粒子群优化算法及其工程应用研究
|
摘要
粒子群优化(PSO)算法是一种基于种群的随机优化方法。与传统的优化方法相比,PSO算法具有结构简单、参数较少、易于实现以及全局寻优能力强等优点。然而,PSO算法的理论基础还不完善,存在早熟收敛、易陷入局部极值等问题,并且在应用于工程实际问题时存在很多值得改进和提高之处。
本文从PSO控制参数策略和实现框架上提出了几种不同的改进算法,并将改进的算法用于PID控制器参数整定以及阵列天线方向图综合。
粒子群优化算法是基于种群的群智能算法,种群的收敛特性直接关系到算法的寻优性能。通过分析粒子群优化算法的收敛特性,明确了控制参数策略以及算法平衡搜索能力与算法性能的关联,并进一步对粒子群优化算法进行了改进：
(1)提出了基于聚集度反馈控制的粒子群优化算法,使得种群的聚集程度可控。这样在种群陷入局部最优情况下,算法可以重新使种群按一种可控的方式重新发散开,从而改善算法的全局寻优能力。
(2)搭建了一个继承学习的算法框架,将单个PSO优化进程纳入到这个框架中。在新的算法框架中,多个并行的PSO进程构成一个循环。上一个循环中各PSO进程结果中较好的一部分,以及随机生成一部分粒子位置,共同构成一个完整的种群位置来作为下一个循环各PSO进程的初始化种群位置。新算法在很大程度上改善了随机性对优化结果的影响,在多维复杂优化问题上具有良好的性能,而且具备很大的灵活性,可以很容易地将此算法框架应用到其他智能优化算法中。
在控制系统中,PID参数整定是一个经典的研究方向。如果将PID控制器的3个参数看做是待优化变量,用控制器响应评价函数作为适应值函数,就可以使用优化算法来处理PID参数整定。本文针对这个问题进行了相应研究：
(1)建立了磁浮列车控制器参数的PSO优化模型,采用改进的PSO算法对磁浮控制器PID参数进行了优化,仿真结果和实验结果表明基于PSO算法的PID参数优化模型具有较好的可行性和适用性。
(2)在实际应用中,有时候无法得到被控对象的准确模型,也无从进行有效的PID参数整定,只能靠经验对PID控制器参数进行整定。为此,将PSO算法用于摊铺机控制系统的模型辨识,并在辨识基础上对摊铺机控制器参数进行了整定,取得了很好的效果。
阵列天线方向图综合是智能算法的一个重要应用领域,本文也针对这个问题进行了研究,主要包括连续变量的方向图综合以及离散变量的方向图综合,具体内容如下：
(1)针对多目标方向图优化,提出了分阶段适应值函数策略。由于各个指标分阶段提高,使得各个阶段更容易平衡各个优化目标,不会导致某个优化目标已经满足收敛条件而另外的优化目标还差距很远。这样在解空间中,局部极值区域的深度更浅,有利于种群跳出局部极值点,实现全局收敛。在实际方向图优化中,可以分两次或者更多阶段将方向图指标逐步提高至设计指标。
(2)将停滞检测PSO算法和基于聚集度反馈控制PSO算法用于均匀间距直线阵的低旁瓣方向图综合中。实验表明两种改进算法能有效生成多零陷,抑制旁瓣电平值。
(3)将继承学习粒子群优化算法(ILPSO)用于不等距线阵天线低旁瓣方向图综合,仿真结果表明ILPSO可以使用较少的优化次数取得与国内外最新文献相当或更好的结果。
(4)针对阵列天线方向图综合中的离散优化问题,提出了基于实数PSO算法和粒子位置取整相结合的优化策略,有效地处理了4bit数字移相器阵列的方向图综合、稀疏直线阵列的方向图综合和不等距稀疏阵列方向图综合。仿真结果表明此策略可以有效地将实数PSO算法用于方向图综合中的离散优化问题,优化结果优于已有二进制粒子群优化算法和其他智能优化算法。为了有效处理带稀疏比例约束的大型稀疏平面阵列方向图综合,在前面算法基础上进一步加入了概率调整策略,结果优于其他离散粒子群优化算法。
最后,对本文的工作进行了总结,并提出了进一步研究工作的方向。
Particle Swarm Optimization (PSO) algorithm is a typical swarm intelligence optimization algorithm. Comparing with traditional optimization methods, PSO algorithm has many advantages, such as simple structure, less parameter, easy to implement and strong global optimization capability. However, the theoretical basis of PSO is still far from mature. PSO has problems of premature convergence and easy to fall into local optimum trap, there is still a lot of room for improvement when applying PSO to engineering practice.
The paper proposes several distinct improved algorithms, including the parameters control strategy improvement and new implementation framework. These improved PSO versions are appled into PID tunning and array antenna pattern synthesis.
PSO is an intelligent optimization technique based on swarm intelligence, its swarm convergence directly relations with the optimization performance. After analyzing the convergence performance of PSO, the paper improves PSO in the aspects of parameter control strategy improvement and enhancing the balanced search capacity of algorithm:
(1) The paper proposes an improved PSO on the basis of convergence control, so the swarm convergence becomes controllable. When swarm is converged in a local optimum trap, the algorithm makes swarm diverge again.In this way, the global search ability of the algorithm can be improved a lot.
(2) The paper establishes an algorithm framework based on inheritance learning strategy, and single PSO process is incorporates into this framework as a basic unit. Under the new framework, several parallel PSO processes construe one cycle. The better part of the results of last cycle and the randomly generated results composed the whole initial swarm positions of next cycle. New algorithm has greatly reduced the impact of randomness, and has good performance in multidimensional optimization problems. The improved algorithm also has great flexibility, and the algorithm frame is easy to apply in other intelligent optimization algorithms.
In the control system, PID parameter tunning is a classical research direction. If3parameters of PID controller are deemed as promising optimization variants, and the controller's response is used as fitness value, then optimization algorithm can be applied to handle PID parameter tunning. To solve this problem, the paper makes relevant studies:
(1) The paper establishes PSO optimization model for Maglev train controller PID tunning and the improved PSO algorithm is used. The simulation and experimental results show that PID tunning by PSO algorithm has good feasibility and applicability.
(2) In practical application, sometimes it is impossible to obtain accurate model for the control objects, so it is hard to tune PID parameter and the feasible way is to use the experience tuning method. To improve this situation, PSO algorithm is applied in model identification of paver's control system. The identification paver model is used to PID tunning and the experimental results show that this method is very effective.
Array antenna pattern synthesis is a key application field of intelligent algorithm. The paper also studies this issue, mainly consisting of pattern synthesis with continuous variants and discrete variants. The details are as below:
(1) As for multi-objective pattern optimization, the paper proposes the strategy of stage fitness function. For new strategy, different indicators increase by stages, and it is much easier to balance each optimization objective in different stage. Compared with fixed fitness function strategy, new strategy can avoid a certain indicators being satisfied convergence conditions while the others far from the convergence conditions. As a result, local optimum trap's depth becomes shallower in the solution space, which is helpful for the PSO swarm to escape the local optimum trap and can help PSO swarm realize global convergence. In pattern optimization applications, the fitness function can be divided into two or more stages.
(2) The paper applies stagnation detecting PSO algorithm and PSO algorithm based on convergence control into uniform linear array's low sidelobe pattern synthesis. The simulation results show that these two improved algorithms can effectively applicate in multi-null and low sidelobe pattern synthesis.
(3) The paper applies ILPSO into unequal spaced linear array's low sidelobe pattern synthesis. Simulation results show that ILPSO obtains results equal to or better than the results of the latest domestic and foreign researches by using less computation.
(4) In order to solve the discrete optimization problems in antenna array pattern synthesis, the paper proposes an optimization strategy based on the combination of PSO algorithm and particle position rounding. Therefore, it effectively handles the pattern synthesis of4bit digital phase shifter array, the pattern synthesis of thinned linear array, and the pattern synthesis of non-uniform thinning linear array. Simulation results show that this strategy can effectively apply real number PSO algorithm into the discrete optimization in pattern synthesis, and the optimization results are better than existed binary PSO and other intelligent optimization algorithms. In order to handle the pattern synthesis of large thinned plannar array with thinned element proportion constraint, the probability adjustment strategy is added, and the optimization results are superior to results of other discrete particle swarm optimization algorithms.
