基于诺兰模型思想的改进混沌粒子群优化算法及评价
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摘要
针对粒子群优化算法(PSO)在处理高维复杂函数时容易陷入局部极值、收敛速度慢的缺陷,从系统的认知分析过程和角度出发,提出一种基于诺兰模型(NM)思想的改进PSO算法.该算法在Tent混沌映射选择的参数的基础上,结合NM信息融合和协调的思想,在速度更新过程中增加均衡项,并设计粒子群的欧氏距离指数以防止早熟,从而实现对粒子的自动调整、保证多样性和提高算法的全局搜索能力.最后,运用典型函数对所提出算法进行测试,并与最新相关算法进行比较,结果表明,所提出算法在全局搜索能力、效率和稳定性方面均具有明显的优势.
Aiming at the problem that the particle swarm optimization(PSO) algorithm trends to trap in local extreme, and performs high dimensional complex functions inefficiently, from perspectives of the cognitive analysis process of the system,a PSO algorithm based on Nolan model is proposed. The Tent chaotic map is introduced to improve the ergodicity of the algorithm, and the Euclidean distance index is given based on particle average position to automatically adjust particles' position and ensure diversity to improve the global search capacity of the algorithm. Finally, typical functions are used to test the proposed method. Compared with the current algorithms, it is showed that the proposed method has the advantages in global search, efficiency and stability.
Aiming at the problem that the particle swarm optimization(PSO) algorithm trends to trap in local extreme, and performs high dimensional complex functions inefficiently, from perspectives of the cognitive analysis process of the system,a PSO algorithm based on Nolan model is proposed. The Tent chaotic map is introduced to improve the ergodicity of the algorithm, and the Euclidean distance index is given based on particle average position to automatically adjust particles' position and ensure diversity to improve the global search capacity of the algorithm. Finally, typical functions are used to test the proposed method. Compared with the current algorithms, it is showed that the proposed method has the advantages in global search, efficiency and stability.
引文
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[18]匡芳君,徐蔚鸿,张思扬.基于改进混沌粒子群的混合核SVM参数优化及应用[J].计算机应用研究,2013,31(3):671-674.(Kuang F J,Xu W H,Zhang S Y.Parameter optimization and application of SVM with mixtures kernels based on improved chaotic particle swarm optimization[J].Application Research of Computers,2013,31(3):671-674.)
[19]唐苏妍,朱一凡,张伟,等.一种基于创造性思维的粒子群优化算法[J].控制与决策,2011,26(8):1181-1186.(Tang S Y,Zhu Y F,Zhang W,et al.Particle swarm optimization algorithm based on creative thinking[J].Control and Decision,2011,26(8):1181-1186.)
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[24]Chen X,Li Y.An improved stochastic PSO with high exploration ability[C].Proc of the IEEE Congress on Swarm Intellgence Symposium.Indianapolis:IEEE,2006:228-235.
[25]赵欣.不同一维混沌映射的优化性能比较研究[J].计算机应用研究,2012,29(3):913-915.(Zhao X.Research on optimization performance comparison of different one-dimensional chaotic maps[J].Application Research of Computers,2012,29(3):913-915.)
[26]张浩,张铁男,沈继红,等.Tent混沌粒子群算法及其在结构优化决策中的应用[J].控制与决策,2008,23(8):857-862.(Zhang H,Zhang T N,Shen J H,et al.Research on decision-makings of structure optimization based on improved Tent PSO[J].Control and Decision,2008,23(8):857-862.)
[27]李玉英.带创造性思维的混沌蚂蚁优化算法[J].控制与决策,2014,29(5):937-940.(Li Y Y.Chaotic ant swarm optimization algorithm with creative thinking[J].Control and Decision,2014,29(5):937-940.)
[28]Mendes R,Kennedy J,Neves J.The fully informed particle swarm:Simpler,maybe better[J].IEEE Trans on Evolutionary Computation,2004,8(3):204-210.
[2]Kennedy J,Eberhart R.Particle swarm optimization[C].IEEE Int Conf on Networks.Perth:IEEE Press,1995:1942-1948.
[3]Yin P Y,Yu S S,Wang P P,et al.Multi-objective task allocation in distributed computing systems by hybrid particle swarm optimization[J].Applied Mathematics and Computation,2007,184(2):407-420.
[4]del Valle Y,Venayagamoorthy G,Mohagheghi S,et al.Particle swarm optimization:Basic concepts,variants and applications in power systems[J].IEEE Trans on Evolutionary Computation,2008,12(2):171-195.
[5]Rainer Storn.Designing nonstandard filters with differential evolution[J].IEEE Signal Processing Magazine,2005,22(1):103-106.
[6]Park J,Choi K,Allstot D J.Parasitic-aware RF circuit design and optimization[J].IEEE Trans on Circuits and Systems I:Fundamental Theory and Applications,2004,51(10):1953-1966.
[7]Mukherjee V,Ghoshal S P.Intelligent particle swarm optimized fuzzy PID controller for AVR system[J].Electric Power Systems Research,2006,77(12):1689-1698.
[8]Wu H,Sun F C,Sun Z Q,et al.Optimal trajectory planning of a flexible dual-arm space robot with vibration reduction[J].J of Intelligent&Robotic Systems,2004,40(2):147-163.
