Abstract:

For the problem of lacking of unity and universality for existing population diversity definitions in  GA premature convergence research, we design a unified mathematical model of population diversity for real and binary coded GA based on the essence of gene population diversity. Firstly, the population matrix of real coded GA is converted into the same form as that of binary coded GA. Secondly, we define the concept of the homologous random variable and its characteristic measures, including the mathematical expectation, the deviation degree and the variance, based on which the unified population diversity model applicable to both of the two codes is established. The two representation methods (the evolution matrix and graphical representation) for the proposed model  are also given. Simulation analysis of GA test functions show that the proposed model can effectively reflect and analyze the change trend of GA population diversity in the process of evolution, as well as the convergence process and convergence results of genes. Finally, further analysis and research direction are pointed out.

Key words: GA;real and binary codes;population diversity;gene level;gene;homologous random variable;evolution matrix