Abstract
A new Immune Genetic Algorithm (IGA) modeling was completed using Markov chain. The convergence rate of IGA to absorbed-state was deduced using norm and the analysis of transition probability matrix. According to the design and the performance of IGA, the detailed quantitative expressions of convergence rate to absorbed-state which include immune parameters in IGA was presented. Then the discussion was carried out about the effect of the parameters on the convergence rate. It was found that several parameters such as the population size, the population distribution, the string length etc. would all affect the optimization. The conclusions demonstrate that why IGA can maintain the diversity very well so that the optimization is very quick. This paper can also be helpful for the further study on the convergence rate of Immune Genetic Algorithm.
The National Science Foundation, China(No.60405012), Scientific Research Project of Department of Education of Zhejiang(No.20061291) and Zhejiang University City College Scientific Research Project(No.J52305062016) supported this research.
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References
Krishnakumar, K., Neidhoefer, J.: Immunised Neurocontrol. Expert Systems With Application 13(3), 201–214 (1997)
Quagliarella, D., Periauz, J., Poloni, C., Winter, G. (eds.): Genetic Algorithms in Engineering and Computer Science, pp. 85–104. John Wiley & Sons, New York (1997)
Lee, D.-W., Sim, K.-B.: Artificial Immune Network-based cooperative control in Collective Autonomous Mobile Robots, Proceedings. In: 6th IEEE International Workshop on Robot and Human Communication. pp. 58–63 (1997)
Dasgupta, D.: Artificial Immune Systems and Their Applications. Springer, Heidelberg (1999)
Lei, W., Li-cheng, J.: The Immune Genetic Algorithm and Its Converge. In: 1998 Fourth International Conference on Signal Processing Proceedings, vol. 2, pp. 1347–1350 (1998)
Chun, J.S., Jung, H.K., Hahn, S.Y.: A Study on Comparison of Optimization Performance between Immune Algorithm and other Heuristic Algorithms. IEEE Transactions on Magnetics 34(5), 2972–2975 (1998)
Xiaoping, L., Wei, W.: A New Optimization Method on Immunogenetics. ACTA Electronica Sinica 31(1), 59–64 (2003)
Xiaoping, L., Wei, W.: A New Immune Genetic Algorithm and Its Application in Redundant Manipulator Path Planning. Journal of Robotic Systems 21(3), 141–151 (2004)
Xiaoping, L., Wei, W.: Discussion on the Convergence Rate of Immune Genetic Algorithm. In: Proceedings of the World Congress on Intelligent Control and Automation (WCICA), WCICA, June 15-19 2004, pp. 2275–2278 (2004)
Xiaoping, L., Wei, W., Xiaorun, L.: A study on immune genetic algorithm and its performance. In: 7th World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida, July 27-30, 2003, pp. 147–151 (2003)
Hunt, J.E., Cooke, D.E.: An Adaptive, Distributed Learning System based on Immune System. In: 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, vol. 3, pp. 2494–2499 (October 1995)
Lin, H., Kujun, W.: The Convergence Rate Estimation of Genetic Algorithm. Systems Enginering-Theroy Methodology Application 8(3), 22–26 (1999)
Hong, P., Xinghua, W.: The Convergence Rate Estimation of Genetic Algorithm with Elitist. Chinese Science Bulletin 42(2), 144–147 (1997)
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Luo, X., Pang, W., Huang, J. (2007). A Further Discussion on Convergence Rate of Immune Genetic Algorithm to Absorbed-State. In: Wang, Y., Cheung, Ym., Liu, H. (eds) Computational Intelligence and Security. CIS 2006. Lecture Notes in Computer Science(), vol 4456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74377-4_3
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DOI: https://doi.org/10.1007/978-3-540-74377-4_3
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