本文代码为《数学建模算法与应用（第二版）》中改进遗传算法一节中代码，这里只对代码进行解释，适合新手入门
该进点：1、选择优势个体作为下一次循环父代
2、单点交叉
3、变异操作，跳出局部最优解
算法实例：某侦察机由基地出发一次经过100各观测点返回基地，求最短路线。
坐标数据：奇数列为x坐标，偶数列为对应y坐标
请将数据保存为：sj.txt
53.7121 15.3046 51.1758 0.0322 46.3253 28.2753 30.3313 6.9348
56.5432 21.4188 10.8198 16.2529 22.7891 23.1045 10.1584 12.4819
20.1050 15.4562 1.9451 0.2057 26.4951 22.1221 31.4847 8.9640
26.2418 18.1760 44.0356 13.5401 28.9836 25.9879 38.4722 20.1731
28.2694 29.0011 32.1910 5.8699 36.4863 29.7284 0.9718 28.1477
8.9586 24.6635 16.5618 23.6143 10.5597 15.1178 50.2111 10.2944
8.1519 9.5325 22.1075 18.5569 0.1215 18.8726 48.2077 16.8889
31.9499 17.6309 0.7732 0.4656 47.4134 23.7783 41.8671 3.5667
43.5474 3.9061 53.3524 26.7256 30.8165 13.4595 27.7133 5.0706
23.9222 7.6306 51.9612 22.8511 12.7938 15.7307 4.9568 8.3669
21.5051 24.0909 15.2548 27.2111 6.2070 5.1442 49.2430 16.7044
17.1168 20.0354 34.1688 22.7571 9.4402 3.9200 11.5812 14.5677
52.1181 0.4088 9.5559 11.4219 24.4509 6.5634 26.7213 28.5667
37.5848 16.8474 35.6619 9.9333 24.4654 3.1644 0.7775 6.9576
14.4703 13.6368 19.8660 15.1224 3.1616 4.2428 18.5245 14.3598
58.6849 27.1485 39.5168 16.9371 56.5089 13.7090 52.5211 15.7957
38.4300 8.4648 51.8181 23.0159 8.9983 23.6440 50.1156 23.7816
13.7909 1.9510 34.0574 23.3960 23.0624 8.4319 19.9857 5.7902
40.8801 14.2978 58.8289 14.5229 18.6635 6.7436 52.8423 27.2880
39.9494 29.5114 47.5099 24.0664 10.1121 27.2662 28.7812 27.6659
8.0831 27.6705 9.1556 14.1304 53.7989 0.2199 33.6490 0.3980
1.3496 16.8359 49.9816 6.0828 19.3635 17.6622 36.9545 23.0265
15.7320 19.5697 11.5118 17.3884 44.0398 16.2635 39.7139 28.4203
6.9909 23.1804 38.3392 19.9950 24.6543 19.6057 36.9980 24.3992
4.1591 3.1853 40.1400 20.3030 23.9876 9.4030 41.1084 27.7149实现代码
tic%开始计时
clc,clear
sj0 = load('sj.txt');%读取坐标数据，经纬度
x = sj0(:,1:2:8);x = x(:);
y = sj0(:,2:2:8);y = y(:);
sj = [x,y];d1 = [70,40];
sj = [d1;sj;d1];
sj = sj*pi/180;%转化为角度，方便后面三角函数计算
d = zeros(102);
for i = 1:101%此语句用来计算任意两点之间的距离
for j = i+1:102%节约时间，只计算i到j距离，没有计算j到i的距离，（相等）
d(i,j) = 6370*acos(cos(sj(i,1)-sj(j,1))*cos(sj(i,2))*cos(sj(j,2))+sin(sj(i,2))*sin(sj(j,2)));
%计算任意两点间距离，经纬度用极坐标计算，地球半径为6370
end
end
d = d+d';w = 50; g = 100;%d距离矩阵，w种群个数，g进化代数
rand('state',sum(clock));%初始化随机函数发生器
for k=1:w%以下为改良圈算法寻找初始种群
c = randperm(100);%产生1，...,100的随机排列
c1 = [1,c+1,102];%产生初始解，出发点与终点固定，即1,102，其实两者为同一点，即基地所在位置
for t = 1:102;%修改圈
flag = 0;%退出标志,flag == 0时退出
for m = 1:100
for n = m+2:101
if d(c1(m),c1(n))+d(c1(m+1),c1(n+1))<d(c1(m),c1(m+1))+d(c1(n),c1(n+1))
c1(m+1:n) = c1(n:-1:m+1);
flag = 1;
end
end
end
if flag == 0
J(k,c1) = 1:102;break;%记录较好解，退出本层循环
end
end
end
J(:,1) = 0;J = J/102; %运行此语句前J为1...102的整数，第一列全为1，最后一列全为102
%运行后J变为0-1之间的实数，第一列全0，最后一列全1,
%此语句将J转换为染色体编码
for k = 1:g%以下为遗传算法
A = J;%初始自带染色体，A中共有50条染色
for i=1:2:w%w种群个数
ch1(1) = rand;%混沌序列初始值
for j = 2:50 %通过混沌序列找到一个染色体交叉交换位点
ch1(j) = 4*ch1(j-1)*(1-ch1(j-1));%此时ch1中为[0,1]间实数
end
ch1 = 2+floor(100*ch1);%floor()向下取整，将实数转化为[2-101之间的整数，避开始点与终点
temp = A(i,ch1);%交换操作
A(i,ch1) = A(i+1,ch1);
A(i+1,ch1) = temp;
end
by = [];%防止下面产生空地址
while ~length(by)%判断by是否为空
by = find(rand(1,w)<0.1);%产生变异操作的地址
end
num1 = length(by);B = J(by,:);%产生变异操作的染色体，染色体个数远少于50
ch2 = rand;%产生混沌序列，具体见上个for循环中产生交叉位置的注释
for t = 2:2*num1
ch2(t) = 4*ch2(t-1)*(1-ch2(t-1));
end
for j = 1:num1
bw = sort(2+floor(100*rand(1,2)));%找出变异的位置
B(j,bw) = ch2([j,j+1]);%变异操作
end
G = [J;A;B];%子代、父代染色体混合
[SG,ind1] = sort(G,2);%将G中元素每行按升序排列，ind1存储每个元素升序排列前的索引
%例[SG,IND] = sort([0.2,0.1,0.5;0.4,0.2,0.7],2)
%SG = [0.1,0.2,0.5;0.2,0.4,0.7]
%IND = [2,1,3;2,1,3]
%
%sort()见 doc sort
num2 = size(G,1);long = zeros(1,num2);%num2:染色体总个数，long:路径长度初始化
for j = 1:num2
for i=1:101
long(j) = long(j)+d(ind1(j,i),ind1(j,i+1));%计算每条路径的长度
end
end
[slong,ind2] = sort(long);%路径长度升序排列
J = G(ind2(1:w),:);%选取前w个优势个体，其余淘汰
end
path = ind1(ind2(1),:),flong = slong(1)%最终的路径及长度
toc%结束计时
xx = sj(path,1);yy = sj(path,2);
plot(xx,yy,'-o')
%参考文献：司守奎 孙兆亮 《数学建模算法与应用（第二版）》结果：
参考文献：司守奎 孙兆亮 《数学建模算法与应用（第二版）》
