Gene-level population diversity mathematical model of real-coded GA

The calculation and applicability of existing definitions of GA population diversity are not only complicated and poor, but also always applied to binary coded GA, so a Gene-level population diversity mathematical model of real-coded GA was established to overcome the problems. The value range of each dimension decision variable of real-coded GA was divided into several equal length intervals. Interval gene variable that refers to definition of gene in binary coded GA was defined. The interval gene variable was treated as random variable. And its graph method was designed. The interval gene variable indicates the distribution of all coed values of each dimension variable within each equal interval, and the result of the distribution can be used to measure population diversity. The mathematical model presented is effective through analysis to optimization process of two GA test functions. The characteristic of interval gene was analyzed, and the analysis result can be used as experimental knowledge when producing the initial population in complicated nonlinear optimization problem for improving global convergence probability and speed. Finally, further research ideas and direction were pointed out. ©, 2015, Central South University of Technology. All right reserved.