Choosing optimal values from the genetic algorithm

As GA are probabilistic and indetriministic everytime I run the code I am getting different optimas with the same value of objective function.

How to choose the proper and best optima when the function value remains same for different optimias.

Is there any way to choose the best optima.

Thank you in Advance!!

Answer 1

[Sam Chak]

Hi @Vivek

You can try setting the rng to 'default' for the reproducibility of the result.

If the function has multiple extrema, I'd probably set the lower and upper bounds on the design variables, so that the solution is searched and found in the range of interest.

xx     = linspace(-pi, pi, 51);
yy     = linspace(-pi, pi, 51);
[X, Y] = meshgrid(xx, yy);
Z      = (sin(X)).^2 + (cos(Y)).^2;
% contour(X, Y, Z)
surfc(X, Y, Z)
xlabel('x_1'), ylabel('x_2'), zlabel('f(x_1, x_2)')

rng default         % For reproducibility
fun = @(x) (sin(x(1))).^2 + (cos(x(2))).^2;
lb = [-pi -pi];     % lower bound
ub = [pi pi];       % upper bound
x   = ga(fun, 2, [], [], [], [], lb, ub)

Optimization terminated: average change in the fitness value less than options.FunctionTolerance.

x = 1×2

-0.0000 1.5708

[Vivek]

Below shown is my objective function and related m and b function files are external function files.

function P1=f(x0)
M=5;
%x0=[5,8];
% x0=[12,13];
M2=m(M,x0(1));
M3=m(M2,x0(2));
M4=m(M3,(x0(1)+x0(2))); 
beta1=b(M,(x0(1)));
beta2=b(M2,(x0(2)));
beta3=b(M3,((x0(1)+x0(2))));
s1=sin(beta1);
s2=sin(beta2);
s3=sin(beta3);
t1n=(13.824)*((M2*M3*M)^2)*((s1*s2*s3)^2);
t1d=(((0.4)*(M3^2)*(s3^2))+2)*(((0.4)*(M2^2)*(s2^2))+2)*(((0.4)*(M^2)*(s1^2))+2);
t1=(t1n/t1d)^(3.5);
t2n=13.824;
t2d=((2.8*(M3^2)*(s3^2))-0.4)*((2.8*(M2^2)*(s2^2))-0.4)*((2.8*(M^2)*(s1^2))-0.4);
t2=(t2n/t2d)^(2.5);
    
P1=(t1*t2);
P= P1*(-1);
%  surf(
% fplot(x0,f)
end

%-----------------------------------------------------------------------
%-----------------------------------------------------------------------
%This is the separate script file 

x0=[x1,x2];

% Lower bounds
lb=[1,5];

% Upper Bounds
ub=[40,38];

nonlcon=@area

% 
rng default     
 x1   = linspace(1,100,55);
 x2   = linspace(1,100,55);
 [X, Y]  = meshgrid(x1, x2);
 Z      = f(x0);
 %contour(X, Y, Z)
 surfc(X, Y, Z)
 xlabel('x_1'), ylabel('x_2'), zlabel('f(x_1, x_2)')


% opts = optimoptions('fmincon','PlotFcn',["optimplotx","optimplotfunccount","optimplotfvalconstr","optimplotfval"],'Display','iter');
% opts1 = optimoptions(opts,'MaxIterations',100); % Recommended
% [x,fval,exitflag,output]= fmincon(@f,x0,[],[],[],[],lb,ub,[],opts1);
options=optimoptions('ga','ConstraintTolerance',1e-8,'Display','iter');
[x,fval,exitflag,output,population,scores]=ga(@f,2,[],[],[],[],lb,ub,nonlcon,[],options)

After using the above code it is showing the error as shown below.

Ig it is taking single value of x0

Error using surfc
The surface Z must contain more than one row or column.

Error in z (line 18)
surfc(X, Y, Z)