In the end, the paper makes final conclusion and proposes further research directions.
本文从PSO控制参数策略和实现框架上提出了几种不同的改进算法,并将改进的算法用于PID控制器参数整定以及阵列天线方向图综合。
粒子群优化算法是基于种群的群智能算法,种群的收敛特性直接关系到算法的寻优性能。通过分析粒子群优化算法的收敛特性,明确了控制参数策略以及算法平衡搜索能力与算法性能的关联,并进一步对粒子群优化算法进行了改进：
(1)提出了基于聚集度反馈控制的粒子群优化算法,使得种群的聚集程度可控。这样在种群陷入局部最优情况下,算法可以重新使种群按一种可控的方式重新发散开,从而改善算法的全局寻优能力。
(2)搭建了一个继承学习的算法框架,将单个PSO优化进程纳入到这个框架中。在新的算法框架中,多个并行的PSO进程构成一个循环。上一个循环中各PSO进程结果中较好的一部分,以及随机生成一部分粒子位置,共同构成一个完整的种群位置来作为下一个循环各PSO进程的初始化种群位置。新算法在很大程度上改善了随机性对优化结果的影响,在多维复杂优化问题上具有良好的性能,而且具备很大的灵活性,可以很容易地将此算法框架应用到其他智能优化算法中。
在控制系统中,PID参数整定是一个经典的研究方向。如果将PID控制器的3个参数看做是待优化变量,用控制器响应评价函数作为适应值函数,就可以使用优化算法来处理PID参数整定。本文针对这个问题进行了相应研究：
(1)建立了磁浮列车控制器参数的PSO优化模型,采用改进的PSO算法对磁浮控制器PID参数进行了优化,仿真结果和实验结果表明基于PSO算法的PID参数优化模型具有较好的可行性和适用性。
(2)在实际应用中,有时候无法得到被控对象的准确模型,也无从进行有效的PID参数整定,只能靠经验对PID控制器参数进行整定。为此,将PSO算法用于摊铺机控制系统的模型辨识,并在辨识基础上对摊铺机控制器参数进行了整定,取得了很好的效果。
阵列天线方向图综合是智能算法的一个重要应用领域,本文也针对这个问题进行了研究,主要包括连续变量的方向图综合以及离散变量的方向图综合,具体内容如下：
(1)针对多目标方向图优化,提出了分阶段适应值函数策略。由于各个指标分阶段提高,使得各个阶段更容易平衡各个优化目标,不会导致某个优化目标已经满足收敛条件而另外的优化目标还差距很远。这样在解空间中,局部极值区域的深度更浅,有利于种群跳出局部极值点,实现全局收敛。在实际方向图优化中,可以分两次或者更多阶段将方向图指标逐步提高至设计指标。
(2)将停滞检测PSO算法和基于聚集度反馈控制PSO算法用于均匀间距直线阵的低旁瓣方向图综合中。实验表明两种改进算法能有效生成多零陷,抑制旁瓣电平值。
(3)将继承学习粒子群优化算法(ILPSO)用于不等距线阵天线低旁瓣方向图综合,仿真结果表明ILPSO可以使用较少的优化次数取得与国内外最新文献相当或更好的结果。
(4)针对阵列天线方向图综合中的离散优化问题,提出了基于实数PSO算法和粒子位置取整相结合的优化策略,有效地处理了4bit数字移相器阵列的方向图综合、稀疏直线阵列的方向图综合和不等距稀疏阵列方向图综合。仿真结果表明此策略可以有效地将实数PSO算法用于方向图综合中的离散优化问题,优化结果优于已有二进制粒子群优化算法和其他智能优化算法。为了有效处理带稀疏比例约束的大型稀疏平面阵列方向图综合,在前面算法基础上进一步加入了概率调整策略,结果优于其他离散粒子群优化算法。
最后,对本文的工作进行了总结,并提出了进一步研究工作的方向。
Particle Swarm Optimization (PSO) algorithm is a typical swarm intelligence optimization algorithm. Comparing with traditional optimization methods, PSO algorithm has many advantages, such as simple structure, less parameter, easy to implement and strong global optimization capability. However, the theoretical basis of PSO is still far from mature. PSO has problems of premature convergence and easy to fall into local optimum trap, there is still a lot of room for improvement when applying PSO to engineering practice.
The paper proposes several distinct improved algorithms, including the parameters control strategy improvement and new implementation framework. These improved PSO versions are appled into PID tunning and array antenna pattern synthesis.
PSO is an intelligent optimization technique based on swarm intelligence, its swarm convergence directly relations with the optimization performance. After analyzing the convergence performance of PSO, the paper improves PSO in the aspects of parameter control strategy improvement and enhancing the balanced search capacity of algorithm:
(1) The paper proposes an improved PSO on the basis of convergence control, so the swarm convergence becomes controllable. When swarm is converged in a local optimum trap, the algorithm makes swarm diverge again.In this way, the global search ability of the algorithm can be improved a lot.
(2) The paper establishes an algorithm framework based on inheritance learning strategy, and single PSO process is incorporates into this framework as a basic unit. Under the new framework, several parallel PSO processes construe one cycle. The better part of the results of last cycle and the randomly generated results composed the whole initial swarm positions of next cycle. New algorithm has greatly reduced the impact of randomness, and has good performance in multidimensional optimization problems. The improved algorithm also has great flexibility, and the algorithm frame is easy to apply in other intelligent optimization algorithms.
In the control system, PID parameter tunning is a classical research direction. If3parameters of PID controller are deemed as promising optimization variants, and the controller's response is used as fitness value, then optimization algorithm can be applied to handle PID parameter tunning. To solve this problem, the paper makes relevant studies:
(1) The paper establishes PSO optimization model for Maglev train controller PID tunning and the improved PSO algorithm is used. The simulation and experimental results show that PID tunning by PSO algorithm has good feasibility and applicability.
(2) In practical application, sometimes it is impossible to obtain accurate model for the control objects, so it is hard to tune PID parameter and the feasible way is to use the experience tuning method. To improve this situation, PSO algorithm is applied in model identification of paver's control system. The identification paver model is used to PID tunning and the experimental results show that this method is very effective.
Array antenna pattern synthesis is a key application field of intelligent algorithm. The paper also studies this issue, mainly consisting of pattern synthesis with continuous variants and discrete variants. The details are as below:
(1) As for multi-objective pattern optimization, the paper proposes the strategy of stage fitness function. For new strategy, different indicators increase by stages, and it is much easier to balance each optimization objective in different stage. Compared with fixed fitness function strategy, new strategy can avoid a certain indicators being satisfied convergence conditions while the others far from the convergence conditions. As a result, local optimum trap's depth becomes shallower in the solution space, which is helpful for the PSO swarm to escape the local optimum trap and can help PSO swarm realize global convergence. In pattern optimization applications, the fitness function can be divided into two or more stages.
(2) The paper applies stagnation detecting PSO algorithm and PSO algorithm based on convergence control into uniform linear array's low sidelobe pattern synthesis. The simulation results show that these two improved algorithms can effectively applicate in multi-null and low sidelobe pattern synthesis.
(3) The paper applies ILPSO into unequal spaced linear array's low sidelobe pattern synthesis. Simulation results show that ILPSO obtains results equal to or better than the results of the latest domestic and foreign researches by using less computation.
(4) In order to solve the discrete optimization problems in antenna array pattern synthesis, the paper proposes an optimization strategy based on the combination of PSO algorithm and particle position rounding. Therefore, it effectively handles the pattern synthesis of4bit digital phase shifter array, the pattern synthesis of thinned linear array, and the pattern synthesis of non-uniform thinning linear array. Simulation results show that this strategy can effectively apply real number PSO algorithm into the discrete optimization in pattern synthesis, and the optimization results are better than existed binary PSO and other intelligent optimization algorithms. In order to handle the pattern synthesis of large thinned plannar array with thinned element proportion constraint, the probability adjustment strategy is added, and the optimization results are superior to results of other discrete particle swarm optimization algorithms.
In the end, the paper makes final conclusion and proposes further research directions.
引文
[1]陈宝林.最优化理论与算法(第2版).清华大学出版社,2005.
