Journal of Computers, Vol 6, No 10 (2011), 2173-2179, Oct 2011

Study of An Improved Genetic Algorithm Based on Fixed Point theory and hJ1 triangulation in Euclidean Space

Jingjun Zhang, Hongxia Wang, Ruizhen Gao


Aiming at the convergence precision defects of standard genetic algorithm, the fixed point theory is introduced into the genetic algorithms. The population of individual is regarded as the triangulation of the point. Hence the vertex label information of the individual simplex would guide the algorithm to the optimization researching and convergence judgment which could be calculated with the hJ1 triangulation and integer label. When the loading simplexes of individuals are transferred into the completely labeled simplexes, the algorithm will be terminated and the global optimal solution will be got. Finally, some functions are used to demonstrate the effectiveness and strong stability of the algorithm through solving the minimum points distinguished by using the Hessian Matrix and then compared with the standard genetic algorithms and J1 triangulation.


Genetic algorithm; Fixed point theory; hJ1 triangulation; Integer labels; Hessian Matrix


[1]Wehage R.A., Barman N.C. Design Sensitivity Analysis of Planar Mechanism and Machine Dynamics. ASME J. Mech, Des., 1981, 103, 560-570

[2]Haug E.J., Arora J.S. Applied optimal design: mechanical and structural systems [M]. John Wiley & Sons, New York, 1979.

[3]Deb. K., Multi-objective Optimization Using Evolutionary Algorithms[M], John Wiley Sons, Ltd, 2001.

[4]Mahfoud S.W. Niching Methods for Genetic Algorithms, IlliGAL Technical Report 95001, Illinois Genetic Algorithms Laboratory, University of Illinois, Urbana, Illinois, 1995.

[5]Holland, J., Adoptation in Natural and Artificial Systems[M], University of Michigan Press, 44~50: 1992.

[6]Xichun Liu, Shouyi Yu. A genetic algorithm with fast local adjustment[J]. Chinese Journal of Computers, 29(1):100~105 2006.

[7]Jingjun Zhang, Wei Cui, Nan Wang. Niche genetic algorithm for optimization deign of dynamic parameters of rigid multibody systems[J]. Chinese Journal of Mechanical Engineering, 40(3):66-70,2004.

[8]Q. Zhang, H. Li . A Multi-objective Evolutionary Algorithm Based on Decomposition, IEEE Trans. on Evolutionary Computation, vol.11, no. 6, pp712-731 2007.

[9]Huang Shao-hui, Cao Xiao-tao, Li Yuan-chun. Force/position control algorithm for manipulator based on wavelet network. Journal of Jilin University (Engineering and Technology Edition,38(1):163-167,2008.

[10]Yin Qiang, Zhou Li, Structural damage identification based on GA optimized least square estimation,Journal of Vibration and Shock, Vo.l 29, No. 8, 2010, pp. 155-159.

[11]Xiaoming Dai, Chao Xu, Xiangyang Gong, Huihe Shao. Convergence Analysis of Parallel Genetic Algorithm and Its Application to Optimization[J], Computer Engineering, 28(6): 92~95,2002.

[12]Li Hang, Li Minqiang, Kou Jisong, Dynamieal Behavior of Genetie Algorithms on Multi-modal Optimization, Acta Automatica Sinica, Vol.34, No.2, February, 2008, pp. 180-187.

[13]Zeke Wang. Simplicial fixed points algorithm. press of national university of defense technology[M], 1993.

[14]Hiroshi N. Chikahiro T. Hideki A., An Efficient Learning Algorithm for Finding Multiple Solutions Based on Fixed-Point Homotopy Method[J], Proceedings of International Joint Conference on Neural Networks, Montreal, Canada, 2005.

[15]Scarf H.E. the approximation of fixed points of a continuous mapping. SIAM. J. Appl. Math., 1967, 15, 1328-1341.

[16]Wu Zheng-peng, Liu Si-feng, Cui Li-zhi, Study on new weakening buffer operator based on Fixed Point, Control and Decision, Vol.24, No.12, Dec. 2009, pp. 1805-1809.

[17]Song Dan, Zhang Xiao-Lin, Study of the multi-system compatible receiver’s frequency selection problem based on fixed point theory and its genetic algorithm realization, Acta Physica Sinica, Vol.59, No.9, September, 2010, pp. 6698-6705.

[18]Dugundji J., Granas A. Fixed Point Theory. Springer Monographs in Mathematics, 2003.

Full Text: PDF

Journal of Computers (JCP, ISSN 1796-203X)

Copyright @ 2006-2014 by ACADEMY PUBLISHER – All rights reserved.