基于Matlab遗传算法的非线性方程组优化程序

基于Matlab遗传算法的非线性方程组优化程序

clear,clc;%清理内存，清屏 circleN=200;%迭代次数 format long

%构造可能解的空间，确定染色体的个数、长度 solutionSum=4;leftBoundary=-10;rightBoundary=10; distance=1;chromosomeSum=500;solutionSumError=0.1; oneDimensionSet=leftBoundary:distance:rightBoundary;

oneDimensionSetN=size(oneDimensionSet,2);%返回oneDimensionSet中的元素个数 solutionN=oneDimensionSetN^solutionSum;%解空间(解集合)中可能解的总数 binSolutionN=dec2bin(solutionN);%把可能解的总数转换成二进制数

chromosomeLength=size(binSolutionN,2);%由解空间中可能解的总数(二进制数)计算染色体的长度

%程序初始化

%随机生成初始可能解的顺序号,+1是为了防止出现0顺序号 solutionSequence=fix(rand(chromosomeSum,1)*solutionN)+1; for i=1:chromosomeSum%防止解的顺序号超出解的个数 if solutionSequence(i)>solutionN; solutionSequence(i)=solutionN; end end

%把解的十进制序号转成二进制序号

fatherChromosomeGroup=dec2bin(solutionSequence,chromosomeLength); holdLeastFunctionError=Inf;%可能解的最小误差的初值 holdBestChromosome=0;%对应最小误差的染色体的初值 %计算 circle=0;

while circle

%1:由可能解的序号寻找解本身(关键步骤)

x=chromosome_x(fatherChromosomeGroup,oneDimensionSet,solutionSum); %2：把解代入非线性方程计算误差

functionError=nonLinearSumError1(x);%把解代入方程计算误差 [solution,minError,isTrue]=isSolution(x,functionError,solutionSumError); if isTrue==1 '方程得解' solution minError circle

return%结束程序 end

%3：选择最好解对应的最优染色体

[bestChromosome,leastFunctionError]=best_worstChromosome(fatherChromosomeGroup,functionError);

%4：保留每次迭代产生的最好的染色体 [holdBestChromosome,holdLeastFunctionError]...

=compareBestChromosome(holdBestChromosome,holdLeastFunctionError,... bestChromosome,leastFunctionError); %circle %minError %solution

%holdLeastFunctionError

%5:把保留的最好的染色体holdBestChromosome加入到染色体群中 order=round(rand(1)*chromosomeSum); if order==0 order=1; end

fatherChromosomeGroup(order,:)=holdBestChromosome; functionError(order)=holdLeastFunctionError;

%6:为每一条染色体(即可能解的序号)定义一个概率(关键步骤) [p,trueP]=chromosomeProbability(functionError); if trueP =='Fail'

'可能解严重不适应方程，请重新开始' return%结束程序 end

%7：按照概率筛选染色体(关键步骤)

ú=bin2dec(fatherChromosomeGroup)%显示父染色体

fatherChromosomeGroup=varianceCh(sonChromosomeGroup,0.1,solutionN);

fatherChromosomeGroup=checkSequence(fatherChromosomeGroup,solutionN);%检查变异后的染色体是否越界 end

%这个函数找出染色体(可能解的序号)对应的可能解x

function x=chromosome_x(chromosomeGroup,oneDimensionSet,solutionSum) [row oneDimensionSetN]=size(oneDimensionSet);

chromosomeSum=size(chromosomeGroup);%chromosomeSum:染色体的个数

xSequence=bin2dec(chromosomeGroup);%把可能解的二进制序号(染色体)转换成十进制序号 for i=1:chromosomeSum%i:染色体的编号 remainder=xSequence(i); for j=1:solutionSum

dProduct=oneDimensionSetN^(solutionSum-j);%sNproduct: quotient=remainder/dProduct;

remainder=mod(remainder,dProduct);%mod:取余函数 if remainder==0

oneDimensionSetOrder=quotient; else

oneDimensionSetOrder=fix(quotient)+1;%fix:取整函数 end

if oneDimensionSetOrder==0

oneDimensionSetOrder=oneDimensionSetN; end

x(i,j)=oneDimensionSet(oneDimensionSetOrder); end end

function funtionError=nonLinearSumError1(X)%方程的解是-7,5,1,-3 funtionError=... [

abs(X(:,1).^2-sin(X(:,2).^3)+X(:,3).^2-exp(X(:,4))-50.566253390821)+... abs(X(:,1).^3+X(:,2).^2-X(:,4).^2+327)+...

abs(cos(X(:,1).^4)+X(:,2).^4-X(:,3).^3-624.679868769613)+... abs(X(:,1).^4-X(:,2).^3+2.^X(:,3)-X(:,4).^4-2197) ];

%判断方程是否解开

function [solution,minError,isTrue]=isSolution(x,functionError,precision) [minError,xi]=min(functionError);%找到最小误差，最小误差所对应的行号 solution=x(xi,:); if minError

[bestChromosome,leastFunctionError]=best_worstChromosome(chromosomeGroup,functionError) [leastFunctionError minErrorOrder]=min(functionError); %[maxFunctionError maxErrorOrder]=max(functionError); bestChromosome=chromosomeGroup(minErrorOrder,:); %worstChromosome=chromosomeGroup(maxErrorOrder,:);

function [newBestChromosome,newLeastFunctionError]...

=compareBestChromosome(oldBestChromosome,oldLeastFunctionError,... bestChromosome,leastFunctionError) if oldLeastFunctionError>leastFunctionError newLeastFunctionError=leastFunctionError;

newBestChromosome=bestChromosome; else

newLeastFunctionError=oldLeastFunctionError; newBestChromosome=oldBestChromosome; end

function [p,isP]=chromosomeProbability(x_Error) InfN=sum(isinf(x_Error));%估计非线性方程计算的结果 NaNN=sum(isnan(x_Error)); if InfN>0 || NaNN>0 isP='Fail'; p=0; return else isP='True';

errorReciprocal=1./x_Error;

sumReciprocal=sum(errorReciprocal);

p=errorReciprocal/sumReciprocal;%p:可能解所对应的染色体的概率 end

function chromosome=selecteChromosome(chromosomeGroup,p)

cumuP=cumsum(p);%累积概率,也就是把每个染色体的概率映射到0~1的区间 [chromosomeSum,chromosomeLength]=size(chromosomeGroup); for i=1:chromosomeSum%这个循环产生概率值 rN=rand(1); if rN==1

chromosome(i,:)=chromosomeGroup(chromosomeSum,:); elseif (0<=rN) && (rN

chromosome(i,:)=chromosomeGroup(1,:);%第1条染色体被选中 else

for j=2:chromosomeSum%这个循环确定第1条以后的哪一条染色体被选中 if (cumuP(j-1)<=rN) && (rN

function sonChromosome=crossChromosome(fatherChromosome,parameter) [chromosomeSum,chromosomeLength]=size(fatherChromosome); switch parameter

case 1%随机选择父染色体进行交叉重组