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Based on the analysis of particle swarm optimization algorithm, the particle is described in the quantum space and the potential energy field model is created. And then according to the swarms gregariousness, the quantum-behaved particle swarm optimization (QPSO) algorithm is derived. Within the framework of random algorithms global convergence theorem, the convergence of QPSO algorithm is discussed and is proved to be a kind of global convergence algorithm. Three kinds of control strategy are proposed for the unique parameter of QPSO algorithm and they are tested on five benchmark functions. According to the test results, some conclusions concerning the selection of the parameter are drawn.
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Keywords:
- quantum system /
- potential well /
- global convergence /
- particle swarm optimization
[1] ［1］ Kennedy J, Eberhart R C 1995 IEEE International Conference on Neural Networks (Perth: IEEE) p1942
[2] ［2］Poli R, Kennedy J, Blackwell T, Freitas A 2008 J. Artif. Evol. Appl. 2008 1
[3] ［3］Clerc M, Kennedy J 2002 IEEE Trans. Evolut. Comput. 6 58
[4] ［4］Gao H B, Zhou C, Gao L 2005 Chin. J. Comput. 28 1980 (in Chinese) ［高海兵、周驰、高亮 2005 计算机学报 28 1980］
[5] ［5］Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) ［高飞、童恒庆 2006 物理学报 55 577］
[6] ［6］Wang D F, Han P 2006 Acta Phys. Sin. 55 1644 (in Chinese) ［王东风、韩璞 2006 物理学报 55 1644］
[7] ［7］Pan F, Chen J, Gan M G 2006 Acta Autom. Sin. 32 368 (in Chinese) ［潘峰、陈杰、甘明刚 2006 自动化学报 32 368］
[8] ［8］Zeng J C, Cui Z H 2006 J. Comput. Res. Dev. 43 96 (in Chinese) ［曾建潮、崔志华 2006 计算机研究与发展 43 96］
[9] ［9］Zhao Z J, Xu S Y, Zheng S L, Yang X N 2009 Acta Phys. Sin. 58 5118 (in Chinese) ［赵知劲、徐世宇、郑仕链、杨小牛 2009 物理学报 58 5118］
[10] ］Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) ［王校锋、薛红军、司守奎、姚跃亭 2009 物2理学报 58 3729］
[11] ］Van den Bergh F 2001 Ph. D. Dissertation (Pretoria: University of Pretoria)
[12] ］Eberhart R C, Shi Y 2001 IEEE Conference on Evolutionary Computation (Seoul: IEEE) p81
[13] ］Sun J, Feng B, Xu W B 2004 IEEE Congress on Evolutionary Computation (Hawaii: IEEE) p325
[14] ］Dos Santos Coelho L, Alotto P 2008 IEEE Trans. Magn. 44 1074
[15] ］Dos Santos Coelho L 2008 Chaos Solitons Fract. 37 1409
[16] ］Clerc M, Kennedy J 2002 IEEE Trans. Evolut. Comput. 6 58
[17] ］Sun J, Feng B, Xu W B 2004 IEEE Conference on Cybernetics and Intelligent Systems (Singapore: IEEE) p111
[18] ］Zeng J C, Jie J, Cui Z H 2004 Particle Swarm Algorithm (Beijing: Science Press) (in Chinese) ［曾建潮、介婧、崔志华 2004 微粒群算法 (北京: 科学出版社)］
[19] ］Wang L 2001 Intelligent Optimization Algorithms with Applications (Beijing: Tsinghua University Press) (in Chinese) ［王凌 2001 智能优化算法及其应用 (北京: 清华大学出版社)］
[20] ］Sun J, Xu W B, Feng B 2005 IEEE International Conference on Systems, Man and Cybernetics (Hawaii: IEEE) p3049
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[1] ［1］ Kennedy J, Eberhart R C 1995 IEEE International Conference on Neural Networks (Perth: IEEE) p1942
[2] ［2］Poli R, Kennedy J, Blackwell T, Freitas A 2008 J. Artif. Evol. Appl. 2008 1
[3] ［3］Clerc M, Kennedy J 2002 IEEE Trans. Evolut. Comput. 6 58
[4] ［4］Gao H B, Zhou C, Gao L 2005 Chin. J. Comput. 28 1980 (in Chinese) ［高海兵、周驰、高亮 2005 计算机学报 28 1980］
[5] ［5］Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese) ［高飞、童恒庆 2006 物理学报 55 577］
[6] ［6］Wang D F, Han P 2006 Acta Phys. Sin. 55 1644 (in Chinese) ［王东风、韩璞 2006 物理学报 55 1644］
[7] ［7］Pan F, Chen J, Gan M G 2006 Acta Autom. Sin. 32 368 (in Chinese) ［潘峰、陈杰、甘明刚 2006 自动化学报 32 368］
[8] ［8］Zeng J C, Cui Z H 2006 J. Comput. Res. Dev. 43 96 (in Chinese) ［曾建潮、崔志华 2006 计算机研究与发展 43 96］
[9] ［9］Zhao Z J, Xu S Y, Zheng S L, Yang X N 2009 Acta Phys. Sin. 58 5118 (in Chinese) ［赵知劲、徐世宇、郑仕链、杨小牛 2009 物理学报 58 5118］
[10] ］Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) ［王校锋、薛红军、司守奎、姚跃亭 2009 物2理学报 58 3729］
[11] ］Van den Bergh F 2001 Ph. D. Dissertation (Pretoria: University of Pretoria)
[12] ］Eberhart R C, Shi Y 2001 IEEE Conference on Evolutionary Computation (Seoul: IEEE) p81
[13] ］Sun J, Feng B, Xu W B 2004 IEEE Congress on Evolutionary Computation (Hawaii: IEEE) p325
[14] ］Dos Santos Coelho L, Alotto P 2008 IEEE Trans. Magn. 44 1074
[15] ］Dos Santos Coelho L 2008 Chaos Solitons Fract. 37 1409
[16] ］Clerc M, Kennedy J 2002 IEEE Trans. Evolut. Comput. 6 58
[17] ］Sun J, Feng B, Xu W B 2004 IEEE Conference on Cybernetics and Intelligent Systems (Singapore: IEEE) p111
[18] ］Zeng J C, Jie J, Cui Z H 2004 Particle Swarm Algorithm (Beijing: Science Press) (in Chinese) ［曾建潮、介婧、崔志华 2004 微粒群算法 (北京: 科学出版社)］
[19] ］Wang L 2001 Intelligent Optimization Algorithms with Applications (Beijing: Tsinghua University Press) (in Chinese) ［王凌 2001 智能优化算法及其应用 (北京: 清华大学出版社)］
[20] ］Sun J, Xu W B, Feng B 2005 IEEE International Conference on Systems, Man and Cybernetics (Hawaii: IEEE) p3049
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