[9]Pavlidis N G,Parsopoulos K E,Vrahatis M N.Computing nash equilibria through computational intelligence methods[J].J of Computational and Applied Mathematics,2005,175(1):113-136.
[10]Rasmussen T K,Krink T.Improved hidden Markov model training for multiple sequence alignment by a particle swarm optimization-evolutionary algorithm hybrid[J].Biosystems,2003,72(1/2):5-17.
[11]Shen Q,Jiang J H,Jiao C X,et al.Modified particle swarm optimization algorithm for variable selection in mlr and pls modeling:Qsar studies of antagonism of angiotensin ii antagonists[J].European J of Pharmaceutical Sciences,2004,22(2/3):145-152.
[12]沈林成,霍霄华,牛轶峰.离散粒子群优化算法研究现状综述[J].系统工程与电子技术,2008,30(10):1986-1990.(Shen L C,Huo X H,Niu Y F.Survey of discrete particle swarm optimization algorithm[J].Systems Engineering and Electronics,2008,30(10):1986-1990.)
[13]Gregorio Toscano Pulido,Carlos A Coello Coello.A constraint-handling mechanism for particle swarm optimization[C].IEEE CEC06.Portland:IEEE,2004:1396-1403.
[14]Margarita Reyes-Sierra,Carlos A Coello Coello.Multiobjective particle swarm optimizers:a survey of the stateof-the-art[J].Int J of Computational Intelligence Research,2006,2(3):287-308.
[15]Carlisle A,Dozierv G.Adapting particle swarm optimization to dynamic environments[C].Proc of the Int Conf on Artificial Intelligence.Las Vegas:CSREA Press,2000:429-434.
[16]齐名军,杨爱红.一种混沌优化机制的双量子粒子群优化算法[J].计算机工程与应用,2009,45(30):34-36.(Qi M J,Yang A H.Double quantum delta particle swarm optimization based on chaos optimization strategy[J].Computer Engineering and Applications,2009,45(30):34-36.)
[17]刘道华,原思聪,兰洋,等.混沌映射的粒子群优化设计[J].西安电子科技大学学报,2010,37(4):764-768.(Liu D H,Yuan S C,Lan Y,et al.Method of particle swarm optimization based on the chaos map[J].J of Xidian University,2010,37(4):764-768.)
[18]匡芳君,徐蔚鸿,张思扬.基于改进混沌粒子群的混合核SVM参数优化及应用[J].计算机应用研究,2013,31(3):671-674.(Kuang F J,Xu W H,Zhang S Y.Parameter optimization and application of SVM with mixtures kernels based on improved chaotic particle swarm optimization[J].Application Research of Computers,2013,31(3):671-674.)
[19]唐苏妍,朱一凡,张伟,等.一种基于创造性思维的粒子群优化算法[J].控制与决策,2011,26(8):1181-1186.(Tang S Y,Zhu Y F,Zhang W,et al.Particle swarm optimization algorithm based on creative thinking[J].Control and Decision,2011,26(8):1181-1186.)
[20]赵辉.诺兰模型的启示[Z].中国计算机报,2007-5-28(B16).(Zhao H.The enlightenment of nolan model[Z].China Information Word,2007-5-28(B16).)
[21]韩崇昭,朱洪艳,段战胜.多源信息融合[M].第2版.北京:清华大学出版社,2010:1-25.(Han C Z,Zhu H Y,Duan Z S.Multi-source information fusion[M].2nd ed.Beijing:Tsinghua University Press,2010:1-25.)
[22]Shi Y,Eberhart R.A modified particle swarm optimization[C].Proc of the IEEE Congress on Evolutionary Computation.Piscataway:IEEE Press,1998:303-308.
[23]Shi Y,Eberhart R.Empirical study of particle swarm optimization[C].Proc of the Congress on Evolutionary Computation.Washington DC:IEEE,1999:1945-1950.
[24]Chen X,Li Y.An improved stochastic PSO with high exploration ability[C].Proc of the IEEE Congress on Swarm Intellgence Symposium.Indianapolis:IEEE,2006:228-235.
[25]赵欣.不同一维混沌映射的优化性能比较研究[J].计算机应用研究,2012,29(3):913-915.(Zhao X.Research on optimization performance comparison of different one-dimensional chaotic maps[J].Application Research of Computers,2012,29(3):913-915.)
[26]张浩,张铁男,沈继红,等.Tent混沌粒子群算法及其在结构优化决策中的应用[J].控制与决策,2008,23(8):857-862.(Zhang H,Zhang T N,Shen J H,et al.Research on decision-makings of structure optimization based on improved Tent PSO[J].Control and Decision,2008,23(8):857-862.)
[27]李玉英.带创造性思维的混沌蚂蚁优化算法[J].控制与决策,2014,29(5):937-940.(Li Y Y.Chaotic ant swarm optimization algorithm with creative thinking[J].Control and Decision,2014,29(5):937-940.)
[28]Mendes R,Kennedy J,Neves J.The fully informed particle swarm:Simpler,maybe better[J].IEEE Trans on Evolutionary Computation,2004,8(3):204-210.