，2006，28(6)：601-604．
[31]祁春清，宋正强．基于粒子群优化模糊控制器永磁同步电机控制[J]．中国电机工程学报，2006，26(17)：158-162．
[32]唐旭东，庞永杰，李晔．水下机器人运动的免疫控制方法[J]．电机与控制学报，2007，11(6)：676-680．
[33]唐旭东，庞永杰，李晔.水下机器人运动的免疫控制方法[J].电机与控制学报，2007,11(6):676-680.
[34]孙昌志，曲春雨，杨红敏，陈冬阳．混沌蚁群算法及其在电机设计中的应用[J]．自动化技术与应用，2007，26(3)：11-14，29．
[35] Coelho, L S．Novel gaussian quantum-behaved particle swarm optimiserapplied to electromagnetic design[J]． IET Science, measurement&technology,2007,1(5)：290-294．
[36] Lin F J, Teng L T, Chu H．Modified Elman neural network controller withimproved particle swarm optimisation for linear synchronous motor drive[J]．IET Electr．Power Appl.,2008,2(3)：201-214．
[37] Faa Jeng Lin, Li Tao Teng, Hen Chu．A robust recurrent wavelet neuralnetwork controller with improved particle swarm optimization for linearsynchronous motor drive[J]． IEEE Transactions on power electronics,2008,23(6)：3067-3078．
[38]侯云鹤，熊信艮，吴耀武，鲁丽娟．基于广义蚁群算法的电力系统经济负荷分配[J]．中国电机工程学报，2008，23(3)：59-64．
[39]郭亮，卢琴芬，叶云岳．基于粒子群算法的直线振动发电机优化设计[J]．电机与控制学报，2008，12(4)：442-446．
[40]江岳文，陈冲，温步瀛．随机模拟粒子群算法在风电场无功补偿中的应用[J]．中国电机工程学报，2008，28(13)：47-52．
[41]何娜，黄丽娜，武健，徐殿国．基于粒子群优化算法的混合有源滤波器中无源滤波器的多目标优化设计[J]．中国电机工程学报，2008，28(27)：63-69．
[42]刘佳，李丹，高立群，宋立新．多目标无功优化的向量评价自适应粒子群算法[J]．中国电机工程学报，2008，28(31)：22-28．
[43]刘晓胜，戚佳金，宋其涛，李琰，徐殿国．基于蚁群算法的低压配电网电力线通信组网方法[J]．中国电机工程学报，2008，28(1)：71-76．
[44] Coelho L S, Alotto, P．Global optimization of electromagnetic devicesusing an exponential quantum-behaved particle swarm optimizer [J]. IEEETransactions on magnetics,2008,44(6)：1074-1077．
[45] Faa-Jeng Lin, Syuan-Yi Chen, Li-Tao Teng, Hen Chu． Recurrentfunctional-link-based fuzzy neural network controller with improvedparticle swarm optimization for a linear synchronous motor drive[J]．IEEETransactions on magnetics,2009,45(8)：3151-3165．
[46] El-Gammal, A A A, El-Samahy, A A．A modified design of PID controllerfor DC motor drives using particle swarm optimization[C]．Internationalconference on power engineering, energy and electrical drives, Lisbon,Portugal,2009：419-424．
[47] Zhihui Zhu, Yunlian Sun．Application of quantum immune algorithm forfault-section estimation[C]．The2nd international conference on powerelectronics and intelligent transportation system, Shenzhen, China,2009：317-320．
[48] Navidi N, Bavafa M, Hesami, S．A new approach for designing of PIDcontroller for a linear brushless DC motor with using ant colony searchalgorithm, Asia-pacific power and energy engineering conference, Wuhan,China,2009：1-5．
[49]寇攀高，周建中，何耀耀，向秀桥，李超顺．基于菌群-粒子群算法的水轮发电机组PID调速器参数优化[J]．中国电机工程学报，2009，29(26)：101-106．
[50]石丁丁，潘宏侠．蚁群算法在电机故障诊断中的应用[J]．大电机技术，2009，(1)：26-30．
[51] Qiuyi Wu, Licheng Jiao, Xiaoying Pan, Yifei Sun． Quantum-inspiredimmune memory algorithm for self-structuring antennaoptimization[C]． International conference on computer science andsoftware engineering, Wuhan, China,2009：513-516．
[52] Hasanien, H．Particle swarm design optimization of transverse flux linearmotor for weight reduction and improvement thrust force [J]． IEEETransactions on industrial electronics,2010,3(6)：51-58．
[53] Therdbankerd T, Sanposh P, Chayopitak N, Fujita, H． Parameteridentification of a linear permanent magnet motor using particle swarmoptimization[C]. International conference on electrical engineering/electronics computer telecommunications and information technology,Chiang Mai, Thailand,2010：173-177．
