基于S型函数的自适应粒子群优化算法
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摘要
针对粒子群算法求解精度低和后期收敛速度慢等问题,提出了一种基于S型函数的自适应粒子群优化算法SAPSO (S-shaped function based Adaptive Particle Swarm Optimization)。该算法利用倒S型函数的特点,实现了对惯性权重的非线性调整,从而更好地平衡算法的全局搜索能力和局部搜索能力;同时,在算法的位置更新公式中引入S型函数,并利用个体粒子自身的适应度值与群体平均适应度值的比值自适应地调整搜索步长,从而提高算法的搜索效率。在若干经典测试函数上的仿真实验结果表明,与已有的几种改进粒子群算法相比,SAPSO在收敛速度和求解精度方面均有较大优势。
Aiming at the problems of low solution precision and slow convergence speed in the later stage of particle swarm optimization algorithm,this paper presented an S-shaped function based adaptive particle swarm optimization algorithm(SAPSO).This algorithm takes advantage of the characteristics of upside-down S-shaped function to adjust the inertia weight nonlinearly,better balancing the global search ability and local search ability.In addition,an S-shape function is introduced into the position updating equation,and the ratio of the individual particle's fitness value to the swarm's average fitness value is used to adaptively adjust the step size in the search,thus enhancing the efficiency of the algorithm.Simulation results on a set of typical test functions show that SAPSO is superior to several existing improved PSO algorithms significantly in terms of the convergence rate and solution accuracy.
Aiming at the problems of low solution precision and slow convergence speed in the later stage of particle swarm optimization algorithm,this paper presented an S-shaped function based adaptive particle swarm optimization algorithm(SAPSO).This algorithm takes advantage of the characteristics of upside-down S-shaped function to adjust the inertia weight nonlinearly,better balancing the global search ability and local search ability.In addition,an S-shape function is introduced into the position updating equation,and the ratio of the individual particle's fitness value to the swarm's average fitness value is used to adaptively adjust the step size in the search,thus enhancing the efficiency of the algorithm.Simulation results on a set of typical test functions show that SAPSO is superior to several existing improved PSO algorithms significantly in terms of the convergence rate and solution accuracy.
引文
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[16]GOU J,LEI Y X,GUO W P,et al.A novel improved particle swarm optimization algorithm based on individual difference evolution[J].Applied Soft Computing,2017,57:468-481.
[17]CHENG T,CHEN M,YANG Z,et al.A novel hybrid teaching learning based multi-objectiveparticle swarm optimization[J].Neurocomputing,2016,222(C):11-25.
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[19]DAI W Z,YANG X L.Particle swarm optimization algorithm based on inertia weight logarithmic decreasing[J].Computer Engineeringand Application,2015,51(17):14-19.(in Chinese)戴文智,杨新乐.基于惯性权重对数递减的粒子群优化算法[J].计算机工程与应用,2015,51(17):14-19.
[20]LI H L,LUO L,PU D M,et al.Improved particle optimization algorithm based on Cauchy distribution[J].Electronic Science and Technology,2016,29(1):33-35.(in Chinese)黎红玲,罗林,蒲冬梅,等.基于柯西分布的粒子群优化算法改进[J].电子科技,2016,29(1):33-35.
[21]JIANG J G,TIAN W,WANG X Q,et al.Adaptive particle swarm optimization via disturbing acceleration coefficients[J].Journal of Xidian University,2012,39(4):74-80.(in Chinese)姜建国,田旻,王向前,等.采用扰动加速因子的自适应粒子群优化算法[J].西安电子科技大学学报,2012,39(4):74-80.
[22]ZHANG J K,LIU S Y,ZHANG X Q.Improved particle swarm optimization[J].Computer Engineering and Design,2007,28(17):4215-4216.(in Chinese)张建科,刘三阳,张晓清.改进的粒子群算法[J].计算机工程与设计,2007,28(17):4215-4216.