[2]王凌.智能优化算法及其应用.清华大学出版社,2001.
[3]蔡宣三.最优化与最优控制.清华大学出版社,1982.
[4]D. L.C.W., S. G.P. Towards global optimisation:proceedings of a workshop. Amsterdam [etc.]:North-Holland,1974.
[5]林川.粒子群优化与差分进化算法研究及其应用.西南交通大学博士学位论文.2009.
[6]J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of the 1995 IEEE International Conference on Neural Networks Part 1 (of 6), Perth, Aust,1995. IEEE,1995:1942-1948.
[7]E. Ozcan, C. K. Mohan. Particle swarm optimization:surfing the waves. Proceedings of the 1999 Congress on Evolutionary Computation, CEC 99 Washington, DC,1999. IEEE,1999:1944-1953.
[8]M. Clerc, J. Kennedy. The particle swarm-Explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation. 2002,6(1):58-73.
[9]F. van den Bergh, A. P. Engelbrecht. A study of particle swarm optimization particle trajectories. Information Sciences.2006,176(8):937-971.
[10]K. Yasuda, A. Ide, N. Iwasaki. Adaptive particle swarm optimization.2003. IEEE: 1554-1559
[11]T. M. Blackwell. Particle swarms and population diversity. Soft Computing-A Fusion of Foundations, Methodologies and Applications.2005,9(11):793-802.
[12]B. Brandstatter, U. Baumgartner. Particle swarm optimization-mass-spring system analogon. Magnetics, IEEE Transactions on.2002,38(2):997-1000.
[13]E. F. Campana, G. Fasano, A. Pinto. Dynamic system analysis and initial particles position in particle swarm optimization.2006.
[14]E. F. Campana, G. Fasano, D. Peri, A. Pinto. Particle swarm optimization:Efficient globally convergent modifications.2006.
[15]M. Clerc. Stagnation analysis in particle swarm optimisation or what happens when nothing happens, alea.2006,5:0.
[16]V. Kadirkamanathan, K. Selvarajah, P. J. Fleming. Stability analysis of the particle dynamics in particle swarm optimizer. Evolutionary Computation, IEEE Transactions on.2006,10(3):245-255.
[17]R. Poli. Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. Evolutionary Computation, IEEE Transactions on.2009,13(4): 712-721.
[18]R. C. Eberhart, Y. Shi, J. Kennedy. Swarm intelligence[M]. Elsevier,2001.
[19]J. Kennedy. Small worlds and mega-minds:effects of neighborhood topology on particle swarm performance.1999. IEEE.
[20]J. Kennedy, R. Mendes. Population structure and particle swarm performance.2002. IEEE:1671-1676.
[21]J. Kennedy, R. Mendes. Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. Systems, Man, and Cybernetics, Part C. Applications and Reviews, IEEE Transactions on.2006,36(4):515-519.
[22]R. C. Eberhart, Y. Shi. Particle swarm optimization:developments, applications and resources.2001. Piscataway, NJ, USA:IEEE:81-86.
[23]X. Hu, Y. Shi, R. Eberhart. Recent advances in particle swarm.2004. Ieee:90-97 Vol. 91.
[24]H. Fan, Y. Shi. Study on Vmax of particle swarm optimization.2001. Indianapolis, IN, Apr.
[25]A. Abido. Particle swarm optimization for multimachine power system stabilizer design.2001. IEEE:1346-1351 vol.1343.
[26]M. Abido. Optimal power flow using particle swarm optimization. International Journal of Electrical Power& Energy Systems.2002,24(7):563-571.
[27]Y Shi, R. Eberhart. A modified particle swarm optimizer.1998. IEEE:69-73.
[28]Y. Shi, R. C. Eberhart. Empirical study of particle swarm optimization. Evolutionary Computation, Proceedings of the 1999 Congress on 1999. IEEE.
[29]X. Chen, Y. Li. An improved stochastic PSO with high exploration ability.2006. May: 228X235.
[30]彭宇,彭喜元,刘兆庆.微粒群算法参数效能的统计分析.电子学报.2004,32(002)：209-213.
[31]R. C. Eberhart, Y Shi. Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the 2000 Congress on Evolutionary Computation CEC 00, July 16,2000-July 19,2000, California, CA, USA,2000. IEEE:84-88.
[32]Y. Shi, R. Eberhart. Parameter selection in particle swarm optimization.1998. Springer:591-600.
[33]Y. Shi, R. C. Eberhart. Fuzzy adaptive particle swarm optimization.2001. IEEE: 101-106 vol.101.
[34]Y. Shi, R. Eberhart. Particle swarm optimization with fuzzy adaptive inertia weight. 2001:1011℃106.
[35]S. Doctor, G. K. Venayagamoorthy, V. G. Gudise. Optimal PSO for collective robotic search applications.2004. IEEE:1390-1395 Vol.1392.
[36]M. Khajenejad, F. Afshinmanesh, A. Marandi, B. N. Araabi. Intelligent particle swarm optimization using Q-learning.2006. Citeseer:7"C12.
[37]J. Liang, A. Qin, P. N. Suganthan, S. Baskar. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. Evolutionary Computation, IEEE Transactions on.2006,10(3):281-295.
[38]Z. Zhan, J. Zhang, O. Liu. Orthogonal learning particle swarm optimization.2009. ACM:1763-1764.
[39]C. Yang, D. Simon. A new particle swarm optimization technique.2005.
[40]A. I. Selvakumar, K. Thanushkodi. A new particle swarm optimization solution to nonconvex economic dispatch problems. Power Systems, IEEE Transactions on. 2007,22(1):42-51.
[41]温雯,郝志峰.一种基于动态拓扑结构的PSO改进算法.计算机工程与应用.2006,41(34)：82-85.
[42]P. N. Suganthan. Particle swarm optimiser with neighbourhood operator.1999. IEEE.
[43]J. Kennedy. Stereotyping:Improving particle swarm performance with cluster analysis.2000. IEEE:1507-1512 vol.1502.
[44]王雪飞,王芳,邱玉辉.一种具有动态拓扑结构的粒子群算法研究.计算机科学2007,34(003)：205-207.
[45]C. L. Q. Feng. A Hierarchical Subpopulation Particle Swarm Optimization Algorithm.
[46]B. Niu, Y. Zhu, X. He, H. Wu. MCPSO:A multi-swarm cooperative particle swarm optimizer. Applied Mathematics and Computation.2007,185(2):1050-1062.
[47]S. K. S. Fan, E. Zahara. A hybrid simplex search and particle swarm optimization for unconstrained optimization. European Journal of Operational Research.2007, 181(2):527-548.
[48]J. Kennedy. Bare bones particle swarms.2003. IEEE:80-87.
[49]J. Kennedy. Probability and dynamics in the particle swarm. IEEE:340-347 Vol.341.
[50]J. Kennedy. Why does it need velocity?,2005. IEEE:38-44.
[51]J. Kennedy. In search of the essential particle swarm.2006. IEEE:1694-1701.
[52]林川,冯全源.基于微粒群本质特征的混沌微粒群优化算法.西南交通大学学报.2007,42(006)：665-669.
[53]R. Mendes, J. Kennedy. Stochastic barycenters and beta distribution for gaussian particle swarms. Progress in Artificial Intelligence.2007:259-270.
[54]M. Lovbjerg, T. Krink. Extending particle swarm optimisers with self-organized criticality.2002. IEEE:1588-1593.
[55]T. M. Blackwell, P. Bentley. Don't push me! Collision-avoiding swarms.2002. IEEE: 1691-1696.
[56]T. Krink, J. S. VesterstrOm, J. Riget. Particle swarm optimisation with spatial particle extension.2002. IEEE:1474-1479.
[57]S. He, Q. Wu, J. Wen, J. Saunders, R. Paton. A particle swarm optimizer with passive congregation. Biosystems.2004,78(1-3):135-147.
[58]S. Selleri, M. Mussetta, P. Pirinoli, R. E. Zich, L. Matekovits. Some insight over new variations of the particle swarm optimization method. Antennas and Wireless Propagation Letters, IEEE.2006,5(1):235-238.
[59]M. Higashitani, A. Ishigame, K. Yasuda. Particle swarm optimization considering the concept of predator-prey behavior.2006. IEEE:434-437.
