三個(gè)遺傳算法matlab程序?qū)嵗?/span>
遺傳算法程序（一）:
說(shuō)明: fga.m 為遺傳算法的主程序; 采用二進(jìn)制Gray編碼,采用基于輪盤(pán)賭法的非線(xiàn)性排名選擇, 均勻交叉,變異操作,而且還引入了倒位操作!
function[BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
% Finds amaximum of a function of several variables.
% fmaxga solvesproblems of the form:
% max F(X) subject to: LB <= X <=UB
%BestPop - 最優(yōu)的群體即為最優(yōu)的染色體群
%Trace - 最佳染色體所對(duì)應(yīng)的目標(biāo)函數(shù)值
%FUN - 目標(biāo)函數(shù)
% LB - 自變量下限
%UB - 自變量上限
%eranum - 種群的代數(shù),取100--1000(默認(rèn)200)
%popsize - 每一代種群的規(guī)模；此可取50--200(默認(rèn)100)
%pcross - 交叉概率,一般取0.5--0.85之間較好(默認(rèn)0.8)
%pmutation - 初始變異概率,一般取0.05-0.2之間較好(默認(rèn)0.1)
%pInversion - 倒位概率,一般取0.05－0.3之間較好(默認(rèn)0.2)
%options - 1*2矩陣,options(1)=0二進(jìn)制編碼(默認(rèn)0),option(1)~=0十進(jìn)制編
%碼,option(2)設(shè)定求解精度(默認(rèn)1e-4)
%
%------------------------------------------------------------------------
T1=clock;
if nargin<3,error('FMAXGA requires at least three input arguments'); end
if nargin==3,eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[01e-4];end
if nargin==4,popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==5,pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==6,pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==7,pInversion=0.15;options=[0 1e-4];end
iffind((LB-UB)>0)
error('數(shù)據(jù)輸入錯(cuò)誤,請(qǐng)重新輸入(LB<UB):');
end
s=sprintf('程序運(yùn)行需要約%.4f 秒鐘時(shí)間,請(qǐng)稍等......',(eranum*popsize/1000));
disp(s);
global m nNewPop children1 children2 VarNum
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
precision=options(2);%由求解精度確定二進(jìn)制編碼長(zhǎng)度
bits=ceil(log2((bounds(:,2)-bounds(:,1))'./ precision));%由設(shè)定精度劃分區(qū)間
[Pop]=InitPopGray(popsize,bits);%初始化種群
[m,n]=size(Pop);
NewPop=zeros(m,n);
children1=zeros(1,n);
children2=zeros(1,n);
pm0=pMutation;
BestPop=zeros(eranum,n);%分配初始解空間BestPop,Trace
Trace=zeros(eranum,length(bits)+1);
i=1;
while i<=eranum
for j=1:m
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%計(jì)算適應(yīng)度
end
[MaxValue,Index]=max(value);
BestPop(i,:)=Pop(Index,:);
Trace(i,1)=MaxValue;
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非線(xiàn)性排名選擇
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
%采用多點(diǎn)交叉和均勻交叉，且逐步增大均勻交叉的概率
%round(unidrnd(eranum-i)/eranum)
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%變異
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
Pop=InversionPop;%更新
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
%隨著種群向前進(jìn)化，逐步增大變異率至1/2交叉率
p(i)=pMutation;
i=i+1;
end
t=1:eranum;
plot(t,Trace(:,1)');
title('函數(shù)優(yōu)化的遺傳算法');xlabel('進(jìn)化世代數(shù)(eranum)');ylabel('每一代最優(yōu)適應(yīng)度(maxfitness)');
[MaxFval,I]=max(Trace(:,1));
X=Trace(I,(2:length(bits)+1));
hold on;plot(I,MaxFval,'*');
text(I+5,MaxFval,['FMAX='num2str(MaxFval)]);
str1=sprintf ('進(jìn)化到 %d 代 ,自變量為 %s 時(shí),得本次求解的最優(yōu)值 %f\n對(duì)應(yīng)染色體是：%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));
disp(str1);
