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To improve the prediction accuracy of the chaotic time series prediction model, a composite optimization method of the differential evolution (DE) algorithm that is based on the phase space reconstruction and least square supported vector machine (LSSVM), is proposed. The phase space parameters and LSSVM model parameters are taken as differential evolution algorithm individuals while the prediction accuracy of the chaotic time series is used as the evaluation function of DE algorithm. The optimal parameters are obtained by mutation, crossover, and selection operators of DE algorithm. Several numerical simulation results show that not only four parameters are determined at the same time, but also the performance of chaotic time series prediction is improved.
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Keywords:
- chaotic time series /
- differential evolution algorithm /
- parameter composite optimization /
- prediction
[1] Peng S G, Yu S M 2009 Chin. Phys. B 18 3758
[2] Xiang C S, Yuan Z M, Zhou Z Y 2011 Information and Control 40 673(in Chinese) [向昌盛, 袁哲明, 周子英 2011 信息与控制 40 673]
[3] Fraser A M 1989 IEEE Trans. Inform. Theory 35 245
[4] Albano A M 1988 Phys. Rev. A 38 3017
[5] Kugiumtzis D 1996 Physica D 95 13
[6] Kim H S, Eykholt R Salas J D 1999 Physica D 127 48
[7] Ataei M, Lohmann B, Khaki-Sedigh A, Lucas C 2004 Chaos, Solitons and Fractals 19 1131
[8] Chen D Y, Liu Y, Ma S Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义2012 61 100501]
[9] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[10] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120(in Chinese) [王永生, 孙瑾, 王昌金, 范洪达 2008 57 6120]
[11] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[12] Ye M Y, Wang X D 2004 Chin. Phys. 13 454
[13] Long W, Liang X M, Long Z Q, Li Z H 2011 J. Central South University 42 3408 (in Chinese) [龙文, 梁昔明, 龙祖强, 李朝辉 中南大学学报 42 3408]
[14] Zhang Q R, Ma Q L, Peng H 2010 Acta Phys.Sin. 59 7623(in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[15] Storn R, Price K 1997 J. Global Optim. 11 341
[16] Wang Y, Cai Z X, Zhang Q F 2011 IEEE Trans. Evolu. Comput. 15 55
[17] Ren Z W, San Y 2007 Acta Elec. Sin. 35 269 (in Chinese) [任子武, 伞冶 2007 电子学报 35 269]
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[1] Peng S G, Yu S M 2009 Chin. Phys. B 18 3758
[2] Xiang C S, Yuan Z M, Zhou Z Y 2011 Information and Control 40 673(in Chinese) [向昌盛, 袁哲明, 周子英 2011 信息与控制 40 673]
[3] Fraser A M 1989 IEEE Trans. Inform. Theory 35 245
[4] Albano A M 1988 Phys. Rev. A 38 3017
[5] Kugiumtzis D 1996 Physica D 95 13
[6] Kim H S, Eykholt R Salas J D 1999 Physica D 127 48
[7] Ataei M, Lohmann B, Khaki-Sedigh A, Lucas C 2004 Chaos, Solitons and Fractals 19 1131
[8] Chen D Y, Liu Y, Ma S Y 2012 Acta Phys. Sin. 61 100501 (in Chinese) [陈帝伊, 柳烨, 马孝义2012 61 100501]
[9] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[10] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120(in Chinese) [王永生, 孙瑾, 王昌金, 范洪达 2008 57 6120]
[11] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[12] Ye M Y, Wang X D 2004 Chin. Phys. 13 454
[13] Long W, Liang X M, Long Z Q, Li Z H 2011 J. Central South University 42 3408 (in Chinese) [龙文, 梁昔明, 龙祖强, 李朝辉 中南大学学报 42 3408]
[14] Zhang Q R, Ma Q L, Peng H 2010 Acta Phys.Sin. 59 7623(in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[15] Storn R, Price K 1997 J. Global Optim. 11 341
[16] Wang Y, Cai Z X, Zhang Q F 2011 IEEE Trans. Evolu. Comput. 15 55
[17] Ren Z W, San Y 2007 Acta Elec. Sin. 35 269 (in Chinese) [任子武, 伞冶 2007 电子学报 35 269]
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