Week 4.1 - Genetic Algorithm

https://in.mathworks.com/help/gads/ga.html#d123e47530

error for this program 

i got got many errors in this pogram

i can't get solution also

for the stage-3 ga increasing the iterations i did't got the plot or figure

i tried figure it but i cant have the solution for it

and i acnt find the solution for the errors in picture what i have shared

if possible share me solutions of the specify errors thanks

explation of the optimise the stalagmite function and find the global maxima of the function program and syntax of ga in three stages

Here we are writing a program for the optimise the stalagmite function and find the global maxima of the function And also explaining the syntax of the ga.

Starting with the Clear all,close all and clc commands to clear all data, close all plots and figures and clear the command window


x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
the above lines are for the defining the ‘x’ and ‘y’ using linspace command with 150 values from 0 to 0.6 and add the num_cases with 50 to run the ga 50 times.


%creating a 2D mesh
[xx yy] = meshgrid(x,y);

For creating the 2dimensional we are using the above line with meshgrid


for i = 1:length(xx)
     for j = 1:length(yy)

         input_vector(1) = xx(i,j);
         input_vector(2) = yy(i,j);

         f(i,j) = stalagmite(input_vector);
     end
 end


by using the i,j we are creating the input_vector(1) & input_vector(2) array for the each value of the x&y.

now we are creating the function ‘stalagmite’ taking the input_vector values for the values for the ‘f’.


now creating the program for the Stalagmite Function 

for that we having the formulas 


f(x,y) = f1,x*f2,x*f1,y*f4,y

f1,x = [sin(5.1πx+0.5)]6
f1,y = [sin(5.1πy+0.5)]6
f2,x = exp[-4ln(2) (x-0.0667)2/0.64]
f2,y = exp[-4ln(2) (y-0.0667)2/0.64]


for the above formulas we have to create the stalagmite function program


function[f] = stalagmite(input_vector)
f1_x = (sin(5.1*pi*input_vector(1) +  0.5 ))^6;

f1_y = (sin(5.1*pi*input_vector(2) +  0.5 ))^6;

f2_x = exp(-4*log(2)*((input_vector(1)-0.0667)^2 / 0.64));
f2_y = exp(-4*log(2)*((input_vector(2)-0.0667)^2 / 0.64));
 
f = f1_x * f1_y * f2_x * f2_y;

end


with using the simple program as above.


Now we are studying in 3 stages using the ga

Study-1 satistical behaviour


for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end



 in 1st study we are using the ga with 2 variables and storing the xoptium and yoptium values and optium values of the function

figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
shading interp

adding the figure,subplot,surfc and shading interp for the creating the all figure,subplot anf surfc

plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')

using the plot3 command for 3 values are xopt, yopt, fpot among the 50 values of ga predicates

adding the title for the plot and creating another subplot for the optium values of function as ga predicates

later adding the xlabel and y label

xlabel('iterations')
ylabel('function minimum')

syntax for the ga in study – 1

[inputs, fopt(i)] = ga(@stalagmite, 2)

x = ga(fun,nvars,A,b)
finds a local minimum x to fun,
fun = stalagmite function
nvars  = 2 variables 





study-2 statistical behaviour with upper and lower bounds

 
for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1]);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end


syntax for ga in study – 2 for upper and lower bounds

[inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1]);

x = ga(fun,nvars,A,b,Aeq,beq) finds a local minimum x to fun, 

A,B and Aeq,beq  will be linear inequaity constraint and linear equality constraints, if we don’t hv the values we will [ ], [ ]

And remaining all commands will be the same


Study – 3 Increasing the ga iterations

options = optimoptions('ga');
options = optimoptions(options,'PopulationSize',170)


for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1],options);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end


syntax for ga in study – 3 for Increasing the ga iterations

[inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1],options);

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options)

here where,

nonlcon =  nonlinear constraints
option = optimization options

And remaining all commands will be the same

Program for the Stalagmite function using the given formula

function[f] = stalagmite(input_vector)
f1_x = (sin(5.1*pi*input_vector(1) +  0.5 ))^6;

f1_y = (sin(5.1*pi*input_vector(2) +  0.5 ))^6;

f2_x = exp(-4*log(2)*((input_vector(1)-0.0667)^2 / 0.64));
 
f2_y = exp(-4*log(2)*((input_vector(2)-0.0667)^2 / 0.64));
 
f = f1_x * f1_y * f2_x * f2_y;

end

Program for the optimise the stalagmite function and find the global maxima of the function.

clear all
close all
clc

x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
num_cases = 50;

%creating a 2D mesh
[xx yy] = meshgrid(x,y);

%Evaluating the stalagmite function
 for i = 1:length(xx)
     for j = 1:length(yy)

         input_vector(1) = xx(i,j);
         input_vector(2) = yy(i,j);

         f(i,j) = stalagmite(input_vector);
     end
 end


% study 1 - satistiacl behaviour

tic

for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end


study1_time = toc;

figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Unbounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('iterations')
ylabel('function minimum')


%study2 : stastical behaviour with upper and lower bounds

tic

for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1]);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end

study2_time= toc

figure(2)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('iterations')
ylabel('function minimum')

%study3 : increasing GA iterations

options = optimoptions('ga');
options = optimoptions(options,'PopulationSize',170)

tic

for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1],options);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end

study3_time= toc

figure(3)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('iterations')
ylabel('function minimum')