%figure(2);plot(t,p);%繪制變異值增大過(guò)程
T2=clock;
elapsed_time=T2-T1;
ifelapsed_time(6)<0
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
end
ifelapsed_time(5)<0
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
end %像這種程序當(dāng)然不考慮運(yùn)行上小時(shí)啦
str2=sprintf('程序運(yùn)行耗時(shí) %d 小時(shí) %d 分鐘 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
disp(str2);
%初始化種群
%采用二進(jìn)制Gray編碼,其目的是為了克服二進(jìn)制編碼的Hamming懸崖缺點(diǎn)
function[initpop]=InitPopGray(popsize,bits)
len=sum(bits);
initpop=zeros(popsize,len);%Thewhole zero encoding individual
fori=2:popsize-1
pop=round(rand(1,len));
pop=mod(([0 pop]+[pop 0]),2);
%i=1時(shí),b(1)=a(1);i>1時(shí),b(i)=mod(a(i-1)+a(i),2)
%其中原二進(jìn)制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
initpop(i,:)=pop(1:end-1);
end
initpop(popsize,:)=ones(1,len);%Thewhole one encoding individual
%解碼
function [fval]= b2f(bval,bounds,bits)
%fval - 表征各變量的十進(jìn)制數(shù)
%bval - 表征各變量的二進(jìn)制編碼串
% bounds - 各變量的取值范圍
%bits - 各變量的二進(jìn)制編碼長(zhǎng)度
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1);%The range of the variables
numV=size(bounds,1);
cs=[0cumsum(bits)];
for i=1:numV
a=bval((cs(i)+1):cs(i+1));
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
end
%選擇操作
%采用基于輪盤(pán)賭法的非線(xiàn)性排名選擇
%各個(gè)體成員按適應(yīng)值從大到小分配選擇概率：
%P(i)=(q/1-(1-q)^n)*(1-q)^i,其中 P(0)>P(1)>...>P(n), sum(P(i))=1
function[selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
global m n
selectpop=zeros(m,n);
fit=zeros(m,1);
for i=1:m
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函數(shù)值為適應(yīng)值做排名依據(jù)
end
selectprob=fit/sum(fit);%計(jì)算各個(gè)體相對(duì)適應(yīng)度(0,1)
q=max(selectprob);%選擇最優(yōu)的概率
x=zeros(m,2);
x(:,1)=[m:-1:1]';
[yx(:,2)]=sort(selectprob);
r=q/(1-(1-q)^m);%標(biāo)準(zhǔn)分布基值
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成選擇概率
newfit=cumsum(newfit);%計(jì)算各選擇概率之和
rNums=sort(rand(m,1));
fitIn=1;newIn=1;
whilenewIn<=m
if rNums(newIn)<newfit(fitIn)
selectpop(newIn,:)=pop(fitIn,:);
newIn=newIn+1;
else
fitIn=fitIn+1;
end
end
%交叉操作
function[NewPop]=CrossOver(OldPop,pCross,opts)
%OldPop為父代種群，pcross為交叉概率
global m nNewPop
r=rand(1,m);
y1=find(r<pCross);
y2=find(r>=pCross);
len=length(y1);
iflen>2&mod(len,2)==1%如果用來(lái)進(jìn)行交叉的染色體的條數(shù)為奇數(shù)，將其調(diào)整為偶數(shù)
y2(length(y2)+1)=y1(len);
y1(len)=[];
end
iflength(y1)>=2
fori=0:2:length(y1)-2
if opts==0
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
else
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
end
end
end
NewPop(y2,:)=OldPop(y2,:);
%采用均勻交叉
function[children1,children2]=EqualCrossOver(parent1,parent2)
global nchildren1 children2
hidecode=round(rand(1,n));%隨機(jī)生成掩碼
crossposition=find(hidecode==1);
holdposition=find(hidecode==0);
children1(crossposition)=parent1(crossposition);%掩碼為1，父1為子1提供基因
children1(holdposition)=parent2(holdposition);%掩碼為0，父2為子1提供基因
children2(crossposition)=parent2(crossposition);%掩碼為1，父2為子2提供基因
children2(holdposition)=parent1(holdposition);%掩碼為0，父1為子2提供基因