[60]W. Jian, Y. Xue, J. Huang. Combined algorithm for time-varying system based on improved particle swarm optimization and EWRLS algorithm. IEEE:1474-1477 Vol. 1473.
[61]孟红记,郑鹏,梅国晖,谢植.基于混沌序列的粒子群优化算法[J].控制与决策.2006,21(3):263-266.
[62]J. Kennedy, R. C. Eberhart. A discrete binary version of the particle swarm algorithm. IEEE Int Conf Man Syst, Cyber,1997. IEEE:4104-4108 vol.4105.
[63]J. Kennedy, W. M. Spears. Matching algorithms to problems:an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. 1998. IEEE:78-83.
[64]C. Mohan, B. Al-Kazemi. Discrete particle swarm optimization.2001.
[65]X. Hu, R. C. Eberhart, Y. Shi. Swarm intelligence for permutation optimization:a case study of n-queens problem.2003. IEEE:243-246.
[66]M. Clerc. Discrete particle swarm optimization, illustrated by the traveling salesman problem. New optimization techniques in engineering.2004:219-239.
[67]G. Pampara, N. Franken, A. Engelbrecht. Combining Particle Swarm Optimisation with angle modulation to solve binary problems.2005. IEEE:89-96 Vol.81.
[68]K. E. Parsopoulos, M. N. Vrahatis. Particle swarm optimization method in multiobjective problems.2002. ACM:603-607.
[69]T. Ray, K. Liew. A swarm metaphor for multiobjective design optimization. Engineering Optimization.2002,34(2):141-153.
[70]C. A. C. Coello, G. T. Pulido, M. S. Lechuga. Handling multiple objectives with particle swarm optimization. Evolutionary Computation, IEEE Transactions on.2004, 8(3):256-279.
[71]G. T. Pulido, C. A. Coello Coello. Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer.2004. Springer:225-237.
[72]X. Li. A non-dominated sorting particle swarm optimizer for multiobjective optimization.2003. Springer:198-198.
[73]A. El-Gallad, M. El-Hawary, A. Sallam, A. Kalas. Swarm intelligence for hybrid cost dispatch problem.2001. IEEE:753-757 vol.752.
[74]A. El-Gallad, M. El-Hawary, A. Sallam, A. Kalas. Particle swarm optimizer for constrained economic dispatch with prohibited operating zones.2002. IEEE:78-81 vol.71.
[75]J. B. Park, Y. W. Jeong, J. R. Shin, K. Y. Lee. An improved particle swarm optimization for nonconvex economic dispatch problems. Power Systems, IEEE Transactions on.2010,25(1):156-166.
[76]H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, Y. Nakanishi. A particle swarm optimization for reactive power and voltage control considering voltage security assessment. Power Systems, IEEE Transactions on.2000,15(4):1232-1239.
[77]Y. Fukuyama, H. Yoshida. A particle swarm optimization for reactive power and voltage control in electric power systems.2001. IEEE:87-93 vol.81.
[78]A. Mantawy, M. Al-Ghamdi. A new reactive power optimization algorithm.2003. IEEE:6 pp. Vol.4.
[79]Y. Wang, K. Chan, T. Pong. Dynamic voltage security constrained optimal coordinated voltage control using enhanced particle swarm optimisation. Generation, Transmission & Distribution, IET.2011,5(2):239-248.
[80]B. Zhao, C. Guo, Y. Cao. Improved particle swam optimization algorithm for OPF problems.2004. IEEE:233-238 vol.231.
[81]S. He, J. Wen, E. Prempain, Q. Wu, J. Fitch, S. Mann. An improved particle swarm optimization for optimal power flow.2004. IEEE:1633-1637 Vol.1632.
[82]D. Huynh, M. Dunnigan. Parameter estimation of an induction machine using advanced particle swarm optimisation algorithms. Electric Power Applications, IET. 2010,4(9):748-760.
[83]M. Hassan, M. Abido. Optimal Design of Microgrids in Autonomous and Grid-Connected Modes Using Particle Swarm Optimization. Power Electronics, IEEE Transactions on. (99):1-1.
[84]H. Taghizadeh, M. T. Hagh. Harmonic Elimination of Cascade Multilevel Inverters with Nonequal DC Sources Using Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on.2010,57(11):3678-3684.
[85]Q. Li, W. Chen, Y. Wang, S. Liu, J. Jia. Parameter identification for PEM Fuel Cell Mechanism Model Based on Effective Informed Adaptive Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on. (99):1-1.
[86]C. H. Liu, Y. Y. Hsu. Design of a self-tuning PI controller for a STATCOM using particle swarm optimization. Industrial Electronics, IEEE Transactions on.2010, 57(2):702-715.
[87]R. J. Wai, J. D. Lee, K. L. Chuang. Real-Time PID Control Strategy for Maglev Transportation System via Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on.2011,58(2):629-646.
[88]R. Jiang, H. Wang, S. Tian, B. Long. Multidimensional Fitness Function DPSO Algorithm for Analog Test Point Selection. Instrumentation and Measurement, IEEE Transactions on.2010,59(6):1634-1641.
[89]L. Tang, X. Wang. An Improved Particle Swarm Optimization Algorithm for the Hybrid Flowshop Scheduling to Minimize Total Weighted Completion Time in Process Industry. Control Systems Technology, IEEE Transactions on.2010,18(6): 1303-1314.
[90]林晶晶,周国华.基于粒子群算法的关键链多项目调度管理.统计与决蔗2012,10.
[91]林晶晶.考虑资源可替代性的关键链识别与缓冲设置方法研究.西南交通大学博士论文.2011.
[92]R. V. Kulkarni, G. K. Venayagamoorthy. Particle swarm optimization in wireless-sensor networks:A brief survey. Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on.2011, (99):1-7.
[93]刘东,冯全源,蒋启龙.基于改进PSO算法的磁浮列车PID控制器参数优化.西南交通大学学报.2010,45(003)：405-410.
[94]C. Lin, A. Qing, Q. Feng. Synthesis of unequally spaced antenna arrays by using differential evolution[J]. IEEE Transactions on Antennas and Propagation.2010,58: 2553-2561.
[95]W. T. Li, X. W. Shi, Y. Q. Hei, S. F. Liu, J. Zhu. A hybrid optimization algorithm and its application for conformal array pattern synthesis. Antennas and Propagation, IEEE Transactions on.2010,58(10):3401-3406.
[96]S. K. Goudos, V. Moysiadou, T. Samaras, K. Siakavara, J. N. Sahalos. Application of a comprehensive learning particle swarm optimizer to unequally spaced linear array synthesis with sidelobe level suppression and null control. Antennas and Wireless Propagation Letters, IEEE.2010,9:125-129.
[97]T. H. Ismail, Z. M. Hamici. Array Pattern Synthesis Using Digital Phase Control by Quantized Particle Swarm Optimization. Antennas and Propagation, IEEE Transactions on.2010,58(6):2142-2145.
[98]金荣洪,袁智皓,耿军平,范瑜,李佳靖.基于改进粒子群算法的天线方向图综合技术.电波科学学报.2006,21(006)：873-878.
[99]刘鸣.智能天线技术与应用.机械工业出版社,2007.
[100]C. K. Ng, N. K. Noordin, S. Khatun, B. M. AH, S. S. Jamuar, M. Ismail. Directional Diversity of Smart Antenna in LAS CDMA Systems. Wireless Personal Communications.2008,46(3):305-316.
[101]尚飞,蔡亚星,张颖,高本庆.阵列天线的双种群遗传算法综合.电波科学学报.2007,22(002)：224-228.
[102]C. B. Dietrich Jr, W. L. Stutzman, B. K. Kim, K. Dietze. Smart antennas in wireless communications:Base-station diversity and handset beamforming. Antennas and Propagation Magazine, IEEE.2000,42(5):142-151.
[103]Z. Zaharis. Radiation pattern shaping of a mobile base station antenna array using a particle swarm optimization based technique. Electrical Engineering (Archiv fur Elektrotechnik).2008,90(4):301-311.
[104]杨林.阵列天线综合方法研究.哈尔滨工程大学.2006.
[105]叶剑锋.基于免疫优化算法的阵列天线综合的研究.哈尔滨工程大学.2009.