[54]王超学，崔杜武，崔颖安，谢炎林．使用基于中医思想的蚁群算法求解配电网重构[J]．中国电机工程学报，2008，28(7)：13-18．
[55]王旭东，刘金凤，张雷．蚁群神经网络算法在电动车用直流电机起动过程中的应用[J]．中国电机工程学报，2010，30(24)：95-100．
[56]姚舜才，潘宏侠．粒子群优化同步电机分数阶鲁棒励磁控制器[J]．中国电机工程学报，2010，25(9)：17-22．
[57]任海鹏，朱峰．基于免疫克隆选择算法的无刷直流电动机速度自抗扰控制器优化设计[J]．电机与控制学报，2010，14(9)：69-74．
[58]孟大伟，庞向东，潘波，赵勇．YKK系列高效高压三相异步电动机的优化设计[J]．电机与控制学报，2010，14(4)：31-35．
[59] Coelho, L S, Barbosa, L Z, Lebensztajn, L．Multiobjective particle swarmapproach for the design of a brushless DC wheel motor [J]. IEEEtransactions on magnetics,2010,46(8)：2994-2997．
[60] M A Nielsen, I L Chuang． Quantum computation and quantuminformation[M]．London：Cambridge University Press．2000：38-45．
[61] M Dorigo, M Birattari, T Stutzle． Ant colony optimization[J]． IEEEcomputational intelligence magazine,2006,1(4)：28-39．
[62] M Dorigo, V Maniezzo, A Colorni. The ant system：An autocatalyticoptimizing process[J]．Dipartimento di Elettronica, Politecnico di Milano,Milan, Italy, Tech．Rep．91-016,1991．
[63] M Dorigo, V Maniezzo, A Colorni． Ant system： Optimization by acolony of cooperating agents[J]．IEEE Transaction on system, man, andcybernetics,1996,26(1)：29-41．
[64] M Dorigo, L M Gambardella．Ant colony system：a cooperative learningapproach to the traveling salesman problem[J]． IEEE Transaction onevolutionary computation,1997,1(1)：53-66．
[65] G Leguizamon, Z Michalewicz．A new version of ant system for subsetproblems [C]． Proceedings of the1999international congress onevolutionary computation, Washington DC, USA, IEEE Press,1999：1459-1464．
[66] A Colorni, M Dorigo, V Maniezzo． Ant colony system for job-shopscheduling[J]． Belgian journal of operations research statistics andcomputer science,1994,34(1)：39-53．
[67] V Maniezzo． Exact and approximate non-deterministic tree searchprocedures for the quadratic assignment problem[J]．Informs journal ofcomputer,1999,11(4)：358-369．
[68] L Wang, Q D Wu．Ant system algorithm for optimization in continuousspace[C]． Proceedings of the2001IEEE international conference oncontrol applications, Mexico city, Mexico, IEEE Press,2001：395-400．
[69] V K Jayaraman, B D Kulkarni, K Sachin．Ant colony framework foroptimal design and scheduling of batch plants．Computer and chemicalengineering．2000,24(8)：1901-1912．
[70] M Dorigo, T Stutzle著；张军等译． Ant colony optimization [M]．北京：清华大学出版社，2007：7-32．
[71] H K Han, J H Kim．Quantum-inspired evolutionary algorithms with a newtermination criterion, H gate and two-phase scheme[J]． IEEETransactions on evolutionary computation,2004,8(2)：156-169．
[72] Stephen P Gillette．Market development of microturbine combined heatand power applications[J]． Cogeneration and distributed generationjournal,2004,19(2)：46-59．
[73] Ahn J B, Jeong Y H, Kang D H, Park J H．Development of high speedPMSM for distributed generation using microturbine[C]． Annualconference of the IEEE industrial electronics society, Busan, South Korea,2004：2879-2882．
[74] M A Rahman, A Chiba, T Fukao．Super high speed electrical machines-summary [C]． Power engineering society general meeting, Denver,Colorado, US,2004：1272-1275．
[75] Chebak A, Viarouge P, Cros J．Analytical computation of the full loadmagnetic losses in the soft magnetic composite stator of high-speed slotlesspermanent magnet machines[J]．IEEE Transactions on magnetics,2009,45(3)：952-955．
