use ga optimization but got error for ga process

%fitness function Gomez and Levy

function y=fitnessfunctiongl(x)

x1=x(1);
x2=x(2);

y=(4*x1.^2)-2.1*x1.^4+1/3*x1.^6+(x1*x2)-4*x2.^2+4*x2.^4;

end

­­­­­%constraints

function [c ,ceq]=constraintgl(x)
x1=x(1);
x2=x(2);
c=-sin(4*pi*x1)+2*sin(2*pi*x2)^2-1.5;
ceq=[];
end

%main script to pass function and constraints to ga for optimization 
ObjFcn=@fitnessfunctiongl;
nvars=2;
lb=[-1, -1];
ub=[0.75, 1];

nonlcon=@constraintgl;
options = optimoptions('ga','ConstraintTolerance',1e-6,'Display','iter','PlotFcn',{@gaplotrange,@gaplotbestf,@gaplotselection,@gaplotmaxconstr}); %plotting the process of finding the solution 
%solution and function value
[x , fval,exitFlag,output,population,scores]= ga(ObjFcn,nvars,[],[],[],[],lb,ub,nonlcon,options);

----------------------------------but I got these errors------------------------------

Error in gadsplot (line 141)

[state,optimvalues] = callOnePlotFcn(fname,plotNames{i},state,options.OutputPlotFcnOptions,optimvalues,'init',args{i}{:});

Error in gacon (line 55)

state = gadsplot(options,state,'init','Genetic Algorithm');

Error in ga (line 406)

[x,fval,exitFlag,output,population,scores] = gacon(FitnessFcn,nvars, ...

Error in maingl (line 11)

[x , fval,exitFlag,output,population,scores]= ga(ObjFcn,nvars,[],[],[],[],lb,ub,nonlcon,options);

Answer 1

[Walter Roberson]

syms x [1 2]

x1=x(1);
x2=x(2);
y=(4*x1.^2)-2.1*x1.^4+1/3*x1.^6+(x1*x2)-4*x2.^2+4*x2.^4;

c=-sin(4*pi*x1)+2*sin(2*pi*x2)^2-1.5;

sol1 = solve(c, x1)

sol1 = 

eqn2 = subs(y, x1, sol1)

eqn2 = 

sol2a = vpasolve(eqn2(1), x2)

sol2a = 

sol2b = vpasolve(eqn2(2), x2)

sol2b = 

0.087919847529159662140915717986356

back1a = vpa(subs(eqn2(1), x2, sol2a))

back1a = 

back1b = vpa(subs(eqn2(2), x2, sol2b))

back1b = 

ya = vpa(subs(y, {x1, x2}, {back1a, sol2a}))

ya = 

yb = vpa(subs(y, {x1, x2}, {back1b, sol2b}))

yb = 

Beyond this, you need to test at least one c value less than that equality, such as c=-sin(4*pi*x1)+2*sin(2*pi*x2)^2-1.6; in case the minima is not right at the constraint bound.

Answer 2

[Matt J]

Perhaps you meant to have,

y=(4*x1.^2)-2.1*x1.^4+1/3*x1.^6+(x1*x2)-4*x1.^2+4*x2.^4;

or

y=(4*x1.^2)-2.1*x1.^4+1/3*x1.^6+(x1*x2)-4*x2.^2+4*x2.^4;

[sogol bandekian]

I did what you said but I have errors

Error in gadsplot (line 141)

[state,optimvalues] = callOnePlotFcn(fname,plotNames{i},state,options.OutputPlotFcnOptions,optimvalues,'init',args{i}{:});

Error in gacon (line 55)

state = gadsplot(options,state,'init','Genetic Algorithm');

Error in ga (line 406)

[x,fval,exitFlag,output,population,scores] = gacon(FitnessFcn,nvars, ...

Error in maingl (line 11)

[x , fval,exitFlag,output,population,scores]= ga(ObjFcn,nvars,[],[],[],[],lb,ub,nonlcon,options);

[Matt J]

Here's what I'm seeing.

%main script to pass function and constraints to ga for optimization 
ObjFcn=@fitnessfunctiongl;
nvars=2;
lb=[-1, -1];
ub=[0.75, 1];

nonlcon=@constraintgl;
options = optimoptions('ga','ConstraintTolerance',1e-6,'Display','iter','PlotFcn',{@gaplotrange,@gaplotbestf,@gaplotselection,@gaplotmaxconstr}); %plotting the process of finding the solution 

%solution and function value
[x , fval,exitFlag,output,population,scores]= ga(ObjFcn,nvars,[],[],[],[],lb,ub,nonlcon,options);

function y=fitnessfunctiongl(x)

    x1=x(1);
    x2=x(2);
    
    y=(4*x1.^2)-2.1*x1.^4+1/3*x1.^6+(x1*x2)-4*x2.^2+4*x2.^4;

end

function [c ,ceq]=constraintgl(x)
    x1=x(1);
    x2=x(2);
    c=-sin(4*pi*x1)+2*sin(2*pi*x2)^2-1.5;
    ceq=[];
end

[sogol bandekian]

how I can fix the plots ,sice they are empty of data

[Matt J]

They don't look empty to me. Zoom in on the early part of the plots.

[sogol bandekian]

yes,you are right,thank you so much,but is there a way to increase the data on plots?

[Alan Weiss]

You have nonlinear constraints. Therefore, the algorithm has few iterations, and plot functions are called just once per iteration. For an explanation of what nonlinear constraints do to the ga algorithm, see Nonlinear Constraint Solver Algorithms. For an example showing this behavior, see Constrained Minimization Using the Genetic Algorithm.

Alan Weiss

MATLAB mathematical toolbox documentation