%采用多點(diǎn)交叉，交叉點(diǎn)數(shù)由變量數(shù)決定
function[Children1,Children2]=MultiPointCross(Parent1,Parent2)
global nChildren1 Children2 VarNum
Children1=Parent1;
Children2=Parent2;
Points=sort(unidrnd(n,1,2*VarNum));
for i=1:VarNum
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
end
%變異操作
function[NewPop]=Mutation(OldPop,pMutation,VarNum)
global m nNewPop
r=rand(1,m);
position=find(r<=pMutation);
len=length(position);
if len>=1
fori=1:len
k=unidrnd(n,1,VarNum); %設(shè)置變異點(diǎn)數(shù)，一般設(shè)置1點(diǎn)
for j=1:length(k)
if OldPop(position(i),k(j))==1
OldPop(position(i),k(j))=0;
else
OldPop(position(i),k(j))=1;
end
end
end
end
NewPop=OldPop;
%倒位操作
function[NewPop]=Inversion(OldPop,pInversion)
global m nNewPop
NewPop=OldPop;
r=rand(1,m);
PopIn=find(r<=pInversion);
len=length(PopIn);
if len>=1
for i=1:len
d=sort(unidrnd(n,1,2));
if d(1)~=1&d(2)~=n
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
end
end
end
遺傳算法程序（二）:
functionyouhuafun
D=code;
N=50; % Tunable
maxgen=50; % Tunable
crossrate=0.5;%Tunable
muterate=0.08;%Tunable
generation=1;
num = length(D);
fatherrand=randint(num,N,3);
score =zeros(maxgen,N);
whilegeneration<=maxgen
ind=randperm(N-2)+2; % 隨機(jī)配對(duì)交叉
A=fatherrand(:,ind(1:(N-2)/2));
B=fatherrand(:,ind((N-2)/2+1:end));
% 多點(diǎn)交叉
rnd=rand(num,(N-2)/2);
ind=rnd tmp=A(ind);
A(ind)=B(ind);
B(ind)=tmp;
% % 兩點(diǎn)交叉
% for kk=1:(N-2)/2
% rndtmp=randint(1,1,num)+1;
% tmp=A(1:rndtmp,kk);
% A(1:rndtmp,kk)=B(1:rndtmp,kk);
% B(1:rndtmp,kk)=tmp;
% end
fatherrand=[fatherrand(:,1:2),A,B];
% 變異
rnd=rand(num,N);
ind=rnd [m,n]=size(ind);
tmp=randint(m,n,2)+1;
tmp(:,1:2)=0;
fatherrand=tmp+fatherrand;
fatherrand=mod(fatherrand,3);
% fatherrand(ind)=tmp;
%評(píng)價(jià)、選擇
scoreN=scorefun(fatherrand,D);% 求得N個(gè)個(gè)體的評(píng)價(jià)函數(shù)
score(generation,:)=scoreN;
[scoreSort,scoreind]=sort(scoreN);
sumscore=cumsum(scoreSort);
sumscore=sumscore./sumscore(end);
childind(1:2)=scoreind(end-1:end);
fork=3:N
tmprnd=rand;
tmpind=tmprnd difind=[0,diff(tmpind)];
if ~any(difind)
difind(1)=1;
end
childind(k)=scoreind(logical(difind));
end
fatherrand=fatherrand(:,childind);
generation=generation+1;
end
% score
maxV=max(score,[],2);
minV=11*300-maxV;
plot(minV,'*');title('各代的目標(biāo)函數(shù)值');
F4=D(:,4);
FF4=F4-fatherrand(:,1);
FF4=max(FF4,1);
D(:,5)=FF4;
save DData D
function D=code
load youhua.mat
% properties F2and F3
F1=A(:,1);
F2=A(:,2);
F3=A(:,3);
if(max(F2)>1450)||(min(F2)<=900)
error('DATA property F2 exceed it''s range (900,1450]')
end
% get groupproperty F1 of data, according to F2 value
F4=zeros(size(F1));
for ite=11:-1:1
index=find(F2<=900+ite*50);
F4(index)=ite;
end
D=[F1,F2,F3,F4];
functionScoreN=scorefun(fatherrand,D)
F3=D(:,3);
F4=D(:,4);
N=size(fatherrand,2);
FF4=F4*ones(1,N);
FF4rnd=FF4-fatherrand;
FF4rnd=max(FF4rnd,1);
ScoreN=ones(1,N)*300*11;
% 這里有待優(yōu)化
for k=1:N
FF4k=FF4rnd(:,k);
forite=1:11
F0index=find(FF4k==ite);
