## Journal of Central South University

 第46卷    第3期    总第247期    2015年3月

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(1. 南京晓庄学院 数学与信息技术学院，江苏 南京，211171；
2. 东南大学 自动化学院，江苏 南京，210096；
3. 河海大学 计算机及信息工程学院，江苏 南京，210098
)

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

1. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China;
2. School of Automation, Southeast University, Nanjing 210096, China;
3. College of Computer and Information Engineering, Hohai University, Nanjing 210098, China

Abstract: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.

Key words: genetic algorithm (GA); real-coded; population diversity; gene level; interval gene; random variable

 中南大学学报（自然科学版） ISSN 1672-7207 CN 43-1426/NZDXZAC 中南大学学报（英文版） ISSN 2095-2899 CN 43-1516/TBJCSTFT