基于拓扑结构与粒子变异改进的粒子群优化算法
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摘要
为使粒子群优化算法(PSO)优化过程的多样性与收敛性得到合理解决,以提高算法优化性能,基于种群拓扑结构与粒子变异提出两种粒子群改进算法RSMPSO和RVMPSO.改进算法将具有信息定向流动的闭环拓扑结构与星型拓扑结构或四边形拓扑结构相结合,促使粒子在前期寻优过程中具有较高的多样性,保证搜索的广度,而在后期满足粒子群的整体收敛性,保证寻优的精度.同时,将布谷鸟搜索算法(CS)中的偏好随机游走变异策略引入改进算法中,增强粒子跳出局部最优的能力.对标准测试函数的仿真实验表明,所改进的PSO算法与其他6个对比算法相比不仅操作简单,优化精度高,而且在算法收敛性及稳健性方面都有着更出色的表现.
Two kinds of modified particle swarm optimization(PSO) algorithms called particle swarm optimization with ring-star topology and particle mutation(RSMPSO) and particle swarm optimization with ring-von neumann topology and particle mutation(RVMPSO) are presented based on topology and mutation of particle swarm, which enable the diversity and convergence of the particle swarm to be preserved in optimizing procedure to improve the optimization performance of the PSO algorithm. In the modified PSO algorithms, the ring topology with information directionally flowing is combined with star topology or square topology. This strategy enables the particle to have more diversity during the early-stage optimizing to guarantee the search extent. And in the later period, this strategy enables the particle swarm to be converged to make sure the accuracy of optimizing. Meanwhile, a mutation strategy with random walk in a biased way in cuckoo search(CS) algorithm is introduced to the modified PSO algorithm to improve the ability of particle of escaping the local optimum. The simulation experiment on the standard test function shows that, compared with other six algorithms, the modified PSO algorithm possesses the features of easy operation and high optimizing accuracy, and a better performance in diversity and robustness.
Two kinds of modified particle swarm optimization(PSO) algorithms called particle swarm optimization with ring-star topology and particle mutation(RSMPSO) and particle swarm optimization with ring-von neumann topology and particle mutation(RVMPSO) are presented based on topology and mutation of particle swarm, which enable the diversity and convergence of the particle swarm to be preserved in optimizing procedure to improve the optimization performance of the PSO algorithm. In the modified PSO algorithms, the ring topology with information directionally flowing is combined with star topology or square topology. This strategy enables the particle to have more diversity during the early-stage optimizing to guarantee the search extent. And in the later period, this strategy enables the particle swarm to be converged to make sure the accuracy of optimizing. Meanwhile, a mutation strategy with random walk in a biased way in cuckoo search(CS) algorithm is introduced to the modified PSO algorithm to improve the ability of particle of escaping the local optimum. The simulation experiment on the standard test function shows that, compared with other six algorithms, the modified PSO algorithm possesses the features of easy operation and high optimizing accuracy, and a better performance in diversity and robustness.
引文
[1] Eberhart R, Kennedy J. A new optimizer using particle swarm theory[C]. Proc of the 6th Int Symposium on Micro Machine and Human Science. Nagoya:IEEE,1995:39-43.
[2] Poli R. An analysis of publications on particle swarm optimization applications[R]. London:Department of Computer Science In University of Essex, 2007:1-41.
[3] Shi Y, Eberhart R. A modified particle swarm optimizer[C]. Proce of IEEE Int Conf on Evolutionary Computation. Piscataway:IEEE, 1998:69-73.
[4]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.(Dai W Z, Yang X L. Particle swarm optimization algorithm based on inertia weight logarithmic decreasing[J]. Computer Engineering and Applications,2015, 51(17):14-19.)
[5]吴秋波,王允诚,赵秋亮,等.混沌惯性权值调整策略的粒子群优化算法[J].计算机工程与应用, 2009,45(7):49-51.(Wu Q B, Wang Y C, Zhao Q L, et al. Particle swarm optimization with chaotic inertia weight adjusting strategy[J]. Computer Engineering and Applications,2009, 45(7):49-51.)
[6]赵志刚,黄树运,王伟倩.基于随机惯性权重的简化粒子群优化算法[J].计算机应用研究, 2014, 31(2):361-363.(Zhao Z G, Huang S Y, Wang W Q. Simplified particle swarm optimization algorithm based on stochastic inertia weight[J]. Application Research of Computers, 2014,31(2):361-363.)
[7] Zheng Y J, Ling H F, Guan Q. Adaptive parameters for a modified comprehensive learning particle swarm optimizer[J]. Mathematical Problems in Engineering,2012, 68(3):939-955.