[106]金荣洪,耿军平,范瑜.无线通信中的智能天线.北京邮电大学出版社,2006.
[107]N. Jin, Y. Rahmat-Samii. Advances in particle swarm optimization for antenna designs:Real-number, binary, single-objective and multiobjective implementations. Antennas and Propagation, IEEE Transactions on.2007,55(3):556-567.
[108]D. G. Kurup, M. Himdi, A. Rydberg. Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm. Antennas and Propagation, IEEE Transactions on.2003,51(9):2210-2217.
[109]O. Quevedo-Teruel, E. Rajo-Iglesias. Ant colony optimization in thinned array synthesis with minimum sidelobe level. Antennas and Wireless Propagation Letters, IEEE.2006,5(1):349-352.
[110]C. Dolph. A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proceedings of the IRE.1946,34(6): 335-348.
[111]T. Taylor. Design of circular apertures for narrow beamwidth and low sidelobes. Antennas and Propagation, IRE Transactions on.1960,8(1):17-22.
[112]B. P. Kumar, G. Branner. Design of unequally spaced arrays for performance improvement. Antennas and Propagation, IEEE Transactions on.1999,47(3): 511-523.
[113]B. Kumar, G. Branner. Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry. Antennas and Propagation, IEEE Transactions on.2005,53(2):621-634.
[114]J. M. Johnson, Y. Rahmat-Samii. Genetic algorithm optimization and its application to antenna design.1994. IEEE:326-329 vol.321.
[115]R. L. Haupt. Thinned arrays using genetic algorithms. Antennas and Propagation, IEEE Transactions on.1994,42(7):993-999.
[116]K. K. Yan, Y. Lu. Sidelobe reduction in array-pattern synthesis using genetic algorithm. Antennas and Propagation, IEEE Transactions on.1997,45(7): 1117-1122.
[117]A. Tennant, M. Dawoud, A. Anderson. Array pattern nulling by element position perturbations using a genetic algorithm. Electronics letters.1994,30(3):174-176.
[118]叶剑锋,王玉峰,庞伟正.多映射混沌免疫算法及其在天线阵方向图综合中的应用.哈尔滨工程大学学报.2007,28(011)：1273-1277.
[119]姚昆,杨万麟.最佳稀布直线阵列的分区动态规划法.电子学报.1994,22(12)：87-90.
[120]V. Murino, A. Trucco, C. S. Regazzoni. Synthesis of unequally spaced arrays by simulated annealing. Signal Processing, IEEE Transactions on.1996,44(1):119-122.
[121]范瑜,金荣洪,刘波,耿军平.阵列天线方向图综合中的遗传算法目标函数研究. 电子与信息学报.2005,27(005)：801-804.
[122]刘东,冯全源.基于停滞检测粒子群算法的阵列天线方向图综合.电波科学学报.2009,24(004)：697-701.
[123]李东风,龚中麟.遗传算法应用于超低副瓣线阵天线方向图综合.电子学报.2003,31(1)：82-84.
[124]蒋启龙,张昆仑,连级三.磁浮轴承系统的数学模型与控制分析.西南交通大学学报.1999,34(4)：413-418.
[125]庞中华,崔红.系统辨识与自适应控制MATLAB仿真.北京航空航天大学出版社,2009.
[126]孙晓武,武建华.摊铺机行走系统控制策略研究.液压与气动.2002,(007)：5-6.
[127]俞欢军,张丽平,陈德钊,胡上序.基于反馈策略的自适应粒子群优化算法.浙江大学学报：工学版.2005,39(009)：1286-1291.
[128]Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. C. Hernandez, R. G. Harley. Particle swarm optimization:basic concepts, variants and applications in power systems. Evolutionary Computation, IEEE Transactions on.2008,12(2):171-195.
[129]朱培逸,张宇林.基于动态权值的粒子群算法的多样性分析.石油化工高等学校学报.2008,21(004)：91-94.
[130]朱海梅,吴永萍.一种高速收敛粒子群优化算法.控制与决策.2010,25(1)：20-24.
[131]黄纯,罗伟原,江辉.基于增量式PID的改进粒子群算法.湖南大学学报：自然科学版2009,36(012)：35-39.
[132]S. Mohaghegi, Y. del Valle, G. Venayagamoorthy, R. Harley. A comparison of PSO and backpropagation for training RBF neural networks for identification of a power system with STATCOM.2005. IEEE:381-384.
[133]Y. del Valle, S. Mohagheghi, G. Venayagamoorthy, R. Harley. Training MLP neural networks for identification of a small power system:Comparison of PSO and backpropagation.2005:153℃157.
[134]W. Wang, Q. Feng, D. Liu. APPLICATION OF CHAOTIC PARTICLE SWARM OPTI-MIZATION ALGORITHM TO PATTERN SYNTHESIS OF ANTENNA ARRAYS. Progress In Electromagnetics Research.2011,115:173X189.
[135]W. P. M. N. Keizer. Low Sidelobe Phased Array Pattern Synthesis With Compensation for Errors Due to Quantized Tapering. Antennas and Propagation, IEEE Transactions on.2011, (99):1-1.
[136]M. Smith, Y. Guo. A comparison of methods for randomizing phase quantization errors in phased arrays. Antennas and Propagation, IEEE Transactions on.1983, 31(6):821-828.
[137]Y. Shi, R. Eberhart. A modified particle swarm optimizer. Applied Mathematics and Computation.1998,189(2):69-73.
[138]C. A. Balanis. Antenna theory:analysis and design. J. Wiley, New York,2007.
[139]K. V. Deligkaris, Z. D. Zaharis, D. G. Kampitaki, S. K. Goudos, I. T. Rekanos, M. N. Spasos. Thinned planar array design using Boolean PSO with velocity mutation. Magnetics, IEEE Transactions on.2009,45(3):1490-1493.
[140]L. Zhang, Y. C. Jiao, Z. B. Weng, F. S. Zhang. Design of planar thinned arrays using a Boolean differential evolution algorithm. Microwaves, Antennas & Propagation, IET.2010,4(12):2172-2178.
[141]A. Razavi, K. Forooraghi. Thinned arrays using pattern search algorithms. Progress In Electromagnetics Research.2008,78:61-71.
[142]J. Sun, B. Feng, W. Xu. Particle swarm optimization with particles having quantum behavior. Congress on Evolutionary Computation, Jiangsu, China 2004. IEEE: 325-331 Vol.321.
[143]G. K. Mahanti, N. N. Pathak, P. K. Mahanti. Synthesis of thinned linear antenna arrays with fixed sidelobe level using real-coded genetic algorithm. Progress In Electromagnetics Research.2007,75:319-328.
[144]N. Jin, Y. Rahmat-Samii. Hybrid real-binary particle swarm optimization (HPSO) in engineering electromagnetics. Antennas and Propagation, IEEE Transactions on. 2010,58(12):3786-3794.
[145]W. Keizer. Linear array thinning using iterative FFT techniques. Antennas and Propagation, IEEE Transactions on.2008,56(8):2757-2760.
[146]W. Keizer. Large planar array thinning using iterative FFT techniques. Antennas and Propagation, IEEE Transactions on.2009,57(10):3359-3362.
[147]E. C. Laskari, K. E. Parsopoulos, M. N. Vrahatis. Particle swarm optimization for integer programming.2002. IEEE:1582-1587.
[148]Z. L. Gaing. Constrained optimal power flow by mixed-integer particle swarm optimization.2005. IEEE:243-250 Vol.241.
[149]W. B. Wang, Q. Feng, D. Liu. Synthesis of Thinned Linear and Planar Antenna Arrays Using Binary PSO Algorithm. Progress In Electromagnetics Research.2012, 127:371-387.
[150]S. Mosca, M. Ciattaglia. Ant colony optimization to design thinned arrays.2006. IEEE:4675-4678.
[151]D. Chen, J. Li. GA Design of Large Thinned Arrays.3rd European Conference on Antennas Popag, Berlin,2009:451-455.
[152]X. Li, X. Yao. Cooperatively coevolving particle swarms for large scale optimization. Evolutionary Computation, IEEE Transactions on.2012,16(2):210-224.
[2]王凌.智能优化算法及其应用.清华大学出版社,2001.
