Error using feval Argument must contain a string or function_handle.

Hi I'm having some hard time here with beneath code. This code is not mine but it's supposed to work, unfortunately what I get when I try to execute it is

>> benchmark_func([1 1], 1)

Error using feval Argument must contain a string or function_handle.

Error in benchmark_func (line 41) f=feval(fhd,x)+f_bias(func_num);

Any idea why this might happen? As you can see for feval(fhd,x) in that case we have fhd=str2func('sphere_func'); so it should be fine. Why do I get this error?

Thanks in advance.

function f=benchmark_func(x,func_num)
global initial_flag
persistent fhd f_bias

% benchmark_func.m is the main function for 25 test functions, all minimize
% problems
% e.g. f=benchmark_func(x,func_num)
% x is the variable, f is the function value 
% func_num is the function num,

if initial_flag==0
    if func_num==1 fhd=str2func('sphere_func'); %[-100,100]
    elseif func_num==2 fhd=str2func('schwefel_102'); %[-100,100]
    elseif func_num==3 fhd=str2func('high_cond_elliptic_rot_func'); %[-100,100]
    elseif func_num==4 fhd=str2func('schwefel_102_noise_func'); %[-100,100]
    elseif func_num==5 fhd=str2func('schwefel_206'); %[no bound],initial[-100,100];
    elseif func_num==6 fhd=str2func('rosenbrock_func'); %[-100,100]
    elseif func_num==7 fhd=str2func('griewank_rot_func'); %[-600,600]
    elseif func_num==8 fhd=str2func('ackley_rot_func'); %[-32,32]
    elseif func_num==9 fhd=str2func('rastrigin_func'); %[-5,5]
    elseif func_num==10 fhd=str2func('rastrigin_rot_func'); %[-5,5]
    elseif func_num==11 fhd=str2func('weierstrass_rot'); %[-0.5,0.5]
    elseif func_num==12 fhd=str2func('schwefel_213'); %[-pi,pi]
    elseif func_num==13 fhd=str2func('EF8F2_func'); %[-3,1] 
    elseif func_num==14 fhd=str2func('E_ScafferF6_func'); %[-100,100]
    elseif func_num==15 fhd=str2func('hybrid_func1'); %[-5,5]
    elseif func_num==16 fhd=str2func('hybrid_rot_func1'); %[-5,5]
    elseif func_num==17 fhd=str2func('hybrid_rot_func1_noise'); %[-5,5]        
    elseif func_num==18 fhd=str2func('hybrid_rot_func2'); %[-5,5]    
    elseif func_num==19 fhd=str2func('hybrid_rot_func2_narrow'); %[-5,5]    
    elseif func_num==20 fhd=str2func('hybrid_rot_func2_onbound'); %[-5,5]  
    elseif func_num==21 fhd=str2func('hybrid_rot_func3'); %[-5,5]    
    elseif func_num==22 fhd=str2func('hybrid_rot_func3_highcond'); %[-5,5]  
    elseif func_num==23 fhd=str2func('hybrid_rot_func3_noncont'); %[-5,5]   
    elseif func_num==24 fhd=str2func('hybrid_rot_func4'); %[-5,5]  
    elseif func_num==25 fhd=str2func('hybrid_rot_func4'); %[-5,5]
    end
    load fbias_data;
end

f=feval(fhd,x)+f_bias(func_num);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%Unimodal%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   1.Shifted Sphere Function 
function fit=sphere_func(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load sphere_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-100+200*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
fit=sum(x.^2,2);

%   2.Shifted Schwefel's Problem 1.2
function f=schwefel_102(x)
global initial_flag
persistent o
[ps,D]=size(x);
if initial_flag==0
    load schwefel_102_data
   if length(o)>=D
         o=o(1:D);
    else
         o=-100+200*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
f=0;
for i=1:D
    f=f+sum(x(:,1:i),2).^2;
end

%   3.Shifted Rotated High Conditioned Elliptic Function
function fit=high_cond_elliptic_rot_func(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load high_cond_elliptic_rot_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-100+200*rand(1,D);
    end
    c=1;
    if D==2,load elliptic_M_D2,
    elseif D==10,load elliptic_M_D10,
    elseif D==30,load elliptic_M_D30,
    elseif D==50,load elliptic_M_D50,
    else 
        A=normrnd(0,1,D,D);[M,r]=cGram_Schmidt(A);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
x=x*M;
a=1e+6;
fit=0;
for i=1:D
fit=fit+a.^((i-1)/(D-1)).*x(:,i).^2;
end

%   4.Shifted Schwefel's Problem 1.2 with Noise in Fitness 
function f=schwefel_102_noise_func(x)
global initial_flag
persistent o
[ps,D]=size(x);
if initial_flag==0
    load schwefel_102_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-100+200*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
f=0;
for i=1:D
    f=f+sum(x(:,1:i),2).^2;
end
f=f.*(1+0.4.*abs(normrnd(0,1,ps,1)));