[8] Zhan Z H, Zhang J, Li Y, et al. Adaptive particle swarm optimization[J]. IEEE Trans on Systems, Man,and Cybernetics, Part B, 2009, 39(6):1362-1381.
[9]高哲,廖晓钟.基于平均速度的混合自适应粒子群算法[J].控制与决策, 2012, 27(1):152-155.(Gao Z, Liao X Z. Hybrid adaptive particle swarm optimization based on average velocity[J]. Control and Decision, 2012, 27(1):152-155.)
[10] Kennedy J, Mendes R. Population structure and particle swarm performance[C]. Proc of the 2002 Congress on Evolutionary Computation. Washington:IEEE, 2002, 2:1671-1676.
[11] Van den Bergh F, Engelbrecht A P. A cooperative approach to particle swarm optimization[J]. IEEE Trans on Evolutionary Computation, 2004, 8(3):225-239.
[12] Liang J J, Qin A K, Suganthan P N, et al. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[J]. IEEE Trans on Evolutionary Computation, 2006, 10(3):281-295.
[13] Wang H, Sun H, Li C, et al. Diversity enhanced particle swarm optimization with neighborhood search[J].Information Sciences, 2013, 223:119-135.
[14]石松,陈云.层次环形拓扑结构的动态粒子群算法[J].计算机工程与应用, 2013, 49(8):1-5.(Shi S, Chen Y. Dynamic particle swarm optimization algorithm with hierarchical ring topology[J]. Computer Engineering and Applications, 2013, 49(8):1-5.)
[15]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策, 2005, 20(5):500-504.(Wang H Q, Cao C X. Parallel particle swarm optim ization based on sim ulated annealing[J]. Control and Decision, 2005, 20(5):500-504.)
[16] Sun J, Wu X, Palade V, et al. Random drift particle swarm optimization algorithm:Convergence analysis and parameter selection[J]. Machine Learning, 2015,101(1/3):345-376.
[17]李蓉,沈云波,刘坚.改进的自适应粒子群优化算法[J].计算机工程与应用, 2015, 51(13):31-36.(Li R, Shen Y B, Liu J. Improved adaptive particle swarm optimization algorithm[J]. Computer Engineering and Applications, 2015, 51(13):31-36.)
[18]高云龙,闫鹏.基于多种群粒子群算法和布谷鸟搜索的联合寻优算法[J].控制与决策, 2016, 31(4):601-608.(Gao Y L, Yan P. Unified optimization based on multi-swarm PSO algorithm and cuckoo search algorithm[J]. Control and Decision, 2016, 31(4):601-608.)
[19]周利军,彭卫,邹芳,等.自适应变异粒子群算法[J].计算机工程与应用, 2016, 52(7):50-55.(Zhou L J, Peng W, Zou F, et al. Particle swarm optimization based on self-adaptive mutation[J].Computer Engineering and Applications, 2016, 52(7):50-55.)
[20]袁晗,徐春梅,杨平,等.一种基于子群变异的粒子群优化算法[J].计算机应用研究, 2017, 34(4):1076-1079.(Yuan H, Xu C M, Yang P, et al. New particle swarm optimization based on subswarm mutation[J].Application Research of Computers, 2017, 34(4):1076-1079.)
[21] Clerc M, Kennedy J. The particle swarm-explosion,stability, and convergence in a multidimensional complex space[J]. IEEE Trans on Evolutionary Computation,2002, 6(1):58-73.
[22] Trelea I C. The particle swarm optimization algorithm:convergence analysis and parameter selection[J].Information Processing Letters, 2003, 85(6):317-325.
[23] Yang X S, Deb S. Engineering optimisation by cuckoo search[J]. Int J of Mathematical Modelling&Numerical Optimisation, 2010, 1(4):330-343.
[24] Salomon R. Re-evaluating genetic algorithm perform-ance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms[J]. Bio Systems, 1996,39(3):263-278.
[2] Poli R. An analysis of publications on particle swarm optimization applications[R]. London:Department of Computer Science In University of Essex, 2007:1-41.
[3] Shi Y, Eberhart R. A modified particle swarm optimizer[C]. Proce of IEEE Int Conf on Evolutionary Computation. Piscataway:IEEE, 1998:69-73.
[4]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.(Dai W Z, Yang X L. Particle swarm optimization algorithm based on inertia weight logarithmic decreasing[J]. Computer Engineering and Applications,2015, 51(17):14-19.)
[5]吴秋波,王允诚,赵秋亮,等.混沌惯性权值调整策略的粒子群优化算法[J].计算机工程与应用, 2009,45(7):49-51.(Wu Q B, Wang Y C, Zhao Q L, et al. Particle swarm optimization with chaotic inertia weight adjusting strategy[J]. Computer Engineering and Applications,2009, 45(7):49-51.)
