基于Ackley's function的，差分进化算法和粒子群算法的比较。
以下是matlab源码。
%%%%%%%%%%%%
%%%%%%%%%%%% Ackley's function
clear all; %清除所有变量
close all; %清图
clc; %清屏
x=-5:0.01:5;
y=-5:0.01:5;
N=size(x,2);
for i=1:N
for j=1:N
z(i,j)=-20*exp(-0.2*(0.5*(x(i)^2+y(j)^2))^0.5)-exp(0.5*(cos(2*pi*x(i))+cos(2*pi*y(j))))+20+exp(1);
end
end
mesh(x,y,z)
xlabel('x')
ylabel('y')
粒子群算法：
%%%%%%%%%%%%%%%%%粒子群算法求函数极值%%%%%%%%%%%%%%%%%%%%%%%%%%
tic %程序运行起点
time =[];
for i=1:500
time(i)=1;
end
%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all; %清除所有变量
close all; %清图
clc; %清屏
N=100; %群体粒子个数
D=2; %粒子维数
T=200; %最大迭代次数
c1=1.5; %学习因子1
c2=1.5; %学习因子2
Wmax=0.8; %惯性权重最大值
Wmin=0.4; %惯性权重最小值
Xmax=5; %位置最大值
Xmin=-5; %位置最小值
Vmax=1; %速度最大值
Vmin=-1; %速度最小值
%%%%%%%%%%%%%%%%初始化种群个体（限定位置和速度）%%%%%%%%%%%%%%%%
x=rand(N,D) * (Xmax-Xmin)+Xmin;
v=rand(N,D) * (Vmax-Vmin)+Vmin;
%%%%%%%%%%%%%%%%%%初始化个体最优位置和最优值%%%%%%%%%%%%%%%%%%%
p=x;
pbest=ones(N,1);
for i=1:N
pbest(i)=func_Ackley(x(i,:));
end
%%%%%%%%%%%%%%%%%%%初始化全局最优位置和最优值%%%%%%%%%%%%%%%%%%
g=ones(1,D);
gbest=inf;
for i=1:N
if(pbest(i)<gbest)
g=p(i,:);
gbest=pbest(i);
end
end
gb=ones(1,T);
%%%%%%%%%%%按照公式依次迭代直到满足精度或者迭代次数%%%%%%%%%%%%%
for i=1:T
for j=1:N
%%%%%%%%%%%%%%更新个体最优位置和最优值%%%%%%%%%%%%%%%%%
if (func_Ackley(x(j,:))<pbest(j))
p(j,:)=x(j,:);
pbest(j)=func_Ackley(x(j,:));
end
%%%%%%%%%%%%%%%%更新全局最优位置和最优值%%%%%%%%%%%%%%%
if(pbest(j)<gbest)
g=p(j,:);
gbest=pbest(j);
end
%%%%%%%%%%%%%%%%计算动态惯性权重值%%%%%%%%%%%%%%%%%%%%
w=Wmax-(Wmax-Wmin)*i/T;
%%%%%%%%%%%%%%%%%跟新位置和速度值%%%%%%%%%%%%%%%%%%%%%
v(j,:)=w*v(j,:)+c1*rand*(p(j,:)-x(j,:))...