%   5.Schwefel's Problem 2.6
function f=schwefel_206(x)%after Fletcher and Powell
global initial_flag
persistent A B o
[ps,D]=size(x);
if initial_flag==0
    initial_flag=1;
    load schwefel_206_data
    if length(o)>=D
         A=A(1:D,1:D);o=o(1:D);
    else
         o=-100+200*rand(1,D);
         A=round(-100+2*100.*rand(D,D));
         while det(A)==0
         A=round(-100+2*100.*rand(D,D));
         end
    end
    o(1:ceil(D/4))=-100;o(max(floor(0.75*D),1):D)=100;
    B=A*o';
end
for i=1:ps
f(i,1)=max(abs(A*(x(i,:)')-B));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%Multimodal%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   6.Shifted Rosenbrock's Function
function f=rosenbrock_func(x)
global initial_flag
persistent o
[ps,D]=size(x);
if initial_flag==0
    load rosenbrock_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-90+180*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1)+1;
f=sum(100.*(x(:,1:D-1).^2-x(:,2:D)).^2+(x(:,1:D-1)-1).^2,2);

%   7.Shifted Rotated Griewank's Function
function f=griewank_rot_func(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load griewank_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-600+0*rand(1,D);
    end
    c=3;
    if D==2,load griewank_M_D2,,
    elseif D==10,load griewank_M_D10,
    elseif D==30,load griewank_M_D30,
    elseif D==50,load griewank_M_D50,
    else 
        M=rot_matrix(D,c);
        M=M.*(1+0.3.*normrnd(0,1,D,D));
    end
    o=o(1:D);
    initial_flag=1;
end
x=x-repmat(o,ps,1);
x=x*M;
f=1;
for i=1:D
    f=f.*cos(x(:,i)./sqrt(i));
end
f=sum(x.^2,2)./4000-f+1;

%   8.Shifted Rotated Ackley's Function with Global Optimum on Bounds
function f=ackley_rot_func(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load ackley_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-30+60*rand(1,D);
    end
    o(2.*[1:floor(D/2)]-1)=-32;
    c=100;
    if D==2,load ackley_M_D2,,
    elseif D==10,load ackley_M_D10,
    elseif D==30,load ackley_M_D30,
    elseif D==50,load ackley_M_D50,
    else 
       M=rot_matrix(D,c);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
x=x*M;
f=sum(x.^2,2);
f=20-20.*exp(-0.2.*sqrt(f./D))-exp(sum(cos(2.*pi.*x),2)./D)+exp(1);

%   9.Shifted Rastrign's Function
function f=rastrigin_func(x)
global initial_flag
persistent o
[ps,D]=size(x);
if initial_flag==0
    load rastrigin_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-5+10*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
f=sum(x.^2-10.*cos(2.*pi.*x)+10,2);

%   10.Shifted Rotated Rastrign's Function 
function f=rastrigin_rot_func(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load rastrigin_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-5+10*rand(1,D);
    end
    c=2;
    if D==2,load rastrigin_M_D2,,
    elseif D==10,load rastrigin_M_D10,
    elseif D==30,load rastrigin_M_D30,
    elseif D==50,load rastrigin_M_D50,
    else 
        M=rot_matrix(D,c);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
x=x*M;
f=sum(x.^2-10.*cos(2.*pi.*x)+10,2);

%   11.Shifted Rotated Weierstrass Function
function [f]=weierstrass_rot(x)
global initial_flag
persistent o M
[ps,D]=size(x);
if initial_flag==0
    load weierstrass_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-0.5+0.5*rand(1,D);
    end
    c=5;
    if D==2,load weierstrass_M_D2,,
    elseif D==10,load weierstrass_M_D10,
    elseif D==30,load weierstrass_M_D30,
    elseif D==50,load weierstrass_M_D50,
    else 
        M=rot_matrix(D,c);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1);
x=x*M;
x=x+0.5;
a = 0.5;%0<a<1
b = 3;
kmax = 20;
[ps,D]=size(x);

c1(1:kmax+1) = a.^(0:kmax);
c2(1:kmax+1) = 2*pi*b.^(0:kmax);
c=-w(0.5,c1,c2);
f=0;
for i=1:D
f=f+w(x(:,i)',c1,c2);
end
f=f+repmat(c*D,ps,1);

%--------------------------------

%   12.Schwefel's Problem 2.13
function f=schwefel_213(x)%after Fletcher and Powell
global initial_flag
persistent a b A alpha
[ps,D]=size(x);
if initial_flag==0
    initial_flag=1;
    load schwefel_213_data
    if length(alpha)>=D
        alpha=alpha(1:D);a=a(1:D,1:D);b=b(1:D,1:D);
    else
        alpha=-3+6*rand(1,D);
        a=round(-100+200.*rand(D,D));
        b=round(-100+200.*rand(D,D));
    end
    alpha=repmat(alpha,D,1);
    A=sum(a.*sin(alpha)+b.*cos(alpha),2);
end

for i=1:ps
    xx=repmat(x(i,:),D,1);
    B=sum(a.*sin(xx)+b.*cos(xx),2);
    f(i,1)=sum((A-B).^2,1);
end

