基于遗传算法和非线性规划的函数寻优算法（开源详细）

遗传算法简介

百度上讲的很清楚，笔者这里就不一一赘述了，故附上网址。
https://baike.baidu.com/item/%E9%81%97%E4%BC%A0%E7%AE%97%E6%B3%95/838140?fr=aladdin#2
下面是一般遗传算法的流程图，编程的思想就算基于这个的。

题目与分析

代码

clear
clc
gen = 30;
popsize = 50;
cp = 0.9;
mp = 0.05;
% 个体初始化
chrome = [];
fitness = [];
avgfitness = [];
bestfitness = [];
bestchrome = [];
for i = 1:popsize
    chrome(i,:) = randn(1,2);
    fitness(i) = fx2(chrome(i,:));
end
% 进化开始
for i = 1:gen
    [m,n] = size(chrome);
    % 选择
    chrome = select2(chrome);
    % 交叉
    chrome = cross2(cp,chrome);
    % 变异
    chrome = mutate2(mp,chrome);
    for j = 1:m
        fitness(i) = fx2(chrome(i,:));
    end
    avgfitness(i) = sum(fitness)/m;
    bestfitness(i) = min(fitness);
    [t,u] = min(fitness);
    bestchrome(i,:) = chrome(u,:);
end
plot(avgfitness)
hold on
plot(bestfitness)
plot(bestchrome)

function fval=fx2(x)
% 计算目标函数值即适应度
fval = -20*exp(-0.2*sqrt((x(1)*x(1)+x(2)*x(2))/2))-exp((cos(2*pi*x(1))+cos(2*pi*x(2)))/2)+20+2.71289;

function ret=select2(chrome)
% 采用轮盘赌对种群chrome进行选择
[m,n] = size(chrome);
for i = 1:m
    fitness(i) = fx2(chrome(i,:));
end
sumfitness = sum(fitness);
sumf = fitness/sumfitness;
index = [];
for i = 1:m
    pick = rand;
    while pick == 0
        pick = rand;
    end
    for j = 1:m
        pick = pick - sumf(j);
        if pick < 0
            index = [index j];
            break;
        end
    end
end
for i = 1:length(index)
    ret(i,:) = chrome(i,:);
end

function ret=cross2(pc,chrome)
% 进行种群的交叉
[m,n] = size(chrome);
for i = 1:m
    pick = rand(1,2);
    while prod(pick) == 0
        pick = rand(1,2);
    end
    index = ceil(pick.*m);
    pick = rand;
    while pick == 0
        pick = rand;
    end
    if pick > pc
        continue;
    end
    % 进行交叉
    v1 = chrome(index(1),:);
    v2 = chrome(index(2),:);
    temp1 = v1(1);
    temp2 = v2(1);
    v1(1) = temp2;
    v2(1) = temp1;
    if fx2(v1) < fx2(v2)
        v = v1;
    else
        v = v2;
    end
    ret(i,:) = v;
end

function chrome=mutate2(mp,chrome)
% 该函数用来对种群进行变异
[m,n] = size(chrome);
for i = 1:m
    pick = rand;
    while pick == 0
        pick = rand;
    end
    index = ceil(pick*m);
    pick = rand;
    if pick > mp
        continue;
    end
    while pick == 0
        pick = rand;
    end
    pos = ceil(pick*n);
    chrome(pos) = randn;
end

结果分析

收敛过早可能是交叉和遗传时没有采用二进制编码，所以过程比较简单，且没有使用工具箱造成的结果。但是大体的趋势是一样的，最终都趋于0这个值，在第六代左右时x的值也趋近于0。