%IAGA
function best=ga
clear
MAX_gen=200;            %最大迭代步數(shù)
best.max_f=0;           %當前最大的適應度
STOP_f=14.5;            %停止循環(huán)的適應度
RANGE=[0 255];          %初始取值范圍[0 255]
SPEEDUP_INTER=5;       %進入加速迭代的間隔
advance_k=0;            %優(yōu)化的次數(shù)

popus=init;             %初始化
for gen=1:MAX_gen
    fitness=fit(popus,RANGE);       %求適應度
    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;
function popus=init%初始化
M=50;%種群個體數(shù)目
N=30;%編碼長度
popus=round(rand(M,N));
return;

function fitness=fit(popus,RANGE)%求適應度
[M,N]=size(popus);
fitness=zeros(M,1);%適應度
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)值標準化
fitness.f=f;fitness.f_std=f_std;fitness.x=x;
return;

function picked=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);

%把父代個體按適應度從大到小排序
f_t=sort(f,‘descend‘);%將適應度按降序排列
for k=1:M
    x=find(f==f_t(k));%降序排列的個體序號
    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

for cn=1:choose_N
    picked(cn,1)=roulette(c_p); %輪盤賭
    picked(cn,2)=roulette(c_p); %輪盤賭
    popus=intercross(popus,picked(cn,:));%雜交
end
popus=aberrance(popus,picked);%變異
return;

function popus=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;
function popus=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;

function picked=roulette(c_p) %輪盤賭
[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