[3]蔡宣三.最优化与最优控制.清华大学出版社,1982.
[4]D. L.C.W., S. G.P. Towards global optimisation:proceedings of a workshop. Amsterdam [etc.]:North-Holland,1974.
[5]林川.粒子群优化与差分进化算法研究及其应用.西南交通大学博士学位论文.2009.
[6]J. Kennedy, R. Eberhart. Particle swarm optimization. Proceedings of the 1995 IEEE International Conference on Neural Networks Part 1 (of 6), Perth, Aust,1995. IEEE,1995:1942-1948.
[7]E. Ozcan, C. K. Mohan. Particle swarm optimization:surfing the waves. Proceedings of the 1999 Congress on Evolutionary Computation, CEC 99 Washington, DC,1999. IEEE,1999:1944-1953.
[8]M. Clerc, J. Kennedy. The particle swarm-Explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation. 2002,6(1):58-73.
[9]F. van den Bergh, A. P. Engelbrecht. A study of particle swarm optimization particle trajectories. Information Sciences.2006,176(8):937-971.
[10]K. Yasuda, A. Ide, N. Iwasaki. Adaptive particle swarm optimization.2003. IEEE: 1554-1559
[11]T. M. Blackwell. Particle swarms and population diversity. Soft Computing-A Fusion of Foundations, Methodologies and Applications.2005,9(11):793-802.
[12]B. Brandstatter, U. Baumgartner. Particle swarm optimization-mass-spring system analogon. Magnetics, IEEE Transactions on.2002,38(2):997-1000.
[13]E. F. Campana, G. Fasano, A. Pinto. Dynamic system analysis and initial particles position in particle swarm optimization.2006.
[14]E. F. Campana, G. Fasano, D. Peri, A. Pinto. Particle swarm optimization:Efficient globally convergent modifications.2006.
[15]M. Clerc. Stagnation analysis in particle swarm optimisation or what happens when nothing happens, alea.2006,5:0.
[16]V. Kadirkamanathan, K. Selvarajah, P. J. Fleming. Stability analysis of the particle dynamics in particle swarm optimizer. Evolutionary Computation, IEEE Transactions on.2006,10(3):245-255.
[17]R. Poli. Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. Evolutionary Computation, IEEE Transactions on.2009,13(4): 712-721.
[18]R. C. Eberhart, Y. Shi, J. Kennedy. Swarm intelligence[M]. Elsevier,2001.
[19]J. Kennedy. Small worlds and mega-minds:effects of neighborhood topology on particle swarm performance.1999. IEEE.
[20]J. Kennedy, R. Mendes. Population structure and particle swarm performance.2002. IEEE:1671-1676.
[21]J. Kennedy, R. Mendes. Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. Systems, Man, and Cybernetics, Part C. Applications and Reviews, IEEE Transactions on.2006,36(4):515-519.
[22]R. C. Eberhart, Y. Shi. Particle swarm optimization:developments, applications and resources.2001. Piscataway, NJ, USA:IEEE:81-86.
[23]X. Hu, Y. Shi, R. Eberhart. Recent advances in particle swarm.2004. Ieee:90-97 Vol. 91.
[24]H. Fan, Y. Shi. Study on Vmax of particle swarm optimization.2001. Indianapolis, IN, Apr.
[25]A. Abido. Particle swarm optimization for multimachine power system stabilizer design.2001. IEEE:1346-1351 vol.1343.
[26]M. Abido. Optimal power flow using particle swarm optimization. International Journal of Electrical Power& Energy Systems.2002,24(7):563-571.
[27]Y Shi, R. Eberhart. A modified particle swarm optimizer.1998. IEEE:69-73.
[28]Y. Shi, R. C. Eberhart. Empirical study of particle swarm optimization. Evolutionary Computation, Proceedings of the 1999 Congress on 1999. IEEE.
[29]X. Chen, Y. Li. An improved stochastic PSO with high exploration ability.2006. May: 228X235.
[30]彭宇,彭喜元,刘兆庆.微粒群算法参数效能的统计分析.电子学报.2004,32(002)：209-213.
[31]R. C. Eberhart, Y Shi. Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the 2000 Congress on Evolutionary Computation CEC 00, July 16,2000-July 19,2000, California, CA, USA,2000. IEEE:84-88.
[32]Y. Shi, R. Eberhart. Parameter selection in particle swarm optimization.1998. Springer:591-600.
[33]Y. Shi, R. C. Eberhart. Fuzzy adaptive particle swarm optimization.2001. IEEE: 101-106 vol.101.
[34]Y. Shi, R. Eberhart. Particle swarm optimization with fuzzy adaptive inertia weight. 2001:1011℃106.
[35]S. Doctor, G. K. Venayagamoorthy, V. G. Gudise. Optimal PSO for collective robotic search applications.2004. IEEE:1390-1395 Vol.1392.
[36]M. Khajenejad, F. Afshinmanesh, A. Marandi, B. N. Araabi. Intelligent particle swarm optimization using Q-learning.2006. Citeseer:7"C12.
[37]J. Liang, A. Qin, P. N. Suganthan, S. Baskar. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. Evolutionary Computation, IEEE Transactions on.2006,10(3):281-295.
[38]Z. Zhan, J. Zhang, O. Liu. Orthogonal learning particle swarm optimization.2009. ACM:1763-1764.
[39]C. Yang, D. Simon. A new particle swarm optimization technique.2005.
[40]A. I. Selvakumar, K. Thanushkodi. A new particle swarm optimization solution to nonconvex economic dispatch problems. Power Systems, IEEE Transactions on. 2007,22(1):42-51.
[41]温雯,郝志峰.一种基于动态拓扑结构的PSO改进算法.计算机工程与应用.2006,41(34)：82-85.
[42]P. N. Suganthan. Particle swarm optimiser with neighbourhood operator.1999. IEEE.
[43]J. Kennedy. Stereotyping:Improving particle swarm performance with cluster analysis.2000. IEEE:1507-1512 vol.1502.
[44]王雪飞,王芳,邱玉辉.一种具有动态拓扑结构的粒子群算法研究.计算机科学2007,34(003)：205-207.
[45]C. L. Q. Feng. A Hierarchical Subpopulation Particle Swarm Optimization Algorithm.
[46]B. Niu, Y. Zhu, X. He, H. Wu. MCPSO:A multi-swarm cooperative particle swarm optimizer. Applied Mathematics and Computation.2007,185(2):1050-1062.
[47]S. K. S. Fan, E. Zahara. A hybrid simplex search and particle swarm optimization for unconstrained optimization. European Journal of Operational Research.2007, 181(2):527-548.
[48]J. Kennedy. Bare bones particle swarms.2003. IEEE:80-87.
[49]J. Kennedy. Probability and dynamics in the particle swarm. IEEE:340-347 Vol.341.
[50]J. Kennedy. Why does it need velocity?,2005. IEEE:38-44.
[51]J. Kennedy. In search of the essential particle swarm.2006. IEEE:1694-1701.
[52]林川,冯全源.基于微粒群本质特征的混沌微粒群优化算法.西南交通大学学报.2007,42(006)：665-669.
[53]R. Mendes, J. Kennedy. Stochastic barycenters and beta distribution for gaussian particle swarms. Progress in Artificial Intelligence.2007:259-270.
[54]M. Lovbjerg, T. Krink. Extending particle swarm optimisers with self-organized criticality.2002. IEEE:1588-1593.
[55]T. M. Blackwell, P. Bentley. Don't push me! Collision-avoiding swarms.2002. IEEE: 1691-1696.
[56]T. Krink, J. S. VesterstrOm, J. Riget. Particle swarm optimisation with spatial particle extension.2002. IEEE:1474-1479.
[57]S. He, Q. Wu, J. Wen, J. Saunders, R. Paton. A particle swarm optimizer with passive congregation. Biosystems.2004,78(1-3):135-147.
[58]S. Selleri, M. Mussetta, P. Pirinoli, R. E. Zich, L. Matekovits. Some insight over new variations of the particle swarm optimization method. Antennas and Wireless Propagation Letters, IEEE.2006,5(1):235-238.
[59]M. Higashitani, A. Ishigame, K. Yasuda. Particle swarm optimization considering the concept of predator-prey behavior.2006. IEEE:434-437.