[76] P D Pfister, Y Perriard． Very-high-speed slotless permanent magnetmotors： analytical modeling, optimization, design, and torquemeasurement methods[J]． IEEE Transactions on industrial electronics,2010,57(1)：296-303．
[77] T Schneider, A Binder．Design and evaluation of a60000rpm permanentmagnet bearing less high speed motor[C]． The Seventh InternationalConference on power electronics and drive systems, Bangkok, Thailand,2007：1-8．
[78]王继强，王凤翔，孔晓光．高速永磁发电机的设计与电磁性能分析[J]．中国电机工程学报，2008，28(20)：105-110．
[79] Aglen O． Loss calculation and thermal analysis of a high-speedgenerator[C]．IEEE International electric machines and drives conference,Madison, USA,2003：1117-1123．
[80]李伟力，李守法，谢颖，丁树业．感应电动机定转子全域温度场数值计算及相关因素敏感性分析[J]．中国电机工程学报，2007，27(24)：85-91．
[81] L Weili, C Junci, Z Xiaochen．Electro-thermal analysis of induction motorwith compound cage rotor used for PHEV[J]． IEEE Transaction onindustrial electronics,2010,57(2)：660-668．
[82]靳廷船，李伟力，李守法．感应电机定子温度场的数值计算[J]．电机与控制学报，2006，10(5)：492-497．
[83] Kolondzovski, Z Belahcen, A Arkkio A．Comparative thermal analysis ofdifferent rotor types for a high-speed permanent-magnet electrical machine[J]．IET electric power applications,2009,3(4)：279-288．
[84]王红宇，罗应立，李和明，苏鹏声，王祥珩．耦合网络模型和有限元模型计算巨型水轮发电机定子温度场的比较研究[J]．中国电机工程学报，2008，28(14)：113-119．
[85] Z Xiaochen, Li Weili, Cheng Shukang, Kou Baoquan, GengJiamin．Coupling analysis of high speed PM generator used for distributedgeneration system[C]．14th Biennial IEEE conference on electromagneticfield computation, Chicago, USA,2010：1-1．
[86] Co Huynh, Liping Zheng, Dipjyoti Acharya． Losses in high speedpermanent magnet machines used in microturbine applications[J]．Journalof engineering for gas turbines and power,2009,131(2)：1-6．
[87]黄平林，胡虔生，崔杨，黄允凯．PWM逆变器供电下电机铁心损耗的解析计算[J]．中国电机工程学报，2007，27(12)：19-23．
[88] Li Weili, Ding Shuye, Zhou Feng．Diagnostic numerical simulation oflarge hydro generator with insulation aging[J]．Heat transfer engineering,2008,29(10)：902-909．
[89]李伟力，杨雪峰，顾德宝．空冷汽轮发电机冷却气流风量对定子内流体的影响[J]．中国电机工程学报，2009，29(21)：53-61．
[90]李伟力，丁树业，靳慧勇．基于耦合场的大型同步发电机定子温度场的数值计算．中国电机工程学报，2005，25(13)：129-134．
[91] J Kennedy, R C Eberhart．Particle swarms optimization [C]．Proceedingsof the IEEE international conference on neural networks, Perth, WesternAustralia,1995：1942-1948．
[92] M Clerc, J Kennedy． The particle swarm explosion, stability, andconvergence in a multidimensional complex space[J]．IEEE Transactionson evolutionary computation,2002,6(1)：58-73．
[93] A P Engelbrecht．Cooperative learning in neural networks using particleswarm optimizers[J]．South african computer journal,2000：84-90．
[94] Y H Shi, R C Eberhart． A modified particle swarmoptimizer[C]．Proceedings of the IEEE world congress on computationalintelligence, Anchorage,1998：69-73．
[95] M Lovbjerg, T K Rasmussen, T Krink．Hybrid particle swarm optimizerwith breeding and subpopulations[C]．Proceedings of the3rd genetic andevolutionary computation conference, San Francisco, USA,2001：469-476．
[96] Z S Lu, Z R Hou．Particle swarm optimization with adaptive mutation[J]．Acta electronica sinica,2004,32(3)：416-420．