if ~isempty(F0index)
tmpMat=F3(F0index);
tmpSco=sum(tmpMat);
ScoreBin(ite)=mod(tmpSco,300);
end
end
Scorek(k)=sum(ScoreBin);
end
ScoreN=ScoreN-Scorek;
遺傳算法程序（三）：
%IAGA
function best=ga
clear
MAX_gen=200; %最大迭代步數(shù)
best.max_f=0; %當(dāng)前最大的適應(yīng)度
STOP_f=14.5; %停止循環(huán)的適應(yīng)度
RANGE=[0255]; %初始取值范圍[0 255]
SPEEDUP_INTER=5; %進(jìn)入加速迭代的間隔
advance_k=0; %優(yōu)化的次數(shù)
popus=init; %初始化
forgen=1:MAX_gen
fitness=fit(popus,RANGE); %求適應(yīng)度
f=fitness.f;
picked=choose(popus,fitness); %選擇
popus=intercross(popus,picked); %雜交
popus=aberrance(popus,picked); %變異
if max(f)>best.max_f
advance_k=advance_k+1;
x_better(advance_k)=fitness.x;
best.max_f=max(f);
best.popus=popus;
best.x=fitness.x;
end
if mod(advance_k,SPEEDUP_INTER)==0
RANGE=minmax(x_better);
RANGE
advance=0;
end
end
return;
functionpopus=init%初始化
M=50;%種群個(gè)體數(shù)目
N=30;%編碼長(zhǎng)度
popus=round(rand(M,N));
return;
functionfitness=fit(popus,RANGE)%求適應(yīng)度
[M,N]=size(popus);
fitness=zeros(M,1);%適應(yīng)度
f=zeros(M,1);%函數(shù)值
A=RANGE(1);B=RANGE(2);%初始取值范圍[0 255]
for m=1:M
x=0;
for n=1:N
x=x+popus(m,n)*(2^(n-1));
end
x=x*((B-A)/(2^N))+A;
for k=1:5
f(m,1)=f(m,1)-(k*sin((k+1)*x+k));
end
end
f_std=(f-min(f))./(max(f)-min(f));%函數(shù)值標(biāo)準(zhǔn)化
fitness.f=f;fitness.f_std=f_std;fitness.x=x;
return;
functionpicked=choose(popus,fitness)%選擇
f=fitness.f;f_std=fitness.f_std;
[M,N]=size(popus);
choose_N=3; %選擇choose_N對(duì)雙親
picked=zeros(choose_N,2); %記錄選擇好的雙親
p=zeros(M,1); %選擇概率
d_order=zeros(M,1);
%把父代個(gè)體按適應(yīng)度從大到小排序
f_t=sort(f,'descend');%將適應(yīng)度按降序排列
for k=1:M
x=find(f==f_t(k));%降序排列的個(gè)體序號(hào)
d_order(k)=x(1);
end
for m=1:M
popus_t(m,:)=popus(d_order(m),:);
end
popus=popus_t;
f=f_t;
p=f_std./sum(f_std); %選擇概率
c_p=cumsum(p)'; %累積概率
forcn=1:choose_N
picked(cn,1)=roulette(c_p); %輪盤(pán)賭
picked(cn,2)=roulette(c_p); %輪盤(pán)賭
popus=intercross(popus,picked(cn,:));%雜交
end
popus=aberrance(popus,picked);%變異
return;
functionpopus=intercross(popus,picked) %雜交
[M_p,N_p]=size(picked);
[M,N]=size(popus);
for cn=1:M_p
p(1)=ceil(rand*N);%生成雜交位置
p(2)=ceil(rand*N);
p=sort(p);
t=popus(picked(cn,1),p(1):p(2));
popus(picked(cn,1),p(1):p(2))=popus(picked(cn,2),p(1):p(2));
popus(picked(cn,2),p(1):p(2))=t;
end
return;
functionpopus=aberrance(popus,picked) %變異
P_a=0.05;%變異概率
[M,N]=size(popus);
[M_p,N_p]=size(picked);
U=rand(1,2);
for kp=1:M_p
if U(2)>=P_a %如果大于變異概率，就不變異
continue;
end
if U(1)>=0.5
a=picked(kp,1);
else
a=picked(kp,2);
end
p(1)=ceil(rand*N);%生成變異位置
p(2)=ceil(rand*N);
if popus(a,p(1))==1%0 1變換
popus(a,p(1))=0;
else
popus(a,p(1))=1;
end
if popus(a,p(2))==1
popus(a,p(2))=0;
else
popus(a,p(2))=1;
end
end
return;
functionpicked=roulette(c_p) %輪盤(pán)賭
[M,N]=size(c_p);
M=max([M N]);
U=rand;
if U<c_p(1)
picked=1;
return;
end
for m=1:(M-1)
if U>c_p(m) & U<c_p(m+1)
picked=m+1;
break;
end
end
全方位的兩點(diǎn)雜交、兩點(diǎn)變異的改進(jìn)的加速遺傳算法（IAGA）
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