实数GA基因层次种群多样性数学模型  

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

作　　者：赵红[1] 朱杰[1,2] 朱洁[1] 李雯睿[1,3] 

机构地区：[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

出　　处：《中南大学学报（自然科学版）》2015年第3期894-900,共7页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(61202136);江苏省高校自然科学研究项目(13KJD520007);南京晓庄学院校级科研项目(2012NXY14)~~

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。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 fimctions. 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.

关 键 词：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 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]