1940 JOURNAL OF COMPUTERS, VOL. 6, NO. 9, SEPTEMBER 2011 ACKNOWLEDGMENT The authors are grateful to the anonymous referees for their valuable remarks and helpful suggestions, which have significantly improved the paper. This work was supported in part by a grant from the support <strong>of</strong> Key Project <strong>of</strong> Chinese National Programs for Fundamental Research and Development (973 Program) (2007CB7140 06), National Nature Science Foundation <strong>of</strong> China (61074020) and the Fundamental Research Funds for the Central Universities (DC10040101). REFERENCES [1] V. N. Vapnik, The Nature <strong>of</strong> Statistical Learning Theory, chapter 6, New York: Springer-Verlag, 1995. [2] V. N. Vapnik, “An Overview <strong>of</strong> Statistical Learning Theory,” IEEE Trans on Neural Networks, vol. 10, p. 988- 999, 1999. [3] J. A. 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Yang, “Dynamic temperature modeling <strong>of</strong> an SOFC using least squares support vector machines,” <strong>Journal</strong> <strong>of</strong> Power sources, vol. 179, p. 683-692, 2008. [12] P. F. Pai and W. C. Hong, “Support vector machines with simulated annealing algorithms in electricity load forecasting,” Energy Conversion andManagement, vol. 46, p. 2669-2688, 2005. [13] X. L. Tang, L. Zhang, J. Cai and C. B. Li, “Multi-fault classification based on support vector machine trained by chaos particle swarm optimization,” Knowledge-Based Systems, vol. 23, p. 486-490, 2010. [14] S. J. An, W. Q. Liu and S. Venkatesh, “Fast crossvalidation algorithms for least squares support vector machines and kernel ridge regression,” Pattern Recognition, vol. 40, p. 2154-2162, 2007. © 2011 ACADEMY PUBLISHER [15] W. T. Mao, G. R. Yan, L. L. Dong and D. Hu, “Model selection for least squares support vector regression based on small-world strategy,” Expert Systems with Applications, vol. 38, p. 3227-3237, 2011. [16] T. V. Gestel, J. A. K. Suykens and B. Baesens, S. Viaene, J. Vanthienen and G. Dedene, et al., “Benchmarking least squares support vector machine classifiers,” Machine Learning, vol. 54, p. 5-32, 2004. [17] L. X. Li, Y. X. Yang, H. P. Peng and X. D. Wang, “Parameters identification <strong>of</strong> chaotic systems via chaotic ant swarm,” Chaos, Solitons and Fractals, vol. 28, p. 1204–1211, 2006. [18] L. X. Li, Y. X. Yang, H. P. Peng and X. D. Wang, “An optimization method inspired by chaotic ant havior,” International <strong>Journal</strong> <strong>of</strong> Bifurcation Chaos, vol. 16, p. 2351-2364, 2006. [19] J. J. Cai, X. Q. Ma, L. X. Li, Y. X. Yang, H. P. Peng and X. D. Wang, “Chaotic ant swarm optimization to economic dispatch,” Electric Power Systems Research, vol. 77, p. 1373-1380, 2007. [20] L. X. Li, Y. X. Yang and, H. P. Peng, “Computation <strong>of</strong> multiple global optima through chaotic ant swarm,” Chaos, Solitons and Fractals, Vol. 40 (2009), p. 1399-1407. [21] Y. G. Tang, M. Y. Cui, Li L. X., H. P. Peng and X. P. Guan, “Parameter identification <strong>of</strong> time-delay chaotic system using chaotic ant swarm,” Chaos, Solitons and Fractals, vol. 41, p. 2097-2102, 2009. [22] L. X. Li, Y. X. Yang and, H. P. Peng, “Fuzzy system identification through chaotic ant swarm,” Chaos, Solitons and Fractals, vol. 41, p. 401-408, 2009. [23] H. Zhu, L. X. Li, Y. Zhao, Y. Guo and Y. X. Yang, “CAS algorithm-based optimum design <strong>of</strong> PID controller in AVR system,” Chaos, Solitons and Fractals, vol. 42, p. 792-800, 2009. [24] Y. Y. Li, Q. Y. Wen, L. X. Li and H. P. Peng, “Hybrid chaotic ant swarm optimization,” Chaos, Solitons and Fractals, vol. 42, p. 880-889, 2009. [25] W. C. Hong, “Application <strong>of</strong> chaotic ant swarm optimization in electric load forecasting,” Energy Policy, vol. 38, p. 5830-5839, 2010. [26] A. Chatterjee, S. P. Ghoshal and V. Mukherjee, “Chaotic ant swarm optimization for fuzzy-based tuning <strong>of</strong> power system stabilizer”, Electrical Power and Energy Systems, in press. [27] B. J.Cole, “Is animal behavior chaotic? Evidence from the activity <strong>of</strong> ants.” Proc R Soc Lond Ser B biol Sco, vol. 244, p. 253-259, 1991. [28] R. V. Solé, O. Miramontes and B. C. Goodwill, “Oscillations and chaos in ant societies,” <strong>Journal</strong> <strong>of</strong> Theory Biology, vol. 161, p. 343-357, 1993. Chunli Xie Xie received his B.Sc. and M.Sc. degrees from Fushun Petroleum Institute and Liaoning Shihua University, Fushun, China, in 1995 and 2003, respectively. He is currently working toward the Ph.D degree with Dalian University <strong>of</strong> Technology, Dalian, China. His research interests include adaptive control, robust control, machine learning, nonlinear systems, artificial intelligence and application. Cheng Shao was born in Shenyang, P. R. China, on June 7, 1958. Shao received his B.Sc. degree from Liaoning University, Shenyang, China, in 1982. Then he received the M.Sc and Ph.D. degrees from Northeastern University, Shenyang, China, in 1987 and 1992. He is currently a full-time Pr<strong>of</strong>essor and Ph.D. Advisor with School <strong>of</strong> Electronic and Information Engineering, Dalian
JOURNAL OF COMPUTERS, VOL. 6, NO. 9, SEPTEMBER 2011 1941 University <strong>of</strong> Technology, China. His research interest covers complex system modeling and intelligence control. Dandan Zhao was born in Fuxin, P. R. China, on March 4, 1975. Zhao received her B.Sc. and M.Sc. degrees from Fushun Petroleum Institute and Liaoning Shihua University, Fushun, © 2011 ACADEMY PUBLISHER China, in 1997 and 2003, respectively. She is currently a fulltime lecturer <strong>of</strong> School <strong>of</strong> Computer Science and Engineering, Dalian Nationalities University, Dalian, China. Her research interests include electronic commerce, semantic network, swarm intelligent and information processing.
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A Modified Technique for Analysis o