数学建模之路----遗传算法

遗传操作：

遗传操作是优选，强势个体的“选择”，个体间交换基因产生新个体的“交叉”，个体基因信息突变产新个体的“变异”；遗传算法中的搜索最优解过程就是模仿生物的这个进化过程，使用遗传算子来实现的；

即有选择算子，交换算子，变异算子。

有空再写‘’‘’‘’‘’‘’‘’‘’

初始化：

% %%初始化
% %输入：chromes_size,dim维数，lb下界,ub上界
% %输出 chromes
function chromes = init_chromes(chromes_size,dim,lb,ub)
    chromes = rand(chromes_size,dim)*(ub-lb)+lb;
end

选择：

function [newchromes,newfitness] = selection(chromes,fitness)
    weights = 1./fitness;
    totalfit = sum(weights);
    totalf = weights./totalfit;
    index = [];
    for i = 1:size(chromes,1)
        pick = rand;
        while pick == 0
            pick = rand;
        end
        for j = 1:size(chromes,1)
            pick = pick - totalf(j);
            if pick < 0
                index = [index j];
                break
            end
        end
    end
    newchromes = chromes(index,:);
    newfitness = fitness(index);
end

 变异

function newchromes = muatation(chromes,pm,lb,ub)
    for i = 1:size(chromes,1)
        newchromes(i,:) = chromes(i,:);
        if (rand < pm)
            pos = ceil(rand * size(chromes,2));
            newchromes(i,pos) = rand*(ub-lb)+lb;
        end
    end
end

　交换

function newchromes = crossover(chromes, pc)
    newchromes = ones(size(chromes));
    for i = 1 : size(chromes, 1)
        parents = randperm(10,2);
        pos = round(rand*size(chromes,2));
        if (rand < pc)
            newchromes(i,:) = [chromes(parents(1),1:pos),chromes(parents(2),pos+1:size(chromes,2))];
        else
            newchromes(i,:) = chromes(i,:);
        end
    end
end

　主函数

clear
clc
chromes_size = 20;
dim = 2;
pc = 0.9;
pm = 0.2;
lb = -1;
ub = 1;
maxiter = 1000;
%目标方程
namefunc = 'sphere';
fd = str2func(namefunc);
chromes = init_chromes(chromes_size,dim,lb,ub);

for i = 1:chromes_size
    % fitness(i) = feval(fd,chromes);
    x = chromes(i, 1);
    y = chromes(i, 2);
    fitness(i) = sin(x)+cos(y)+0.1*x+0.1*y;
end
[bestfitness,bestindex] = min(fitness);
bestchrome = chromes(bestindex,:);
for iter = 1:maxiter
    [chromes,newfitness] = selection(chromes,fitness);
    chromes = crossover(chromes,pc);
    chromes = muatation(chromes,pm,lb,ub);
    for i = 1:chromes_size
        x = chromes(i, 1);
        y = chromes(i, 2);
        fitness(i) = sin(x)+cos(y)+0.1*x+0.1*y;
        if bestfitness >fitness(i)
            bestfitness = fitness(i);
            bestchrome = chromes(i,:);
        end
    end
    trace(iter) = bestfitness;
end
plot(trace)
title('fitness curve')