智能算法之Matlab实现（1）——遗传算法（1）

遗传算法的过程在这里先不介绍了，可能在接下来的几篇文章会介绍，这里介绍些实用的。

（1）Sheffield遗传算法工具箱的安装

我共享了下修改过文件名和后缀名的原版工具箱，地址为：http://pan.baidu.com/s/1inVKE

安装方法：

将整个文件夹复制到matlab安装文件夹中的toolbox文件夹

例如：C:\Program Files\MATLAB\R2013b\toolbox文件夹。

然后在Command Window里面输入：

str = ['C:\Program Files\MATLAB\R2013b\toolbox\gatbx']

addpath(str)

可能有些同学出现过这个问题，

Undefined function or method 'crtbp' for input arguments of type 'double'

或者是：

Cannot find an exact (case-sensitive) match for 'crtbp.m'
The closest match is C:\Program Files\MATLAB\R2012a\toolbox\gatbx\CRTBP.M

To change the file extension, cd to the file's folder, type:

movefile CRTBP.M CRTBP.m_bad; movefile CRTBP.m_bad CRTBP.m

and then cd back.

这是因为新旧Matlab版本对于M文件的文件名要求不尽相同，将其全部改为小写文件名和文件后缀名即可。

（2）应用实例（1）——单变量函数求最值

类似模板的东西，求解此函数最大值：

有如下代码：

%% Do Some Cleaning
clc
clear all;
close all;
%% Set the initial parameters
lb = 1; ub = 2;%x belongs to [1,2]
%% Plot
figure(1);
hold on;
ezplot('sin(10*pi*X)/X',[lb,ub]);
xlabel('x/X')
ylabel('y/Y')
%% Define the parameters of GA
NIND = 40;%size of the group
MAXGEN = 20;%max generations
PRECI = 20;%length of a individual
GGAP = 0.95;%gap
px = 0.7;%the possibility of cross production
pm = 0.1;%the possibility of mutation
trace = zeros(2,MAXGEN);%init value of algorithm寻优函数
FieldD = [PRECI;lb;ub;1;0;1;1];%区域描述器
Chrom = crtbp(NIND,PRECI);%creat random discrete group
%% Optimizations
gen = 0;%counter of generations
X = bs2rv(Chrom,FieldD);%bin to dec
ObjV = sin(10 * pi * X) ./ X;%cal the f(x)
while gen < MAXGEN
    FitnV = ranking(ObjV);%allocate the adaptness
    SelCh = select('sus',Chrom,FitnV,GGAP);%select
    SelCh = recombin('xovsp',SelCh,px);%recombine
    SelCh = mut(SelCh, pm);%mutate
    X = bs2rv(SelCh,FieldD);%to dec
    ObjVSel = sin(10 * pi * X)./ X;%cal the next-gen's target f(x)
    [Chrom, ObjV] = reins(Chrom, SelCh, 1, 1, ObjV, ObjVSel);%reinsert them to father-gen
    X = bs2rv(Chrom, FieldD);
    gen = gen + 1;%counter+=1
    %get every gen's answers and it's nums, Y stant for best f(x), I for
    %nums;
    [Y I] = min(ObjV);
    trace(1,gen) = X(I);
    trace(2,gen) = Y;
end
%% Plot
plot(trace(1,:),trace(2,:),'bo');%plot every gen's answer
grid on;
plot(X,ObjV,'b*');
hold off
%% Plot the evolution
figure(2);
plot(1:MAXGEN,trace(2,:));
grid on
xlabel('count of generations')
ylabel('answer')
title('procedure')
bestY = trace(2,end)
bestX = trace(1,end)

运行结果：

（3）应用实例（2）——双变量函数求最值

那么有如下代码：

%% Do Some Cleaning
clc
clear all;
close all;
%% Set the initial parameters
lbx = -2; ubx = 2;%x belongs to [-2,2]
lby = -2; uby = 2;%y belongs to [-2,2]
%% Plot
figure(1);
ezmesh('y*sin(2*pi*x) + x*cos(2*pi*y)',[lbx,ubx,lby,uby],50);
xlabel('x/X')
ylabel('y/Y')
hold on;
%% Define the parameters of GA
NIND = 40;%size of the group
MAXGEN = 20;%max generations
PRECI = 20;%length of a individual
GGAP = 0.95;%gap
px = 0.7;%the possibility of cross production
pm = 0.01;%the possibility of mutation
trace = zeros(3,MAXGEN);%init value of algorithm寻优函数
FieldD = [PRECI PRECI;lbx lby;ubx uby;1 1;0 0;1 1;1 1];%Field discriber
Chrom = crtbp(NIND,PRECI*2);%creat random discrete group
%% Optimizations
gen = 0;%counter of generations
XY = bs2rv(Chrom,FieldD);%bin to dec
X = XY(:,1);
Y = XY(:,2);
ObjV = Y.*sin(2*pi*X) + X.*cos(2*pi*Y);%cal the f(x,y)
while gen < MAXGEN
    FitnV = ranking(-ObjV);%allocate the adaptness
    SelCh = select('sus',Chrom,FitnV,GGAP);%select
    SelCh = recombin('xovsp',SelCh,px);%recombine
    SelCh = mut(SelCh, pm);%mutate
    XY = bs2rv(SelCh,FieldD);%bin to dec
    X = XY(:,1);
    Y = XY(:,2);
    ObjVSel = Y.*sin(2*pi*X) + X.*cos(2*pi*Y);%cal the next-gen's target f(x)
    [Chrom, ObjV] = reins(Chrom, SelCh, 1, 1, ObjV, ObjVSel);%reinsert them to father-gen
    XY = bs2rv(Chrom,FieldD);
    gen = gen + 1;%counter+=1
    %get every gen's answers and it's nums, Y stant for best f(x), I for
    %nums;
    [Y, I] = max(ObjV);
    trace(1:2,gen) = XY(I,:);
    trace(3,gen) = Y;
end
%% Plot
plot3(trace(1,:),trace(2,:),trace(3,:),'bo');%plot every gen's answer
grid on;
plot3(XY(:,1),XY(:,2),ObjV,'b*');
hold off
%% Plot the evolution
figure(2);
plot(1:MAXGEN,trace(3,:));
grid on
xlabel('count of generations')
ylabel('answer')
title('procedure')
bestX = trace(1,end)
bestY = trace(2,end)
bestZ = trace(3,end)

运行结果：

（4）应用实例（3）——遗传算法接力优化（采用系统GAtool工具箱）

优化此函数：

第一个文件（主文件）：

%主程序：本程序采用遗传算法接力进化，
%将上次进化结束后得到的最终种群作为下次输入的初始种群
clc;
close all;
clear all;
%进化的代数
T=100;
optionsOrigin=gaoptimset('Generations',T/2);
[x,fval,reason,output,finnal_pop]=ga(@ff,2,optionsOrigin);
%进行第二次接力进化
options1=gaoptimset('Generations',T/2,'InitialPopulation',finnal_pop,...
    'PlotFcns',@gaplotbestf);
[x,fval,reason,output,finnal_pop]=ga(@ff,2,options1);
Bestx=x
BestFval=fval

评价函数文件，与主文件一起保存，名字为ff.m

%子函数：适应度函数同时也是目标函数,函数存储名称为ch14_2f.m
function f=ff(x)
g1=1.5+x(1)*x(2)-x(1)-x(2);
g2=-x(1)*x(2);
if(g1>0||g2>10)
    f=100;
else
    f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1);
end

程序结果：

至此，第一部分结束，下一篇将介绍遗传算法的基本内容。