main.m

遗传算法样例

%主函数
function [x Objective] = Main(PopSize, GEN, P_Crossover, P_Mutation)
[x q] = Init(PopSize);
[Objective chro] = evaluation(0, PopSize, x);
x = chro;
for i=1:GEN
    selection(PopSize, x, q);
    crossover(PopSize, P_Crossover, x);
    mutation(PopSize, P_Mutation, x);
    [Objective chro] = evaluation(i, PopSize, x);
    x = chro;
end
x(1,1)
x(1,2)
x(1,3)
Objective(1)
sqrt(x(1,1))+sqrt(x(1,2))+sqrt(x(1,3))

%边界函数
function [ check ] = checkbound(x)

if power(x(1),2)+2*power(x(2),2)+3*power(x(3),2) > 1
    check = 0;
else
    check = 1;
end

function [ x q ] = Init(PopSize)
%UNTITLED1 Summary of this function goes here
%   Detailed explanation goes here
x = rand(PopSize+1, 3);
a = 0.05;
q(1) = 0.05;
for i=2:PopSize+1
    a = a*0.95;
    q(i) = q(i-1)+a;
end;
for i=2:PopSize+1   
    check = checkbound(x(i,:));
    while x(i,1)<0 || x(i,2)<0 || x(i,3)<0 || check == 0    
        x(i,:) = rand(1,3);
        check = checkbound(x(i,:)); 
    end
end
%目标函数
function [Objective] = objective_function(PopSize, chromosome)

for i=2:PopSize+1
    x1 = chromosome(i,1);
    x2 = chromosome(i,2);
    x3 = chromosome(i,3);
    Objective(i) = sqrt(x1)+sqrt(x2)+sqrt(x3); 
end
Objective(1) = max(Objective);

%评估函数
function [Objective, chro] = evaluation(gen, PopSize, chromosome)

Objective = objective_function(PopSize, chromosome);
[temp IX] = sort(Objective(2:PopSize+1),'descend');
Objective(2:PopSize+1) = temp;
for i=2:PopSize+1
    chro(i,:) = chromosome(IX(i-1)+1,:);
end
if Objective(1) > sqrt(chro(1,1))+sqrt(chro(1,2))+sqrt(chro(1,3))
    chro(1,:) = chromosome(IX(1)+1,:);
end

%选择函数
function selection(PopSize, chromosome, q)

for i=2:PopSize+1
    r = rand*q(PopSize);
    for j=2:PopSize+1
        if r <= q(j)
            temp(i,:) = chromosome(j,:);
            break;
        end
    end
end
for i=2:PopSize+1
    chromosome(i,:) = temp(i,:);
end

%交叉函数
function crossover(PopSize, P_Crossover, chromosome)

pop = PopSize/2;
for i=2:pop+1
    if rand() > P_Crossover
        continue;
    end
    j = round(rand()*PopSize+1);
    jj = round(rand()*PopSize+1);
    r = rand();
    x = r*chromosome(j,:)+(1-r)*chromosome(jj,:);
    y = r*chromosome(jj,:)+(1-r)*chromosome(j,:);
    checkx = checkbound(x);
    checky = checkbound(y);
    if checkx == 1
        chromosome(j,:) = x;
    elseif checky == 1
        chromosome(jj,:) = y;
    end
end

%变异函数
function mutation(PopSize, P_Mutation, chromosome)

INFTY = 10;
precision = 0.0001;
for i=2:PopSize+1
    if rand() > P_Mutation
        continue;
    end
    x = chromosome(i,:);
    for k=1:3
        if rand() < 0.5
            direction(k) = rand()*2-1;
        else
            direction(k) = 0;
        end
    end
    infty = rand()*INFTY;
    while infty > precision
        for j=1:3
            y(j) = x(j)+infty*direction(j);
        end
        check = checkbound(y);
        if check == 1
            chromosome(i,:) = y;
            break;
        end
        infty = rand()*infty;
    end
end