[23]LIU J S,HE J J,LI P F.Improved particle swarm optimization algorithm based on theory of complex adaptive system[J].Computer Engineering and Application,2017,53(5):57-63.(in Chinese)刘举胜,何建佳,李鹏飞.基于CAS理论的改进PSO算法[J].计算机工程与应用,2017,53(5):57-63.
[24]龚纯,王正林.精通MATLAB最优化计算[M].北京:电子工业出版社,2001.
[25]WU R X,SUN H,ZHU D G,et al.Particle swarm optimization algorithm based on optimal particle guidance and Gauss perturbance[J].Journal of Chinese Computer Systems,2016,37(1):146-151.(in Chinese)吴润秀,孙辉,朱德刚,等.具有高斯扰动的最优粒子引导粒子群优化算法[J].小型微型计算机系统,2016,37(1):146-151.
[26]ZHENG C Y,ZHENG Q D,WANG X D,et al.Self-adaptive particle swarm optimization algorithm based on tentative adjusting step factor[J].Computer Science,2009,36(11):193-195.(in Chinese)郑春颖,郑全第,王晓丹,等.基于试探的变步长自适应粒子群算法[J].计算机科学,2009,36(11):193-195.
[2]HOLLAND J H.Adaptation in Natural and Artificial Systems[D].Ann Arbor:University of Michigan press,1975.
[3]COLORNI A,DORIGO M,MANIEZZO V,et al.Distributed optimization by ant colonies[C]∥Proceedings of European Conference on Artificial Life.Paris,1991:134-142.
[4]LIU Z H,WEI H W,ZHONG Q C,et al.Parameter Estimation for VSI-Fed PMSM based on a Dynamic PSO with Learning Strategies[J].IEEE Transactions on Power Electronics,2017,32(4):3154-3165.
[5]LIU Z H,LI X H,ZHANG H Q,et al.An Enhanced Approach for Parameter Estimation Using Immune Dynamic Learning PSOBased on Multi-core Architecture[J].IEEE Systems,Man,and Cybernetics Magazine,2016,2(1):26-33.
[6]LIU Z H,WEI H W,ZHONG Q C,et al.GPU Implementation of DPSO-RE Algorithm for Parameters Identification of Surface PMSM Considering VSI Nonlinearity[J].IEEE Journal of Emerging and Selected Topics in Power Electronics,2017,5(3):1334-1345.
[7]LIU Z H,ZHANG J,ZHOU S W,et al.Coevolutionary Particle Swarm Optimization Using AIS and Its Application in Multi-parameter estimation of PMSM[J].IEEE Transactions on Cybernetics,2013,43(6):1921-1935.
[8]SHI Y,EBERHARTRC.A modified particle swarm optimizer[C]∥Proceedings of the 1998IEEE International Conference on Evolutionary Computation(ICEC’98).NJ:IEEE Press,1998:69-73.
[9]RATNAWEERAA,HALGAMUGE S K,WATSON H C.Selforganizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J].IEEE Transactions on Evolutionary Computation,2004,8(3):240-255.
[10]CLERC M,KENNEDY J.The particle swarm-explosion,stability and convergence in a multidimensional complex space[J].IEEE Transactions on Evolutionary Computation,2002,6(1):58-73.
[11]ZHU T,LI X F,LU M W.Improved particle swarm optimization with position weighted[J].Computer Engineering and Applications,2011,47(5):4-6.(in Chinese)朱童,李小凡,鲁明文.位置加权的改进粒子群算法[J].计算机工程与应用,2011,47(5):4-6.
[12]MELO H,WATADA J.Gaussian-PSO with fuzzy reasoning based on structural learning for training a Neural Network[J].Neurocomputing,2016,172:405-412.
