matlab常见函数绘制

F1 Ackley

Function

1

1

1

cos(2)

()

F2020

D

i

i

x

D

e e e

π

=

∑

=--++ X

F2 Griewank

Function

2

2

11

1

F()1 4000

D

D

i

i i

x

==

=-+

∑∏

X

x1=linspace(-300,300,50); x2=x1;

[X1,X2]=meshgrid(x1,x2); A=X1.^2+X2.^2;

B=cos(X1).*cos(X2/sqrt(2)); Z=(1/4000)*A-B+1; meshc(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Griewank Function') axis square

F3 Michalewics

Function

()

3

2

2

1

F()sin()sin(/);10

D m

i i

i

x ix m

π

=

=-=

∑

X

x1=linspace(-10,pi,80);

x2=x1;

m=10;

[X1,X2]=meshgrid(x1,x2);

X=[X1,X2];

A=sin(X1).*(sin(X1.^2/pi)).^(2*m);

B=sin(X2).*(sin(2*(X2.^2)/pi)).^(2*m); Z=-(A+B);

mesh(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Michalewics')

X1

Griewank Function

X2

Z

X1

Michalewics

X2

Z

F4 Levy Function

()() 4

22222

1

1

()

F sin()(1)110sin(1)(1)110sin(2)

i i D D

i

y y y y y

πππ

=

??

=+-+++-+

??

∑

X

1

1,1,2,,

4

i

i

x

y i D

-

=+=

x1=linspace(-10,10,100);

x2=x1;

[X1,X2]=meshgrid(x1,x2);

X=[X1,X2];

Y1=1+(X1-1)/4;

Y2=1+(X2-1)/4;

A=sin(pi*Y1);

B=(Y1-1).^2;C=1+10*((sin(pi*Y1+1)).^2); D=(Y2-1).^2;E=1+10*((sin(2*pi*Y2)).^2); Z=A.^2+B.*C+D.*E;

mesh(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Levy')

colormap('cool')

F5 Rastrigin

Function

() 5

2

1

()

F1010cos(2)

D

i i

i

D x x

π

=

=+-

∑

X

x1=linspace(-5.12,5.12,100); x2=x1;

[X1,X2]=meshgrid(x1,x2); D=2;

X=[X1,X2];

A=X1.^2-10*cos(2*pi*X1); B=X2.^2-10*cos(2*pi*X2); Z=10*D+A+B;

meshc(X1,X2,Z) colormap('pink')

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Rastrigin ')

F6

Rosenbrock Function

6

222

1

2

()

F()(1)

i i i

i

x x x

-

=

??=-+-

??

∑

X

x1=linspace(-50,50,80);

x2=x1;

[X1,X2]=meshgrid(x1,x2); Z=(X2.^2-X1).^2+(X2-1).^2; meshc(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Rosenbrock ')

colormap('cool')

X1

Levy

X2

Z

X1

Rastrigin

X2

Z

Z

F7 Schwefel 2.26

Function

2 7

1

F()418.982887272434

D

i

i

D x

=

=-∑X

x1=linspace(-435,435,75);

x2=x1;

[X1,X2]=meshgrid(x1,x2);

B=sqrt(abs(X1));A=X1.^2.*sin(B); D=sqrt(abs(X2));C=X2.^2.*sin(D); Z=418.9828872722434*2-(A+C); meshc(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Schwefel ')

F8

Sphere Function

8

2

1 ()

F

D

i

i

x

=

=∑

X

x1=linspace(-50,50,80);

x2=linspace(-50,50,60); [X1,X2]=meshgrid(x1,x2); Z=X1.^2+X2.^2;

meshc(X1,X2,Z)

xlabel('X1')

ylabel('X2')

zlabel('Z')

title('Sphere ')

colormap('cool')

X1

Schwefel

X2

Z

X1

Sphere

X2

Z