[60]W. Jian, Y. Xue, J. Huang. Combined algorithm for time-varying system based on improved particle swarm optimization and EWRLS algorithm. IEEE:1474-1477 Vol. 1473.
[61]孟红记,郑鹏,梅国晖,谢植.基于混沌序列的粒子群优化算法[J].控制与决策.2006,21(3):263-266.
[62]J. Kennedy, R. C. Eberhart. A discrete binary version of the particle swarm algorithm. IEEE Int Conf Man Syst, Cyber,1997. IEEE:4104-4108 vol.4105.
[63]J. Kennedy, W. M. Spears. Matching algorithms to problems:an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. 1998. IEEE:78-83.
[64]C. Mohan, B. Al-Kazemi. Discrete particle swarm optimization.2001.
[65]X. Hu, R. C. Eberhart, Y. Shi. Swarm intelligence for permutation optimization:a case study of n-queens problem.2003. IEEE:243-246.
[66]M. Clerc. Discrete particle swarm optimization, illustrated by the traveling salesman problem. New optimization techniques in engineering.2004:219-239.
[67]G. Pampara, N. Franken, A. Engelbrecht. Combining Particle Swarm Optimisation with angle modulation to solve binary problems.2005. IEEE:89-96 Vol.81.
[68]K. E. Parsopoulos, M. N. Vrahatis. Particle swarm optimization method in multiobjective problems.2002. ACM:603-607.
[69]T. Ray, K. Liew. A swarm metaphor for multiobjective design optimization. Engineering Optimization.2002,34(2):141-153.
[70]C. A. C. Coello, G. T. Pulido, M. S. Lechuga. Handling multiple objectives with particle swarm optimization. Evolutionary Computation, IEEE Transactions on.2004, 8(3):256-279.
[71]G. T. Pulido, C. A. Coello Coello. Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer.2004. Springer:225-237.
[72]X. Li. A non-dominated sorting particle swarm optimizer for multiobjective optimization.2003. Springer:198-198.
[73]A. El-Gallad, M. El-Hawary, A. Sallam, A. Kalas. Swarm intelligence for hybrid cost dispatch problem.2001. IEEE:753-757 vol.752.
[74]A. El-Gallad, M. El-Hawary, A. Sallam, A. Kalas. Particle swarm optimizer for constrained economic dispatch with prohibited operating zones.2002. IEEE:78-81 vol.71.
[75]J. B. Park, Y. W. Jeong, J. R. Shin, K. Y. Lee. An improved particle swarm optimization for nonconvex economic dispatch problems. Power Systems, IEEE Transactions on.2010,25(1):156-166.
[76]H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, Y. Nakanishi. A particle swarm optimization for reactive power and voltage control considering voltage security assessment. Power Systems, IEEE Transactions on.2000,15(4):1232-1239.
[77]Y. Fukuyama, H. Yoshida. A particle swarm optimization for reactive power and voltage control in electric power systems.2001. IEEE:87-93 vol.81.
[78]A. Mantawy, M. Al-Ghamdi. A new reactive power optimization algorithm.2003. IEEE:6 pp. Vol.4.
[79]Y. Wang, K. Chan, T. Pong. Dynamic voltage security constrained optimal coordinated voltage control using enhanced particle swarm optimisation. Generation, Transmission & Distribution, IET.2011,5(2):239-248.
[80]B. Zhao, C. Guo, Y. Cao. Improved particle swam optimization algorithm for OPF problems.2004. IEEE:233-238 vol.231.
[81]S. He, J. Wen, E. Prempain, Q. Wu, J. Fitch, S. Mann. An improved particle swarm optimization for optimal power flow.2004. IEEE:1633-1637 Vol.1632.
[82]D. Huynh, M. Dunnigan. Parameter estimation of an induction machine using advanced particle swarm optimisation algorithms. Electric Power Applications, IET. 2010,4(9):748-760.
[83]M. Hassan, M. Abido. Optimal Design of Microgrids in Autonomous and Grid-Connected Modes Using Particle Swarm Optimization. Power Electronics, IEEE Transactions on. (99):1-1.
[84]H. Taghizadeh, M. T. Hagh. Harmonic Elimination of Cascade Multilevel Inverters with Nonequal DC Sources Using Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on.2010,57(11):3678-3684.
[85]Q. Li, W. Chen, Y. Wang, S. Liu, J. Jia. Parameter identification for PEM Fuel Cell Mechanism Model Based on Effective Informed Adaptive Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on. (99):1-1.
[86]C. H. Liu, Y. Y. Hsu. Design of a self-tuning PI controller for a STATCOM using particle swarm optimization. Industrial Electronics, IEEE Transactions on.2010, 57(2):702-715.
[87]R. J. Wai, J. D. Lee, K. L. Chuang. Real-Time PID Control Strategy for Maglev Transportation System via Particle Swarm Optimization. Industrial Electronics, IEEE Transactions on.2011,58(2):629-646.
[88]R. Jiang, H. Wang, S. Tian, B. Long. Multidimensional Fitness Function DPSO Algorithm for Analog Test Point Selection. Instrumentation and Measurement, IEEE Transactions on.2010,59(6):1634-1641.
[89]L. Tang, X. Wang. An Improved Particle Swarm Optimization Algorithm for the Hybrid Flowshop Scheduling to Minimize Total Weighted Completion Time in Process Industry. Control Systems Technology, IEEE Transactions on.2010,18(6): 1303-1314.
[90]林晶晶,周国华.基于粒子群算法的关键链多项目调度管理.统计与决蔗2012,10.
[91]林晶晶.考虑资源可替代性的关键链识别与缓冲设置方法研究.西南交通大学博士论文.2011.
[92]R. V. Kulkarni, G. K. Venayagamoorthy. Particle swarm optimization in wireless-sensor networks:A brief survey. Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on.2011, (99):1-7.
[93]刘东,冯全源,蒋启龙.基于改进PSO算法的磁浮列车PID控制器参数优化.西南交通大学学报.2010,45(003)：405-410.
[94]C. Lin, A. Qing, Q. Feng. Synthesis of unequally spaced antenna arrays by using differential evolution[J]. IEEE Transactions on Antennas and Propagation.2010,58: 2553-2561.
[95]W. T. Li, X. W. Shi, Y. Q. Hei, S. F. Liu, J. Zhu. A hybrid optimization algorithm and its application for conformal array pattern synthesis. Antennas and Propagation, IEEE Transactions on.2010,58(10):3401-3406.
[96]S. K. Goudos, V. Moysiadou, T. Samaras, K. Siakavara, J. N. Sahalos. Application of a comprehensive learning particle swarm optimizer to unequally spaced linear array synthesis with sidelobe level suppression and null control. Antennas and Wireless Propagation Letters, IEEE.2010,9:125-129.
[97]T. H. Ismail, Z. M. Hamici. Array Pattern Synthesis Using Digital Phase Control by Quantized Particle Swarm Optimization. Antennas and Propagation, IEEE Transactions on.2010,58(6):2142-2145.
[98]金荣洪,袁智皓,耿军平,范瑜,李佳靖.基于改进粒子群算法的天线方向图综合技术.电波科学学报.2006,21(006)：873-878.
[99]刘鸣.智能天线技术与应用.机械工业出版社,2007.
[100]C. K. Ng, N. K. Noordin, S. Khatun, B. M. AH, S. S. Jamuar, M. Ismail. Directional Diversity of Smart Antenna in LAS CDMA Systems. Wireless Personal Communications.2008,46(3):305-316.
[101]尚飞,蔡亚星,张颖,高本庆.阵列天线的双种群遗传算法综合.电波科学学报.2007,22(002)：224-228.
[102]C. B. Dietrich Jr, W. L. Stutzman, B. K. Kim, K. Dietze. Smart antennas in wireless communications:Base-station diversity and handset beamforming. Antennas and Propagation Magazine, IEEE.2000,42(5):142-151.
[103]Z. Zaharis. Radiation pattern shaping of a mobile base station antenna array using a particle swarm optimization based technique. Electrical Engineering (Archiv fur Elektrotechnik).2008,90(4):301-311.
[104]杨林.阵列天线综合方法研究.哈尔滨工程大学.2006.
[105]叶剑锋.基于免疫优化算法的阵列天线综合的研究.哈尔滨工程大学.2009.