[6]赵志刚,黄树运,王伟倩.基于随机惯性权重的简化粒子群优化算法[J].计算机应用研究, 2014, 31(2):361-363.(Zhao Z G, Huang S Y, Wang W Q. Simplified particle swarm optimization algorithm based on stochastic inertia weight[J]. Application Research of Computers, 2014,31(2):361-363.)
[7] Zheng Y J, Ling H F, Guan Q. Adaptive parameters for a modified comprehensive learning particle swarm optimizer[J]. Mathematical Problems in Engineering,2012, 68(3):939-955.
[8] Zhan Z H, Zhang J, Li Y, et al. Adaptive particle swarm optimization[J]. IEEE Trans on Systems, Man,and Cybernetics, Part B, 2009, 39(6):1362-1381.
[9]高哲,廖晓钟.基于平均速度的混合自适应粒子群算法[J].控制与决策, 2012, 27(1):152-155.(Gao Z, Liao X Z. Hybrid adaptive particle swarm optimization based on average velocity[J]. Control and Decision, 2012, 27(1):152-155.)
[10] Kennedy J, Mendes R. Population structure and particle swarm performance[C]. Proc of the 2002 Congress on Evolutionary Computation. Washington:IEEE, 2002, 2:1671-1676.
[11] Van den Bergh F, Engelbrecht A P. A cooperative approach to particle swarm optimization[J]. IEEE Trans on Evolutionary Computation, 2004, 8(3):225-239.
[12] Liang J J, Qin A K, Suganthan P N, et al. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[J]. IEEE Trans on Evolutionary Computation, 2006, 10(3):281-295.
[13] Wang H, Sun H, Li C, et al. Diversity enhanced particle swarm optimization with neighborhood search[J].Information Sciences, 2013, 223:119-135.
[14]石松,陈云.层次环形拓扑结构的动态粒子群算法[J].计算机工程与应用, 2013, 49(8):1-5.(Shi S, Chen Y. Dynamic particle swarm optimization algorithm with hierarchical ring topology[J]. Computer Engineering and Applications, 2013, 49(8):1-5.)
[15]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策, 2005, 20(5):500-504.(Wang H Q, Cao C X. Parallel particle swarm optim ization based on sim ulated annealing[J]. Control and Decision, 2005, 20(5):500-504.)
[16] Sun J, Wu X, Palade V, et al. Random drift particle swarm optimization algorithm:Convergence analysis and parameter selection[J]. Machine Learning, 2015,101(1/3):345-376.
[17]李蓉,沈云波,刘坚.改进的自适应粒子群优化算法[J].计算机工程与应用, 2015, 51(13):31-36.(Li R, Shen Y B, Liu J. Improved adaptive particle swarm optimization algorithm[J]. Computer Engineering and Applications, 2015, 51(13):31-36.)
[18]高云龙,闫鹏.基于多种群粒子群算法和布谷鸟搜索的联合寻优算法[J].控制与决策, 2016, 31(4):601-608.(Gao Y L, Yan P. Unified optimization based on multi-swarm PSO algorithm and cuckoo search algorithm[J]. Control and Decision, 2016, 31(4):601-608.)
[19]周利军,彭卫,邹芳,等.自适应变异粒子群算法[J].计算机工程与应用, 2016, 52(7):50-55.(Zhou L J, Peng W, Zou F, et al. Particle swarm optimization based on self-adaptive mutation[J].Computer Engineering and Applications, 2016, 52(7):50-55.)
[20]袁晗,徐春梅,杨平,等.一种基于子群变异的粒子群优化算法[J].计算机应用研究, 2017, 34(4):1076-1079.(Yuan H, Xu C M, Yang P, et al. New particle swarm optimization based on subswarm mutation[J].Application Research of Computers, 2017, 34(4):1076-1079.)
[21] Clerc M, Kennedy J. The particle swarm-explosion,stability, and convergence in a multidimensional complex space[J]. IEEE Trans on Evolutionary Computation,2002, 6(1):58-73.
[22] Trelea I C. The particle swarm optimization algorithm:convergence analysis and parameter selection[J].Information Processing Letters, 2003, 85(6):317-325.
[23] Yang X S, Deb S. Engineering optimisation by cuckoo search[J]. Int J of Mathematical Modelling&Numerical Optimisation, 2010, 1(4):330-343.
[24] Salomon R. Re-evaluating genetic algorithm perform-ance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms[J]. Bio Systems, 1996,39(3):263-278.
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