Problem in GA algorithm (objective function is not drectly related to the variables)

Hello all,

I am writing an optimization code, in which three variables are considered. The variables are used to find eigenpairs of the problem, and lately, eigenpairs are developing objective function. The objective fuction part of my code is as below.

    function [y] = obj_func(x)

%Input.........................................................
%..............................................................
%number of nodes
num_nod=6;

% nodes coordinates
nod_coor=[720 0;720 360;360 0;360 360;0 0;0 360];

% connectivity table
ele_nod=[6 4;4 2;5 3;3 1;3 4;1 2;6 3;5 4;4 1;3 2;5 6];

%number of elements
num_ele=size(ele_nod,1);

% elements degree of freedom (DOF) 
ele_dof=[11 12 7 8;7 8 3 4;9 10 5 6;...
5 6 1 2;5 6 7 8;1 2 3 4;11 12 5 6;...
9 10 7 8;7 8 1 2;5 6 3 4;9 10 11 12];

% A, E, L are cross sectional area, Young's modulus, length of elements,respectively.

A(1)=14;
A(2)=1;
A(3)=11;
A(4)=7;
A(5)=1;
A(6)=1;
A(7)=6;
A(8)=3;
A(9)=14;
A(10)=1;
A(11)=1;

E(1)=30000;
E(2)=30000;
E(3)=30000;
E(4)=30000;
E(5)=30000;
E(6)=30000;
E(7)=30000;
E(8)=30000;
E(9)=30000;
E(10)=30000;
E(11)=30000;

rho = 9.8759999999999994e-3;
stiffness_damage=zeros(2*num_nod);
mass=zeros(2*num_nod);
%applied loads at DOFs
force(2)=-10;
force(6)=-10;

%Boundary conditions
BC = [9;10;11;12];

%Variables from Phase I
global f_uD;
global f_DM;
global vec_D
global val_D
V_0_col = 2*num_nod - size(BC,1);
%..............................................................
%..............................................................

x1 = x(1);
x2 = x(2);
x3 = x(3);

damage_ele_size = 3;
damage_ele_1 = @(x)[1,x1;5,x2;10,x3];

%Compute stiffness matrix for damaged structure
for e=1:num_ele
    L(e)=sqrt((nod_coor(ele_nod(e,2),1)-nod_coor(ele_nod(e,1),1))^2+...
      (nod_coor(ele_nod(e,2),2)-nod_coor(ele_nod(e,1),2))^2);
 C(e)=(nod_coor(ele_nod(e,2),1)-nod_coor(ele_nod(e,1),1))/L(e);
 S(e)=(nod_coor(ele_nod(e,2),2)-nod_coor(ele_nod(e,1),2))/L(e);
 k_1=(A(e)*E(e)/L(e)*[C(e)*C(e) C(e)*S(e) -C(e)*C(e) -C(e)*S(e);C(e)*S(e) ...
     S(e)*S(e) -C(e)*S(e) -S(e)*S(e);-C(e)*C(e) -C(e)*S(e) C(e)*C(e) ...
     C(e)*S(e); -C(e)*S(e) -S(e)*S(e) C(e)*S(e) S(e)*S(e)]);

for kk = 1:damage_ele_size
    if e == damage_ele_1(kk,1)
        k_1 = k_1*(1-damage_ele_1(kk,2));
    end
end

% Develope mass matrix
m(e) = rho*L(e)*A(e);
m_local = [m(e)/2 0 0 0;0 m(e)/2 0 0;0 0 m(e)/2 0;0 0 0 m(e)/2];

% extract the rows of ele_dof (for each element e)
ele_dof_vec=ele_dof(e,:);
    for i=1:4
        for j=1:4
  stiffness_damage(ele_dof_vec(1,i),ele_dof_vec(1,j))=...
  stiffness_damage(ele_dof_vec(1,i),ele_dof_vec(1,j))+k_1(i,j);
  mass(ele_dof_vec(1,i),ele_dof_vec(1,j))=...
  mass(ele_dof_vec(1,i),ele_dof_vec(1,j))+m_local(i,j);
        end
    end
end

%Damaged Stiffness matrix after applying B.C.
for i = 1:size(BC,1)
    stiffness_damage(BC,:)=0;
    stiffness_damage(:,BC)=0;
end

for j = 1:size(BC)
   stiffness_damage(BC(j),BC(j))=1;
end

%Calculate Eigenpairs
[vec_D_m,val_D_m] = eig(stiffness_damage, mass, 'vector');
f_DA = val_D_m*(1/(2*pi));

%Define change in frequencies
delta_f = (f_uD - f_DM)/norm(f_uD);
round_f = (f_uD - f_DA)/norm(f_uD);
MDLAC = (abs(delta_f'*round_f)^2)/((delta_f'*delta_f)*(round_f'*round_f));

% Define Objective function
sum = zeros(2*num_nod,1);
for ki=1:V_0_col
    sum = sum + (vec_D(:,ki)-vec_D_m(:,ki)/norm(vec_D(:,ki)));
end
y = 1 - MDLAC + sum + 10e4*(MDLAC+abs(MDLAC));
end

The optimization line I use for solving the problem is as follow:

{[x,fval] = ga(@obj_func,3);}

The code is not working and gives me this error:

 Error using obj_func>@(x)[1,x1;5,x2;10,x3]
Too many input arguments.

Error in obj_func (line 85) if e == damage_ele_1(kk,1)

[TIACHACHT SAMIR]

please how to calculate f_uD

Answer 1

[Maryam]

So I was able to change the format of my code and I do not get the error again. However, it gives me a new error:

 Error using makeState (line 56)
Your fitness function must return a scalar value.

Error in gaunc (line 40)
state = makeState(GenomeLength,FitnessFcn,Iterate,output.problemtype,options);

Error in ga (line 356)
            [x,fval,exitFlag,output,population,scores] = gaunc(FitnessFcn,nvars,
            ...

Error in complete_code (line 266)
[x,fval] = ga(@obj_func,3);

Can anyone please tell me what this means? And possibly what do you recommend me to do to make it right? Thank you so very much.

[Matt J]

The "fitness function" means the function you are trying to optimize, in your case obj_func(). It is supposed to return a scalar value, but in your case is returning a non-scalar.

[Alan Weiss]

"Your fitness function must return a scalar value" means your fitness function should return a scalar, as opposed to a vector or matrix or array. To see what your fitness function is returning, evaluate

y = obj_func(x)

for some appropriate input vector x.

Alan Weiss

MATLAB mathematical toolbox documentation

[Maryam]

Thank you so much for the comments. They were really helpful!

Answer 2

[Matt J]

You have called the function damage_ele_1 with two arguments kk and 1 in the line

if e == damage_ele_1(kk,1)

However, you have defined damage_ele_1 as a function of only one argument, x,

damage_ele_1 = @(x)[1,x1;5,x2;10,x3];

It is not at all clear what damage_ele_1 is really supposed to compute. It returns the same 1x6 vector for every input x that you provide. The if statement condition above will never evaluate true.

[Maryam]

Thank you so much for your helpful comment. Actually "1, 5 and 10" are the damage element, and x(1), x(2) and x(3) are the severity of the damage that are supposed to be computed through this optimization code. They are the variables are the optimization problem. How do you think is the best way to define them? Thanks again for your time and help.