自然科学版 英文版
自然科学版 英文版
自然科学版 英文版

您目前所在的位置:首页 - 期刊简介 - 详细页面

中南大学学报(自然科学版)

Journal of Central South University

第46卷    第3期    总第247期    2015年3月

[PDF全文下载]    [Flash在线阅读]

    

文章编号:1672-7207(2015)03-0894-07
实数GA基因层次种群多样性数学模型
赵红1,朱杰1, 2,朱洁1,李雯睿1, 3

(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
)

摘 要: 针对现有GA种群多样性定义往往针对二进制编码且存在计算量大、适用性差等问题,建立实数编码基因层次种群多样性数学模型。将实数编码中每一维决策变量的取值范围划分为若干等长度的区间段,并借鉴二进制编码中基因位的含义,定义区间段基因位变量的概念,将其看作随机变量并设计图形化方法,描述每一维变量所有编码值在各等长度取值区间的分布情况,以此刻画种群多样性,通过2个测试函数的优化分析,验证模型的有效性;分析区间段基因位的特性,指出其可以作为复杂非线性优化问题中产生初始群体的先验知识使用,从而可以显著提高寻得最优解的概率及收敛速度;指出今后进一步的研究思路和方向。

 

关键字: 遗传算法;实数编码;种群多样性;基因层次;区间段基因位;随机变量

Gene-level population diversity mathematical model of real-coded GA
ZHAO Hong1, ZHU Jie1, 2, ZHU Jie1, LI Wenrui1, 3

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/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
版权所有:《中南大学学报(自然科学版、英文版)》编辑部
地 址:湖南省长沙市中南大学 邮编: 410083
电 话: 0731-88879765(中) 88836963(英) 传真: 0731-88877727
电子邮箱:zngdxb@csu.edu.cn 湘ICP备09001153号