[97] R C Eberhart, Y H Shi．Comparing inertia weights and constriction factorsin particle swarm optimization[C]． Proceedings of the internationalcongress on evolutionary computation, San Diego, CA,2000：84-88．
[98] B R Chen, X T Feng．Particle swarm optimization with contracted rangesof both search space and velocity [J]．Journal of northeastern university(Natural science),2005,26(5)：488-491．
[99] T Hey． Quantum computing： an introduction[J]． Computing andcontrol engineering journal,1999,10(3)：105-112．
[100]郭亮，卢琴芬，叶云岳．基于粒子群算法的直线振动发电机优化设计[J]．电机与控制学报，2008，12(4)：442-446．
[101] L N de Castro, F J Von Zuben．Artificial immune systems：part I-basictheory and applications． Campinas, Brazil： FEEC/Univ． Campinas,1999．[Online]． Available： http：//www． Dca． fee． unicamp.br/~lnunes/immune．html．
[102] Castro L N, Von Zuben F J．Learning and optimization using the clonalselection principle[J]．IEEE Transactions on evolutionary computation，2002,6(3)：239-251．
[103] O Nasaroui, F Gonzalez, D Dasgupta． The fuzzy artificial immunesystem：motivations, basic concepts and application to clustering and webprofiling．Fuzzy system,2002,1(2)：711-716．
[104] J S Chun, H K Jung, S Y Hahn．A study on comparison of optimizationperformance between immune algorithm and other heuristic algorithms[J]．IEEE Transactions on magnetic,1998,34(5)：2972-2975．
[2] L K Grover． A fast quantum mechanical algorithm for databasesearch[C]． Proc． of the28th Annual ACM symp． on theory ofcomputing, New York, USA, ACM Press,1996：212-219．
[3] M A N, I L Chuang． Quantum computation and quantuminformation[M]．London：Cambridge University Press,2000：38~65．
[4] A N, M Moore． Quantum-inspired genetic algorithms[C]． Proc． ofIEEE International conference on evolutionary computation, Nagoya, Japan,1996：61-66．
[5] K H Han, J H Kim．Genetic quantum algorithm and its applicationto combinational optimization problem[C]． Proc． of the Internationalcongress on evolutionary computation, IEEE Press, San Diego, CA,2000：1354-1360．
[6] K H Han, K H Park, C H Lee, J H Kim．Parallel quantum-inspired geneticalgorithm for combinatorial optimization problem[C]．Proceedings of theinternational congress on evolutionary computation, Seoul, Korea,2001：1422-1429．
[7] K H Han, J H Kim．Quantum-inspired evolutionary algorithm for aclass of combinatorial optimization[J]．IEEE Transactions on evolutionarycomputation,2002,6(6)：580-593.
[8] H Talbi, A D, M B．A new quantum-inspired genetic algorithm forsolvingthe travelling salesman problem[C]． Proceedings of the internationalconference on industrial technology, Hammamet, Tunisia,2004：1192-1197．
[9] A R Khorsand, M R Akbarzadeh．Quantum gate optimization in a meta-level genetic quantum algorithm[C]．2005IEEE international conferenceon systems, man and cybernetics, Hawaii, USA,2005：3055-3062．
[10] P Moore, G K V．Evolving combinational logic circuits using a hybridquantum evolution and particle swarm inspired algorithm[C]．Proc．of theNASA/DoD conference on evolvable hardware, Washington DC,2005：97-102．
[11] S M Mikki, A A Kishk． Quantum particle swarm optimization forelectromagnetics[J]． IEEE Transactions on antennas and propagation,2006,54(10)：2764-2775．
[12] G X Zhang, W D Jin, L Z Hu． A novel parallel quantum geneticalgorithm[C]． Proceedings of the fourth international conference onparallel and distributed computing, applications and technologies, Chengdu,China,2003：693-697．