+c2*rand*(g-x(j,:));
x(j,:)=x(j,:)+v(j,:);
%%%%%%%%%%%%%%%%%%%%边界条件处理%%%%%%%%%%%%%%%%%%%%%%
for ii=1:D
if (v(j,ii)>Vmax) | (v(j,ii)< Vmin)
v(j,ii)=rand * (Vmax-Vmin)+Vmin;
end
if (x(j,ii)>Xmax) | (x(j,ii)< Xmin)
x(j,ii)=rand * (Xmax-Xmin)+Xmin;
end
end
end
%%%%%%%%%%%%%%%%%%%%记录历代全局最优值%%%%%%%%%%%%%%%%%%%%%
gb(i)=gbest;
end
g; %最优个体
gb(end); %最优值
figure
plot(gb)
xlabel('迭代次数');
ylabel('适应度值');
title('适应度进化曲线')
toc %程序终点,，计时结束
%%%%%%%%%%%%%%%%%%%%%适应度函数%%%%%%%%%%%%%%%%%%%%%%%
function value=func_Ackley(x)
value=-20*exp(-0.2*(0.5*(x(1)^2+x(2)^2)).^0.5)-exp(0.5*(cos(2*pi*x(1))+cos(2*pi*x(2))))+20+exp(1);
差分进化算法：
%%%%%%%%%%%%%%%%%差分进化算法求函数极值%%%%%%%%%%%%%%%%%
tic %程序运行起点
time =[];
for i=1:500
time(i)=1;
end
%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%
clear all; %清除所有变量
close all; %清图
clc; %清屏
NP=20; %个体数目
D=2; %变量的维数
G=200; %最大进化代数
F=0.5; %变异算子
CR=0.1; %交叉算子
Xs=5; %上限
Xx=-5; %下限
%%%%%%%%%%%%%%%%%%%%%%%%%赋初值%%%%%%%%%%%%%%%%%%%%%%%%
x=zeros(D,NP); %初始种群
v=zeros(D,NP); %变异种群
u=zeros(D,NP); %选择种群
x=rand(D,NP)*(Xs-Xx)+Xx; %赋初值
%%%%%%%%%%%%%%%%%%%%计算目标函数%%%%%%%%%%%%%%%%%%%%%%%
for m=1:NP
Ob(m)=func_Ackley(x(:,m));
end
trace(1)=min(Ob);
%%%%%%%%%%%%%%%%%%%%%%%差分进化循环%%%%%%%%%%%%%%%%%%%%%
for gen=1:G
%%%%%%%%%%%%%%%%%%%%%%变异操作%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%r1,r2,r3和m互不相同%%%%%%%%%%%%%%%
for m=1:NP
r1=randint(1,1,[1,NP]);
while (r1==m)
r1=randint(1,1,[1,NP]);
end
r2=randint(1,1,[1,NP]);
while (r2==m)|(r2==r1)
r2=randint(1,1,[1,NP]);
end
r3=randint(1,1,[1,NP]);
while (r3==m)|(r3==r1)|(r3==r2)
r3=randint(1,1,[1,NP]);
end
v(:,m)=x(:,r1)+F*(x(:,r2)-x(:,r3));
end
%%%%%%%%%%%%%%%%%%%%%%交叉操作%%%%%%%%%%%%%%%%%%%%%%%
r=randint(1,1,[1,D]);
for n=1:D
cr=rand(1);
if (cr<=CR)|(n==r)
u(n,:)=v(n,:);
else
u(n,:)=x(n,:);
end
end
%%%%%%%%%%%%%%%%%%%边界条件的处理%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%边界吸收%%%%%%%%%%%%%%%%%%%%%%%%%
for n=1:D
for m=1:NP
if u(n,m)<Xx
u(n,m)=Xx;
end
if u(n,m)>Xs
u(n,m)=Xs;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%选择操作%%%%%%%%%%%%%%%%%%%%%%%
for m=1:NP
Ob1(m)=func_Ackley(u(:,m));
end
for m=1:NP
if Ob1(m)<Ob(m)
x(:,m)=u(:,m);
end
end
for m=1:NP
Ob(m)=func_Ackley(x(:,m));
end
trace(gen+1)=min(Ob);
end
[SortOb,Index]=sort(Ob);
x=x(:,Index);
X=x(:,1); %最优变量
Y=min(Ob); %最优值
%%%%%%%%%%%%%%%%%%%%%%%%%画图%%%%%%%%%%%%%%%%%%%%%%%%%%
figure
plot(trace);
xlabel('迭代次数')
ylabel('目标函数值')
title('DE目标函数曲线')
toc %程序终点,，计时结束
两种算法的运行结果与时间结果如上图，可以看到两种算法均可算出最优解为0，但粒子群算法速度较快。