Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.
[1] Masahiro Nakagawa, Chaos and Fractals in Engineering, World
Science, Singapore, 1999.
[2] Luonan Chen, K. Aihara, "Global searching ability of chaos neural
networks", IEEE Trans. Circuits Syst., 46.8, 1999.
[3] Isao Tokuda, Kazuyuki Aihara, and Tomomasa Nagashima, Adaptive
annealing for chaotic optimization, Phys. Rev. E, 58.4, 1998.
[4] Mohammad Saleh Tavazoei and Mohammad Haeri, "An optimization
algorithm based on chaotic behavior and fractal nature", J. Comput.
Appl. Math., 2006.
[5] Dixiong Yang, Gang Li and Gengdong Cheng, "On the efficiency of
chaos optimization algorithms for global optimization", J. Chaos,
Solitons & Fractals, 2006.
[6] Guo Zilong, Wang Sun-an and Zhuang Jian, "A novel immune
evolutionary algorithm incorporating chaos optimization", Pattern
Recognition Lett., 27.1, 2006,pp. 2-8.
[7] Shengsong Liu; Zhijian Hou, "Weighted gradient direction based
chaos optimization algorithm for nonlinear programming problem",
Proc. Intelligent Control and Automation, 3, 2002, pp. 1779 - 1783.
[8] You Yong; Sheng Wanxing; Wang Sunan; "Study of chaos genetic
algorithms and its application in neural networks", Proc. Computers,
Communication, Control and Power Eng.TENCON,, 1 2002. pp. 232 -
235.
[9] Rongbin Qi; Feng Qian; Shaojun Li; Zhenlei Wang; "Chaos-Genetic
Algorithm for Multiobjective Optimization", Proc. Intelligent Control
and Automation WCICA, 1, 2006, pp 1563 - 1566.
[10] LU Hui-juan, ZHANG Huo-ming, MA Long-hua, A new optimization
algorithm based on chaos, J. Zhejiang University sci. A, 7.4, 2006, pp.
539-542.
[11] Liu Shengsong; Hou Zhijian; Wang Min, "A hybrid algorithm for
optimal power flow using the chaos optimization and the linear
interior point algorithm", Proc. PowerCon, 2, 2002, pp. 793 - 797
[12] Ji MJ, Tang HW, "Application of chaos in simulated annealing", J.
Chaos, Solitons & Fractals, 21, 2004, pp. 933-41.
[13] Liu B, Wang L, Yin HY, Tang F, Huang DX, "Improved particle
swarm optimization combined with chaos", J. Chaos, Solitons &
Fractals 25, 2005, pp. 1261-71.
[14] Behera, L., Kumar, S., Patnaik, A., "On Adaptive Learning Rate That
Guarantees Convergence in Feedforward Networks", IEEE Trans.
Neural Networks, 17.5, 2006, pp. 1116-1125.
[15] Yu, X., Onder Efe, M., Kaynak, O., "A backpropagation learning
framework for feedforward neural networks", IEEE Int. Syposium
Circuits Sys. ISCAS, 3, 2001, pp.700-702.
[16] Terrence L. Fine, Feedforward neural network methodology, Springer,
New York, 1999, pp. 130-131.
[17] K. Bertels1, L. Neuberg1, S. Vassiliadis and D.G. Pechanek, "On
Chaos and Neural Networks: The Backpropagation Paradigm",
Artificial Intelligence Rev. 15, 2001, pp.165-187.
[1] Masahiro Nakagawa, Chaos and Fractals in Engineering, World
Science, Singapore, 1999.
[2] Luonan Chen, K. Aihara, "Global searching ability of chaos neural
networks", IEEE Trans. Circuits Syst., 46.8, 1999.
[3] Isao Tokuda, Kazuyuki Aihara, and Tomomasa Nagashima, Adaptive
annealing for chaotic optimization, Phys. Rev. E, 58.4, 1998.
[4] Mohammad Saleh Tavazoei and Mohammad Haeri, "An optimization
algorithm based on chaotic behavior and fractal nature", J. Comput.
Appl. Math., 2006.
[5] Dixiong Yang, Gang Li and Gengdong Cheng, "On the efficiency of
chaos optimization algorithms for global optimization", J. Chaos,
Solitons & Fractals, 2006.
[6] Guo Zilong, Wang Sun-an and Zhuang Jian, "A novel immune
evolutionary algorithm incorporating chaos optimization", Pattern
Recognition Lett., 27.1, 2006,pp. 2-8.
[7] Shengsong Liu; Zhijian Hou, "Weighted gradient direction based
chaos optimization algorithm for nonlinear programming problem",
Proc. Intelligent Control and Automation, 3, 2002, pp. 1779 - 1783.
[8] You Yong; Sheng Wanxing; Wang Sunan; "Study of chaos genetic
algorithms and its application in neural networks", Proc. Computers,
Communication, Control and Power Eng.TENCON,, 1 2002. pp. 232 -
235.
[9] Rongbin Qi; Feng Qian; Shaojun Li; Zhenlei Wang; "Chaos-Genetic
Algorithm for Multiobjective Optimization", Proc. Intelligent Control
and Automation WCICA, 1, 2006, pp 1563 - 1566.
[10] LU Hui-juan, ZHANG Huo-ming, MA Long-hua, A new optimization
algorithm based on chaos, J. Zhejiang University sci. A, 7.4, 2006, pp.
539-542.
[11] Liu Shengsong; Hou Zhijian; Wang Min, "A hybrid algorithm for
optimal power flow using the chaos optimization and the linear
interior point algorithm", Proc. PowerCon, 2, 2002, pp. 793 - 797
[12] Ji MJ, Tang HW, "Application of chaos in simulated annealing", J.
Chaos, Solitons & Fractals, 21, 2004, pp. 933-41.
[13] Liu B, Wang L, Yin HY, Tang F, Huang DX, "Improved particle
swarm optimization combined with chaos", J. Chaos, Solitons &
Fractals 25, 2005, pp. 1261-71.
[14] Behera, L., Kumar, S., Patnaik, A., "On Adaptive Learning Rate That
Guarantees Convergence in Feedforward Networks", IEEE Trans.
Neural Networks, 17.5, 2006, pp. 1116-1125.
[15] Yu, X., Onder Efe, M., Kaynak, O., "A backpropagation learning
framework for feedforward neural networks", IEEE Int. Syposium
Circuits Sys. ISCAS, 3, 2001, pp.700-702.
[16] Terrence L. Fine, Feedforward neural network methodology, Springer,
New York, 1999, pp. 130-131.
[17] K. Bertels1, L. Neuberg1, S. Vassiliadis and D.G. Pechanek, "On
Chaos and Neural Networks: The Backpropagation Paradigm",
Artificial Intelligence Rev. 15, 2001, pp.165-187.
@article{"International Journal of Information, Control and Computer Sciences:51743", author = "Truong Quang Dang Khoa and Masahiro Nakagawa", title = "Neural Network Learning Based on Chaos", abstract = "Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.
", keywords = "learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.", volume = "1", number = "4", pages = "882-6", }
