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Please answer this question using matlab

MATLAB Question

You are given the function

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Answer #1

%MATLAB PROGRAM MINIMISING f(x1,x2) USING GENETIC ALGORITHM WITHOUT
%CONSTRAINTS

clc
clear

f = @(x) 2.*x(1).^2 - 2.*x(1).*x(2) + 2.*x(2).^2 - 6.*x(1) + 6;
xmin = -4; xmax = 4;
num_vars = 2; % number of variables = 2 (x1 and x2)

%applying ga
[X,fmin] = ga(f,num_vars,[],[],[],[],xmin,xmax,[],[])

%solutions
x1 = X(1)
x2 = X(2)
minimum_f_value = fmin

x1 = 2.0000 x2 = 1.0000 minimum f value = 2.6944e-09

%MATLAB PROGRAM MINIMISING f(x1,x2) USING GENETIC ALGORITHM A CONSTRAINT

function [c,ceq ] = constraint(x)
ceq = x(1)+x(2)-2; %equality constraint x1+x2 = 2
c = []; %inequality constraint
end

-------------------------

clc
clear

f = @(x) 2.*x(1).^2 - 2.*x(1).*x(2) + 2.*x(2).^2 - 6.*x(1) + 6;
xmin = -4; xmax = 4;
num_vars = 2;

%applying ga
[X,fmin] = ga(f,num_vars,[],[],[],[],xmin,xmax,@constraint,[]);

%solutions
x1 = X(1)
x2 = X(2)
minimum_f_value = fmin

x1 - 1.5000 x2 0.5000 minimum f value 0.5000

%MATLAB PROGRAM PLOTTING CONTOURS OF f(x1,x2)

close all
clear
clc

f = @(x1,x2) 2.*x1.^2 - 2.*x1.*x2 + 2.*x2.^2 - 6.*x1 + 6;
x1 = linspace(-4,4);
x2 = linspace(-4,4);
[X1,X2] = meshgrid(x1,x2);
F = f(X1,X2);
num_contours = 100;
figure
[C,h]=contour(X1,X2,F,num_contours)
title('contour plot of f(x1,x2) = 2*x1^2 - 2*x1*x2 + 2*x2^2 - 6*x1 + 6')
xlabel('x1'),ylabel('x2')
%clabel(C,h) % show contour levels (values)

contour plot of f(x1 x2)-2"X12-2X1%2 + 2X22-6X1 + 6 4 2 -2 -4 -3 -2 4 x1

contour plot of f(x1x2)-2x12-2"X1%2 + 2%22-6"X1+ 6 124765 12.4711 229 8.734 7.4865 6 3.744 2.4964 1 2489 4.9915 6.239 4.9915 6.239 7.4865 8.734 8.734 9.9815 -2 13 -4 x1

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Answer 1

%MATLAB PROGRAM MINIMISING f(x1,x2) USING GENETIC ALGORITHM WITHOUT
%CONSTRAINTS

clc
clear

f = @(x) 2.*x(1).^2 - 2.*x(1).*x(2) + 2.*x(2).^2 - 6.*x(1) + 6;
xmin = -4; xmax = 4;
num_vars = 2; % number of variables = 2 (x1 and x2)

%applying ga
[X,fmin] = ga(f,num_vars,[],[],[],[],xmin,xmax,[],[])

%solutions
x1 = X(1)
x2 = X(2)
minimum_f_value = fmin

x1 = 2.0000 x2 = 1.0000 minimum f value = 2.6944e-09

%MATLAB PROGRAM MINIMISING f(x1,x2) USING GENETIC ALGORITHM A CONSTRAINT

function [c,ceq ] = constraint(x)
ceq = x(1)+x(2)-2; %equality constraint x1+x2 = 2
c = []; %inequality constraint
end

-------------------------

clc
clear

f = @(x) 2.*x(1).^2 - 2.*x(1).*x(2) + 2.*x(2).^2 - 6.*x(1) + 6;
xmin = -4; xmax = 4;
num_vars = 2;

%applying ga
[X,fmin] = ga(f,num_vars,[],[],[],[],xmin,xmax,@constraint,[]);

%solutions
x1 = X(1)
x2 = X(2)
minimum_f_value = fmin

x1 - 1.5000 x2 0.5000 minimum f value 0.5000

%MATLAB PROGRAM PLOTTING CONTOURS OF f(x1,x2)

close all
clear
clc

f = @(x1,x2) 2.*x1.^2 - 2.*x1.*x2 + 2.*x2.^2 - 6.*x1 + 6;
x1 = linspace(-4,4);
x2 = linspace(-4,4);
[X1,X2] = meshgrid(x1,x2);
F = f(X1,X2);
num_contours = 100;
figure
[C,h]=contour(X1,X2,F,num_contours)
title('contour plot of f(x1,x2) = 2*x1^2 - 2*x1*x2 + 2*x2^2 - 6*x1 + 6')
xlabel('x1'),ylabel('x2')
%clabel(C,h) % show contour levels (values)

contour plot of f(x1 x2)-2"X12-2X1%2 + 2X22-6X1 + 6 4 2 -2 -4 -3 -2 4 x1

contour plot of f(x1x2)-2x12-2"X1%2 + 2%22-6"X1+ 6 124765 12.4711 229 8.734 7.4865 6 3.744 2.4964 1 2489 4.9915 6.239 4.9915 6.239 7.4865 8.734 8.734 9.9815 -2 13 -4 x1

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