[13]AI B,DONG M G.Improved particle swarm optimization algorithm based on Gaussian disturbance and natural selection[J].Journal of Computer Applications,2016,36(36):687-691.(in Chinese)艾兵,董明刚.基于高斯扰动和自然选择的改进粒子群算法[J].计算机应用,2016,36(36):687-691.
[14]ZHAN Z H,ZHANG J,LI Y,et al.Adaptive particleswarmoptimization[J].IEEE Transactions on Systems Man&Cybernetics,2009,39(6):1362-1381.
[15]JAVIDRAD F,NAZARI M.A new hybrid particle swarm and simulated annealing stochastic optimization method[J].Applied Soft Computing,2017,60:634-654.
[16]GOU J,LEI Y X,GUO W P,et al.A novel improved particle swarm optimization algorithm based on individual difference evolution[J].Applied Soft Computing,2017,57:468-481.
[17]CHENG T,CHEN M,YANG Z,et al.A novel hybrid teaching learning based multi-objectiveparticle swarm optimization[J].Neurocomputing,2016,222(C):11-25.
[18]CHEN G M,JIA J Y,HAN Q.Study on the strategy of decreasing inertia weight in particle swarm optimization algorithm[J].Journal of Xi’an Jiaotong University,2006,40(1):53-56.(in Chinese)陈贵敏,贾建援,韩琪.粒子群优化算法的惯性权值递减策略研究[J].西安交通大学学报,2006,40(1):53-56.
[19]DAI W Z,YANG X L.Particle swarm optimization algorithm based on inertia weight logarithmic decreasing[J].Computer Engineeringand Application,2015,51(17):14-19.(in Chinese)戴文智,杨新乐.基于惯性权重对数递减的粒子群优化算法[J].计算机工程与应用,2015,51(17):14-19.
[20]LI H L,LUO L,PU D M,et al.Improved particle optimization algorithm based on Cauchy distribution[J].Electronic Science and Technology,2016,29(1):33-35.(in Chinese)黎红玲,罗林,蒲冬梅,等.基于柯西分布的粒子群优化算法改进[J].电子科技,2016,29(1):33-35.
[21]JIANG J G,TIAN W,WANG X Q,et al.Adaptive particle swarm optimization via disturbing acceleration coefficients[J].Journal of Xidian University,2012,39(4):74-80.(in Chinese)姜建国,田旻,王向前,等.采用扰动加速因子的自适应粒子群优化算法[J].西安电子科技大学学报,2012,39(4):74-80.
[22]ZHANG J K,LIU S Y,ZHANG X Q.Improved particle swarm optimization[J].Computer Engineering and Design,2007,28(17):4215-4216.(in Chinese)张建科,刘三阳,张晓清.改进的粒子群算法[J].计算机工程与设计,2007,28(17):4215-4216.
[23]LIU J S,HE J J,LI P F.Improved particle swarm optimization algorithm based on theory of complex adaptive system[J].Computer Engineering and Application,2017,53(5):57-63.(in Chinese)刘举胜,何建佳,李鹏飞.基于CAS理论的改进PSO算法[J].计算机工程与应用,2017,53(5):57-63.
[24]龚纯,王正林.精通MATLAB最优化计算[M].北京:电子工业出版社,2001.
[25]WU R X,SUN H,ZHU D G,et al.Particle swarm optimization algorithm based on optimal particle guidance and Gauss perturbance[J].Journal of Chinese Computer Systems,2016,37(1):146-151.(in Chinese)吴润秀,孙辉,朱德刚,等.具有高斯扰动的最优粒子引导粒子群优化算法[J].小型微型计算机系统,2016,37(1):146-151.
[26]ZHENG C Y,ZHENG Q D,WANG X D,et al.Self-adaptive particle swarm optimization algorithm based on tentative adjusting step factor[J].Computer Science,2009,36(11):193-195.(in Chinese)郑春颖,郑全第,王晓丹,等.基于试探的变步长自适应粒子群算法[J].计算机科学,2009,36(11):193-195.
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