[13] J A Yang, B Li, Q Zhuang．Multi-universe parallel quantum geneticalgorithmand its application to blind-source separation[C]．Proceedings ofthe international conference on neural networks and signal processing,Nanjing, China,2003：393-398．
[14] H Chen, J H Zhang, C Zhang．Chaos updating rotated gates quantum-inspired genetic algorithm[C]．Proceedings of the international conferenceon communications, cuircuits and systems, Tainan, Taiwan,2004：1108-1112．
[15] S Y Yang, M Wang, L C Jiao．A genetic algorithm based on quantumchromosome[C]．Proceedings of the7th international conference on signalprocessing, Beijing, China,2004：1622-1625．
[16] L Wang, F Tang, H Wu．Hybrid genetic algorithm based on quantumcomputing for numerical optimization and parameter estimation[J]．Applied mathematics and computation,2005,171(2)：1141-1156．
[17] J Sun, W B Xu, B Feng．A global search strategy of quantum-behavedparticle swarm optimization[C]．Proceedings of the IEEE conference oncybernetics and intelligent systems, Singapore,2004：111-116．
[18] W Fang, J Sun, W B Xu．Analysis of adaptive IIR filters design based onquantum-behaved particle swarm optimization[C]．Proceedings of the6thworld congress on intelligent control and automation, Dalian, China,2006：3396-3400．
[19] W Fang, J Sun, W B Xu．Design of two-dimensional recursive filters byusing quantum-behaved particle swarm optimization[C]．Proceedings ofthe international conference on intelligent information hiding andmultimedia signal processing, California, USA,2006：240-243．
[20]冯斌，王璋，孙俊．基于混沌变异算子的小生境量子粒子群算法[J]．计算机应用与软件，2009，26(1)：50-52．
[21] W Fang, J Sun, W B Xu, J Liu．FIR digital filters design based onquantum-behaved particle swarm optimization[C]．Proceedings of the firstinternational conference on innovative computing, information and control,2006：615-619．
[22] B Feng, W B Xu． Quantum oscillator model of particle swarmsystem[C]．Proceedings of the8th international conference on control,automation, robotics and vision．Kunming, China,2004：1454-1459．
[23] J Liu, W B Xu, J Sun．Quantum-behaved particle swarm optimization withmutation operator[C]． Proceedings of the17th IEEE internationalconference on tools with artificial intelligence, Hong Kong, China,2005：1-4．
[24] B Feng, W B Xu. Adaptive particle swarm optimization based on quantumoscillator model[C]．Proceedings of the IEEE conference on cybemeticsand intelligent systems, Singapore,2004：291-294．
[25] Licheng Jiao, Yangyang Li, Maoguo Gong, Xiangrong Zhang．Quantum-inspired immune clonal algorithm for global optimization[J]． IEEETransactions on systems, man, and cybernetics, part B：cybernetics,2008,38(5)：1234-1253．
[26]杨佳，许强，张金荣，曹长修．一种新的量子蚁群优化算法[J]．中山大学学报：自然科学版，2009，48(3)：22-27．
[27]李盼池，杨雨，张巧翠．相位编码量子蚁群算法及在连续优化中的应用[J]．计算机应用研究，2010，27(12)：4450-4453．
[28]高炜欣，罗先觉．基于蚂蚁算法的配电网网络规划[J]．中国电机工程学报，2004，24(9)：110-114．
[29]孙雅明，王晨力，张智晟，刘尚伟．基于蚁群优化算法的电力系统负荷序列的聚类分析[J]．中国电机工程学报，2005，25(18)：40-45．
[30]孙昌志，曲春雨，陈冬阳．改进蚁群算法及其在永磁同步电机设计中的应用[J]．沈阳工业大学学报，2006，28(6)：601-604．
[31]祁春清，宋正强．基于粒子群优化模糊控制器永磁同步电机控制[J]．中国电机工程学报，2006，26(17)：158-162．
[32]唐旭东，庞永杰，李晔．水下机器人运动的免疫控制方法[J]．电机与控制学报，2007，11(6)：676-680．
[33]唐旭东，庞永杰，李晔.水下机器人运动的免疫控制方法[J].电机与控制学报，2007,11(6):676-680.
