The Genetic Algorithm Parameters Adaptive Control And Convergence Research

The performance of genetic algorithm(GA) is obviously enslaved to the crossover probability p_c and mutation probability p_m.For the values of p_c and p_m are invariable,there are problems as the low convergence rate and premature phenomenon in simple genetic algorithm.Though adaptive genetic algorithm(AGA) has been proven to be able to adjust the control parameters according to the fitness of the overall population,it is not suitable for different problems for the rules to adjust p_c and p_m must be varied with optimization questions so as to find the optimal solution faster and more precisely.It is of great importance to adjust the parameters adaptively.Convergence theory is a core theoretical issue on genetic algorithms.The systematism and universalism of the theories are not enough.So,studying the convergence theory of genetic algorithms is the inevitable requirement for the theory and application of GA.Therefore,parameter adaptive controlling and convergence theory for genetic algorithms are studied in this paper.A kind of nested fuzzy adaptive genetic algorithm(NFAGA)which is suitable for different optimization problems is realized,the simulation platform of the new algorithm is implemented,and the simulation experiments in function optimization problems with several other genetic algorithms are carried out.For the convergence theory,the convergence and convergence rate of elitist genetic algorithm(EGA) based on martingale approach is studied.The detailed contents and innovative work of this paper are as follows:1.According to the defects for regulation law of fuzzy adaptive genetic algorithm based on expertise(EFAGA),the self-learning mechanism to update and optimize the knowledge basis of the fuzzy controller is studied.On the one hand,the values of p_c and p_m are adjusted according to the evolutional process by using the fuzzy control method; on the other hand,the fuzzy rules and the parameters of the membership functions are optimized by another GA.Thus,a kind of nested fuzzy adaptive genetic algorithm which could overcome the defects of the existing adaptive genetice algorithms is realized.2.The simulation platform of NFAGA based on MATLAB GUI is implemented.The efficiency of NFAGA is studied via comparative simulation experiments of other algorithms in solving the function optimization problems.Simulation results demonstrate that the performance of NFAGA is better than the other algorithms obviously.3.The convergence and convergence rate of EGA based on martingale approach is studied.The process of the maximum fitness function which could be transformed into submartingale is used to describe the evolution process of GA.Based on the submartingale convergence theorem,the convergence of EGA is analyzed,the math expression between its convergence rate with the operating parameters is derived,and the maximum evolutional generation to find the global optimal solution of EGA is calculated.