[106]金荣洪,耿军平,范瑜.无线通信中的智能天线.北京邮电大学出版社,2006.
[107]N. Jin, Y. Rahmat-Samii. Advances in particle swarm optimization for antenna designs:Real-number, binary, single-objective and multiobjective implementations. Antennas and Propagation, IEEE Transactions on.2007,55(3):556-567.
[108]D. G. Kurup, M. Himdi, A. Rydberg. Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm. Antennas and Propagation, IEEE Transactions on.2003,51(9):2210-2217.
[109]O. Quevedo-Teruel, E. Rajo-Iglesias. Ant colony optimization in thinned array synthesis with minimum sidelobe level. Antennas and Wireless Propagation Letters, IEEE.2006,5(1):349-352.
[110]C. Dolph. A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proceedings of the IRE.1946,34(6): 335-348.
[111]T. Taylor. Design of circular apertures for narrow beamwidth and low sidelobes. Antennas and Propagation, IRE Transactions on.1960,8(1):17-22.
[112]B. P. Kumar, G. Branner. Design of unequally spaced arrays for performance improvement. Antennas and Propagation, IEEE Transactions on.1999,47(3): 511-523.
[113]B. Kumar, G. Branner. Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry. Antennas and Propagation, IEEE Transactions on.2005,53(2):621-634.
[114]J. M. Johnson, Y. Rahmat-Samii. Genetic algorithm optimization and its application to antenna design.1994. IEEE:326-329 vol.321.
[115]R. L. Haupt. Thinned arrays using genetic algorithms. Antennas and Propagation, IEEE Transactions on.1994,42(7):993-999.
[116]K. K. Yan, Y. Lu. Sidelobe reduction in array-pattern synthesis using genetic algorithm. Antennas and Propagation, IEEE Transactions on.1997,45(7): 1117-1122.
[117]A. Tennant, M. Dawoud, A. Anderson. Array pattern nulling by element position perturbations using a genetic algorithm. Electronics letters.1994,30(3):174-176.
[118]叶剑锋,王玉峰,庞伟正.多映射混沌免疫算法及其在天线阵方向图综合中的应用.哈尔滨工程大学学报.2007,28(011)：1273-1277.
[119]姚昆,杨万麟.最佳稀布直线阵列的分区动态规划法.电子学报.1994,22(12)：87-90.
[120]V. Murino, A. Trucco, C. S. Regazzoni. Synthesis of unequally spaced arrays by simulated annealing. Signal Processing, IEEE Transactions on.1996,44(1):119-122.
[121]范瑜,金荣洪,刘波,耿军平.阵列天线方向图综合中的遗传算法目标函数研究. 电子与信息学报.2005,27(005)：801-804.
[122]刘东,冯全源.基于停滞检测粒子群算法的阵列天线方向图综合.电波科学学报.2009,24(004)：697-701.
[123]李东风,龚中麟.遗传算法应用于超低副瓣线阵天线方向图综合.电子学报.2003,31(1)：82-84.
[124]蒋启龙,张昆仑,连级三.磁浮轴承系统的数学模型与控制分析.西南交通大学学报.1999,34(4)：413-418.
[125]庞中华,崔红.系统辨识与自适应控制MATLAB仿真.北京航空航天大学出版社,2009.
[126]孙晓武,武建华.摊铺机行走系统控制策略研究.液压与气动.2002,(007)：5-6.
[127]俞欢军,张丽平,陈德钊,胡上序.基于反馈策略的自适应粒子群优化算法.浙江大学学报：工学版.2005,39(009)：1286-1291.
[128]Y. del Valle, G. K. Venayagamoorthy, S. Mohagheghi, J. C. Hernandez, R. G. Harley. Particle swarm optimization:basic concepts, variants and applications in power systems. Evolutionary Computation, IEEE Transactions on.2008,12(2):171-195.
[129]朱培逸,张宇林.基于动态权值的粒子群算法的多样性分析.石油化工高等学校学报.2008,21(004)：91-94.
[130]朱海梅,吴永萍.一种高速收敛粒子群优化算法.控制与决策.2010,25(1)：20-24.
[131]黄纯,罗伟原,江辉.基于增量式PID的改进粒子群算法.湖南大学学报：自然科学版2009,36(012)：35-39.
[132]S. Mohaghegi, Y. del Valle, G. Venayagamoorthy, R. Harley. A comparison of PSO and backpropagation for training RBF neural networks for identification of a power system with STATCOM.2005. IEEE:381-384.
[133]Y. del Valle, S. Mohagheghi, G. Venayagamoorthy, R. Harley. Training MLP neural networks for identification of a small power system:Comparison of PSO and backpropagation.2005:153℃157.
[134]W. Wang, Q. Feng, D. Liu. APPLICATION OF CHAOTIC PARTICLE SWARM OPTI-MIZATION ALGORITHM TO PATTERN SYNTHESIS OF ANTENNA ARRAYS. Progress In Electromagnetics Research.2011,115:173X189.
[135]W. P. M. N. Keizer. Low Sidelobe Phased Array Pattern Synthesis With Compensation for Errors Due to Quantized Tapering. Antennas and Propagation, IEEE Transactions on.2011, (99):1-1.
[136]M. Smith, Y. Guo. A comparison of methods for randomizing phase quantization errors in phased arrays. Antennas and Propagation, IEEE Transactions on.1983, 31(6):821-828.
[137]Y. Shi, R. Eberhart. A modified particle swarm optimizer. Applied Mathematics and Computation.1998,189(2):69-73.
[138]C. A. Balanis. Antenna theory:analysis and design. J. Wiley, New York,2007.
[139]K. V. Deligkaris, Z. D. Zaharis, D. G. Kampitaki, S. K. Goudos, I. T. Rekanos, M. N. Spasos. Thinned planar array design using Boolean PSO with velocity mutation. Magnetics, IEEE Transactions on.2009,45(3):1490-1493.
[140]L. Zhang, Y. C. Jiao, Z. B. Weng, F. S. Zhang. Design of planar thinned arrays using a Boolean differential evolution algorithm. Microwaves, Antennas & Propagation, IET.2010,4(12):2172-2178.
[141]A. Razavi, K. Forooraghi. Thinned arrays using pattern search algorithms. Progress In Electromagnetics Research.2008,78:61-71.
[142]J. Sun, B. Feng, W. Xu. Particle swarm optimization with particles having quantum behavior. Congress on Evolutionary Computation, Jiangsu, China 2004. IEEE: 325-331 Vol.321.
[143]G. K. Mahanti, N. N. Pathak, P. K. Mahanti. Synthesis of thinned linear antenna arrays with fixed sidelobe level using real-coded genetic algorithm. Progress In Electromagnetics Research.2007,75:319-328.
[144]N. Jin, Y. Rahmat-Samii. Hybrid real-binary particle swarm optimization (HPSO) in engineering electromagnetics. Antennas and Propagation, IEEE Transactions on. 2010,58(12):3786-3794.
[145]W. Keizer. Linear array thinning using iterative FFT techniques. Antennas and Propagation, IEEE Transactions on.2008,56(8):2757-2760.
[146]W. Keizer. Large planar array thinning using iterative FFT techniques. Antennas and Propagation, IEEE Transactions on.2009,57(10):3359-3362.
[147]E. C. Laskari, K. E. Parsopoulos, M. N. Vrahatis. Particle swarm optimization for integer programming.2002. IEEE:1582-1587.
[148]Z. L. Gaing. Constrained optimal power flow by mixed-integer particle swarm optimization.2005. IEEE:243-250 Vol.241.
[149]W. B. Wang, Q. Feng, D. Liu. Synthesis of Thinned Linear and Planar Antenna Arrays Using Binary PSO Algorithm. Progress In Electromagnetics Research.2012, 127:371-387.
[150]S. Mosca, M. Ciattaglia. Ant colony optimization to design thinned arrays.2006. IEEE:4675-4678.
[151]D. Chen, J. Li. GA Design of Large Thinned Arrays.3rd European Conference on Antennas Popag, Berlin,2009:451-455.
[152]X. Li, X. Yao. Cooperatively coevolving particle swarms for large scale optimization. Evolutionary Computation, IEEE Transactions on.2012,16(2):210-224.