[34]孙昌志，曲春雨，杨红敏，陈冬阳．混沌蚁群算法及其在电机设计中的应用[J]．自动化技术与应用，2007，26(3)：11-14，29．
[35] Coelho, L S．Novel gaussian quantum-behaved particle swarm optimiserapplied to electromagnetic design[J]． IET Science, measurement&technology,2007,1(5)：290-294．
[36] Lin F J, Teng L T, Chu H．Modified Elman neural network controller withimproved particle swarm optimisation for linear synchronous motor drive[J]．IET Electr．Power Appl.,2008,2(3)：201-214．
[37] Faa Jeng Lin, Li Tao Teng, Hen Chu．A robust recurrent wavelet neuralnetwork controller with improved particle swarm optimization for linearsynchronous motor drive[J]． IEEE Transactions on power electronics,2008,23(6)：3067-3078．
[38]侯云鹤，熊信艮，吴耀武，鲁丽娟．基于广义蚁群算法的电力系统经济负荷分配[J]．中国电机工程学报，2008，23(3)：59-64．
[39]郭亮，卢琴芬，叶云岳．基于粒子群算法的直线振动发电机优化设计[J]．电机与控制学报，2008，12(4)：442-446．
[40]江岳文，陈冲，温步瀛．随机模拟粒子群算法在风电场无功补偿中的应用[J]．中国电机工程学报，2008，28(13)：47-52．
[41]何娜，黄丽娜，武健，徐殿国．基于粒子群优化算法的混合有源滤波器中无源滤波器的多目标优化设计[J]．中国电机工程学报，2008，28(27)：63-69．
[42]刘佳，李丹，高立群，宋立新．多目标无功优化的向量评价自适应粒子群算法[J]．中国电机工程学报，2008，28(31)：22-28．
[43]刘晓胜，戚佳金，宋其涛，李琰，徐殿国．基于蚁群算法的低压配电网电力线通信组网方法[J]．中国电机工程学报，2008，28(1)：71-76．
[44] Coelho L S, Alotto, P．Global optimization of electromagnetic devicesusing an exponential quantum-behaved particle swarm optimizer [J]. IEEETransactions on magnetics,2008,44(6)：1074-1077．
[45] Faa-Jeng Lin, Syuan-Yi Chen, Li-Tao Teng, Hen Chu． Recurrentfunctional-link-based fuzzy neural network controller with improvedparticle swarm optimization for a linear synchronous motor drive[J]．IEEETransactions on magnetics,2009,45(8)：3151-3165．
[46] El-Gammal, A A A, El-Samahy, A A．A modified design of PID controllerfor DC motor drives using particle swarm optimization[C]．Internationalconference on power engineering, energy and electrical drives, Lisbon,Portugal,2009：419-424．
[47] Zhihui Zhu, Yunlian Sun．Application of quantum immune algorithm forfault-section estimation[C]．The2nd international conference on powerelectronics and intelligent transportation system, Shenzhen, China,2009：317-320．
[48] Navidi N, Bavafa M, Hesami, S．A new approach for designing of PIDcontroller for a linear brushless DC motor with using ant colony searchalgorithm, Asia-pacific power and energy engineering conference, Wuhan,China,2009：1-5．
[49]寇攀高，周建中，何耀耀，向秀桥，李超顺．基于菌群-粒子群算法的水轮发电机组PID调速器参数优化[J]．中国电机工程学报，2009，29(26)：101-106．
[50]石丁丁，潘宏侠．蚁群算法在电机故障诊断中的应用[J]．大电机技术，2009，(1)：26-30．
[51] Qiuyi Wu, Licheng Jiao, Xiaoying Pan, Yifei Sun． Quantum-inspiredimmune memory algorithm for self-structuring antennaoptimization[C]． International conference on computer science andsoftware engineering, Wuhan, China,2009：513-516．
[52] Hasanien, H．Particle swarm design optimization of transverse flux linearmotor for weight reduction and improvement thrust force [J]． IEEETransactions on industrial electronics,2010,3(6)：51-58．
[53] Therdbankerd T, Sanposh P, Chayopitak N, Fujita, H． Parameteridentification of a linear permanent magnet motor using particle swarmoptimization[C]. International conference on electrical engineering/electronics computer telecommunications and information technology,Chiang Mai, Thailand,2010：173-177．
[54]王超学，崔杜武，崔颖安，谢炎林．使用基于中医思想的蚁群算法求解配电网重构[J]．中国电机工程学报，2008，28(7)：13-18．
[55]王旭东，刘金凤，张雷．蚁群神经网络算法在电动车用直流电机起动过程中的应用[J]．中国电机工程学报，2010，30(24)：95-100．
[56]姚舜才，潘宏侠．粒子群优化同步电机分数阶鲁棒励磁控制器[J]．中国电机工程学报，2010，25(9)：17-22．
[57]任海鹏，朱峰．基于免疫克隆选择算法的无刷直流电动机速度自抗扰控制器优化设计[J]．电机与控制学报，2010，14(9)：69-74．
[58]孟大伟，庞向东，潘波，赵勇．YKK系列高效高压三相异步电动机的优化设计[J]．电机与控制学报，2010，14(4)：31-35．
[59] Coelho, L S, Barbosa, L Z, Lebensztajn, L．Multiobjective particle swarmapproach for the design of a brushless DC wheel motor [J]. IEEEtransactions on magnetics,2010,46(8)：2994-2997．
