The Convergence Analysis of Genetic Algorithm Based on Space Mating

This paper analyzes the convergence properties of the genetic algorithm based on space mating with mutation, crossover and proportional reproduction applied to static optimization on problems. It is proved by means of homogeneous finite Markov chain analysis that genetic algorithm based on space mating will converge to the global optimum. Each process is convergence to the global optimum, at least satisfactory solution under the best individual survives besides the last course. And illuminate a population converge with probability one in the no mutation operator conditions. By comparing the experiment, we can see that the algorithm have better convergence than SGA and consist with the theory.

[1]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[2]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[3]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[4]  David B. Fogel,et al.  Evolving artificial intelligence , 1992 .

[5]  William A. Sethares,et al.  Nonlinear parameter estimation via the genetic algorithm , 1994, IEEE Trans. Signal Process..

[6]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[7]  Günter Rudolph,et al.  Convergence analysis of canonical genetic algorithms , 1994, IEEE Trans. Neural Networks.

[8]  Günter Rudolph,et al.  Convergence analysis of canonical genetic algorithms , 1994, IEEE Trans. Neural Networks.

[9]  Zbigniew Michalewicz,et al.  Genetic algorithms + data structures = evolution programs (3rd ed.) , 1996 .

[10]  Xu Chuan.  Hybrid Approach and its Generalization for Solving Premature Convergence of a Class of Genetic Algorithms , 1998 .

[11]  Stephen Marshall,et al.  Convergence Criteria for Genetic Algorithms , 2000, SIAM J. Comput..

[12]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[13]  Xu Zong.  Almost Sure Convergence of Genetic Algorithms:A Martingale Approach , 2002 .

[14]  R. Sharapov,et al.  Convergence of genetic algorithms , 2006, Pattern Recognition and Image Analysis.

[15]  Zhengjing Jin.  Convergence Analysis of Genetic Algorithm Based on Space Mating , 2010 .