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

gaoptimization problem

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)

Best Answer

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.
Related Question