[60] M A Nielsen, I L Chuang． Quantum computation and quantuminformation[M]．London：Cambridge University Press．2000：38-45．
[61] M Dorigo, M Birattari, T Stutzle． Ant colony optimization[J]． IEEEcomputational intelligence magazine,2006,1(4)：28-39．
[62] M Dorigo, V Maniezzo, A Colorni. The ant system：An autocatalyticoptimizing process[J]．Dipartimento di Elettronica, Politecnico di Milano,Milan, Italy, Tech．Rep．91-016,1991．
[63] M Dorigo, V Maniezzo, A Colorni． Ant system： Optimization by acolony of cooperating agents[J]．IEEE Transaction on system, man, andcybernetics,1996,26(1)：29-41．
[64] M Dorigo, L M Gambardella．Ant colony system：a cooperative learningapproach to the traveling salesman problem[J]． IEEE Transaction onevolutionary computation,1997,1(1)：53-66．
[65] G Leguizamon, Z Michalewicz．A new version of ant system for subsetproblems [C]． Proceedings of the1999international congress onevolutionary computation, Washington DC, USA, IEEE Press,1999：1459-1464．
[66] A Colorni, M Dorigo, V Maniezzo． Ant colony system for job-shopscheduling[J]． Belgian journal of operations research statistics andcomputer science,1994,34(1)：39-53．
[67] V Maniezzo． Exact and approximate non-deterministic tree searchprocedures for the quadratic assignment problem[J]．Informs journal ofcomputer,1999,11(4)：358-369．
[68] L Wang, Q D Wu．Ant system algorithm for optimization in continuousspace[C]． Proceedings of the2001IEEE international conference oncontrol applications, Mexico city, Mexico, IEEE Press,2001：395-400．
[69] V K Jayaraman, B D Kulkarni, K Sachin．Ant colony framework foroptimal design and scheduling of batch plants．Computer and chemicalengineering．2000,24(8)：1901-1912．
[70] M Dorigo, T Stutzle著；张军等译． Ant colony optimization [M]．北京：清华大学出版社，2007：7-32．
[71] H K Han, J H Kim．Quantum-inspired evolutionary algorithms with a newtermination criterion, H gate and two-phase scheme[J]． IEEETransactions on evolutionary computation,2004,8(2)：156-169．
[72] Stephen P Gillette．Market development of microturbine combined heatand power applications[J]． Cogeneration and distributed generationjournal,2004,19(2)：46-59．
[73] Ahn J B, Jeong Y H, Kang D H, Park J H．Development of high speedPMSM for distributed generation using microturbine[C]． Annualconference of the IEEE industrial electronics society, Busan, South Korea,2004：2879-2882．
[74] M A Rahman, A Chiba, T Fukao．Super high speed electrical machines-summary [C]． Power engineering society general meeting, Denver,Colorado, US,2004：1272-1275．
[75] Chebak A, Viarouge P, Cros J．Analytical computation of the full loadmagnetic losses in the soft magnetic composite stator of high-speed slotlesspermanent magnet machines[J]．IEEE Transactions on magnetics,2009,45(3)：952-955．
[76] P D Pfister, Y Perriard． Very-high-speed slotless permanent magnetmotors： analytical modeling, optimization, design, and torquemeasurement methods[J]． IEEE Transactions on industrial electronics,2010,57(1)：296-303．
[77] T Schneider, A Binder．Design and evaluation of a60000rpm permanentmagnet bearing less high speed motor[C]． The Seventh InternationalConference on power electronics and drive systems, Bangkok, Thailand,2007：1-8．
[78]王继强，王凤翔，孔晓光．高速永磁发电机的设计与电磁性能分析[J]．中国电机工程学报，2008，28(20)：105-110．
[79] Aglen O． Loss calculation and thermal analysis of a high-speedgenerator[C]．IEEE International electric machines and drives conference,Madison, USA,2003：1117-1123．
[80]李伟力，李守法，谢颖，丁树业．感应电动机定转子全域温度场数值计算及相关因素敏感性分析[J]．中国电机工程学报，2007，27(24)：85-91．
[81] L Weili, C Junci, Z Xiaochen．Electro-thermal analysis of induction motorwith compound cage rotor used for PHEV[J]． IEEE Transaction onindustrial electronics,2010,57(2)：660-668．
[82]靳廷船，李伟力，李守法．感应电机定子温度场的数值计算[J]．电机与控制学报，2006，10(5)：492-497．
[83] Kolondzovski, Z Belahcen, A Arkkio A．Comparative thermal analysis ofdifferent rotor types for a high-speed permanent-magnet electrical machine[J]．IET electric power applications,2009,3(4)：279-288．
[84]王红宇，罗应立，李和明，苏鹏声，王祥珩．耦合网络模型和有限元模型计算巨型水轮发电机定子温度场的比较研究[J]．中国电机工程学报，2008，28(14)：113-119．
[85] Z Xiaochen, Li Weili, Cheng Shukang, Kou Baoquan, GengJiamin．Coupling analysis of high speed PM generator used for distributedgeneration system[C]．14th Biennial IEEE conference on electromagneticfield computation, Chicago, USA,2010：1-1．
[86] Co Huynh, Liping Zheng, Dipjyoti Acharya． Losses in high speedpermanent magnet machines used in microturbine applications[J]．Journalof engineering for gas turbines and power,2009,131(2)：1-6．
[87]黄平林，胡虔生，崔杨，黄允凯．PWM逆变器供电下电机铁心损耗的解析计算[J]．中国电机工程学报，2007，27(12)：19-23．
[88] Li Weili, Ding Shuye, Zhou Feng．Diagnostic numerical simulation oflarge hydro generator with insulation aging[J]．Heat transfer engineering,2008,29(10)：902-909．
[89]李伟力，杨雪峰，顾德宝．空冷汽轮发电机冷却气流风量对定子内流体的影响[J]．中国电机工程学报，2009，29(21)：53-61．
[90]李伟力，丁树业，靳慧勇．基于耦合场的大型同步发电机定子温度场的数值计算．中国电机工程学报，2005，25(13)：129-134．
[91] J Kennedy, R C Eberhart．Particle swarms optimization [C]．Proceedingsof the IEEE international conference on neural networks, Perth, WesternAustralia,1995：1942-1948．
[92] M Clerc, J Kennedy． The particle swarm explosion, stability, andconvergence in a multidimensional complex space[J]．IEEE Transactionson evolutionary computation,2002,6(1)：58-73．
[93] A P Engelbrecht．Cooperative learning in neural networks using particleswarm optimizers[J]．South african computer journal,2000：84-90．
[94] Y H Shi, R C Eberhart． A modified particle swarmoptimizer[C]．Proceedings of the IEEE world congress on computationalintelligence, Anchorage,1998：69-73．
[95] M Lovbjerg, T K Rasmussen, T Krink．Hybrid particle swarm optimizerwith breeding and subpopulations[C]．Proceedings of the3rd genetic andevolutionary computation conference, San Francisco, USA,2001：469-476．
[96] Z S Lu, Z R Hou．Particle swarm optimization with adaptive mutation[J]．Acta electronica sinica,2004,32(3)：416-420．
[97] R C Eberhart, Y H Shi．Comparing inertia weights and constriction factorsin particle swarm optimization[C]． Proceedings of the internationalcongress on evolutionary computation, San Diego, CA,2000：84-88．
[98] B R Chen, X T Feng．Particle swarm optimization with contracted rangesof both search space and velocity [J]．Journal of northeastern university(Natural science),2005,26(5)：488-491．
[99] T Hey． Quantum computing： an introduction[J]． Computing andcontrol engineering journal,1999,10(3)：105-112．
[100]郭亮，卢琴芬，叶云岳．基于粒子群算法的直线振动发电机优化设计[J]．电机与控制学报，2008，12(4)：442-446．
[101] L N de Castro, F J Von Zuben．Artificial immune systems：part I-basictheory and applications． Campinas, Brazil： FEEC/Univ． Campinas,1999．[Online]． Available： http：//www． Dca． fee． unicamp.br/~lnunes/immune．html．
[102] Castro L N, Von Zuben F J．Learning and optimization using the clonalselection principle[J]．IEEE Transactions on evolutionary computation，2002,6(3)：239-251．
[103] O Nasaroui, F Gonzalez, D Dasgupta． The fuzzy artificial immunesystem：motivations, basic concepts and application to clustering and webprofiling．Fuzzy system,2002,1(2)：711-716．
[104] J S Chun, H K Jung, S Y Hahn．A study on comparison of optimizationperformance between immune algorithm and other heuristic algorithms[J]．IEEE Transactions on magnetic,1998,34(5)：2972-2975．