%   13. Expanded Extended Griewank's plus Rosenbrock's Function (F8F2)
function fit=EF8F2_func(x)
%-3,1
global initial_flag
persistent  o 
[ps,D]=size(x);
if initial_flag==0
    load EF8F2_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-1+1*rand(1,D);
    end
    initial_flag=1;
end
x=x-repmat(o,ps,1)+1;
fit=0;
for i=1:(D-1)
    fit=fit+F8F2(x(:,[i,i+1]));
end
    fit=fit+F8F2(x(:,[D,1]));

function f=F8F2(x)
f2=100.*(x(:,1).^2-x(:,2)).^2+(1-x(:,1)).^2;
f=1+f2.^2./4000-cos(f2);

% ---------------------------------------------------------------  
%   14. Expanded Rotated Extended Scaffer's F6   
function f=E_ScafferF6_func(x)
global initial_flag
persistent  o M
fhd=str2func('ScafferF6');
[ps,D]=size(x);
if initial_flag==0
    load E_ScafferF6_func_data
    if length(o)>=D
         o=o(1:D);
    else
         o=-100+200*rand(1,D);
    end
    initial_flag=1;
    c=3;
    if D==2,load E_ScafferF6_M_D2,,
    elseif D==10,load E_ScafferF6_M_D10,
    elseif D==30,load E_ScafferF6_M_D30,
    elseif D==50,load E_ScafferF6_M_D50,
    else 
       M=rot_matrix(D,c);
    end
end
x=x-repmat(o,ps,1);
x=x*M;
f=0;
for i=1:(D-1)
    f=f+feval(fhd,(x(:,i:i+1)));
end
    f=f+feval(fhd,x(:,[D,1]));

function f=ScafferF6(x)
f=0.5+(sin(sqrt(x(:,1).^2+x(:,2).^2)).^2-0.5)./(1+0.001*(x(:,1).^2+x(:,2).^2)).^2;
%---------------------------------------------------
%   15.Hybrid Composition Function 1
function fit=hybrid_func1(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func1_data % saved the predefined optima
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    func.f1=str2func('frastrigin');
    func.f2=str2func('frastrigin');
    func.f3=str2func('fweierstrass');
    func.f4=str2func('fweierstrass');
    func.f5=str2func('fgriewank');
    func.f6=str2func('fgriewank');
    func.f7=str2func('fackley');
    func.f8=str2func('fackley');
    func.f9=str2func('fsphere');
    func.f10=str2func('fsphere');
    bias=((1:fun_num)-1).*100;
    sigma=ones(1,fun_num);
    lamda=[1; 1; 10; 10; 5/60; 5/60; 5/32; 5/32; 5/100; 5/100];
    lamda=repmat(lamda,1,D);
    for i=1:fun_num
        eval(['M.M' int2str(i) '=diag(ones(1,D));']);
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%---------------------------------------------------------------------
%   16.Rotated Hybrid Composition Function 1  
function fit=hybrid_rot_func1(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func1_data % saved the predefined optima
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    func.f1=str2func('frastrigin');
    func.f2=str2func('frastrigin');
    func.f3=str2func('fweierstrass');
    func.f4=str2func('fweierstrass');
    func.f5=str2func('fgriewank');
    func.f6=str2func('fgriewank');
    func.f7=str2func('fackley');
    func.f8=str2func('fackley');
    func.f9=str2func('fsphere');
    func.f10=str2func('fsphere');
    bias=((1:fun_num)-1).*100;
    sigma=ones(1,fun_num); 
    lamda=[1; 1; 10; 10; 5/60; 5/60; 5/32; 5/32; 5/100; 5/100];
    lamda=repmat(lamda,1,D);
    c=[2,2,2,2,2,2,2,2,2,2,2];
    if D==2,load hybrid_func1_M_D2,
    elseif D==10,load hybrid_func1_M_D10,
    elseif D==30,load hybrid_func1_M_D30,
    elseif D==50,load hybrid_func1_M_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%----------------------------------------------------------------
%   17.  Rotated Hybrid Composition Function 1 with Noise in Fitness  
function fit=hybrid_rot_func1_noise(x)
[ps,D]=size(x);
fit=hybrid_rot_func1(x).*(1+0.2.*abs(normrnd(0,1,ps,1)));
%----------------------------------------------------------------
%   18.  Rotated Hybrid Composition Function 2
function fit=hybrid_rot_func2(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func2_data % saved the predefined optima
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    o(10,:)=0;
    func.f1=str2func('fackley');
    func.f2=str2func('fackley');
    func.f3=str2func('frastrigin');
    func.f4=str2func('frastrigin');
    func.f5=str2func('fsphere');
    func.f6=str2func('fsphere');
    func.f7=str2func('fweierstrass');
    func.f8=str2func('fweierstrass');
    func.f9=str2func('fgriewank');
    func.f10=str2func('fgriewank');
    bias=((1:fun_num)-1).*100;
    sigma=[1 2 1.5 1.5 1 1 1.5 1.5 2 2];
    lamda=[2*5/32; 5/32; 2*1; 1; 2*5/100; 5/100; 2*10; 10; 2*5/60; 5/60];
    lamda=repmat(lamda,1,D);
    c=[2 3 2 3 2 3 20 30 200 300];
    if D==2,load hybrid_func2_M_D2,
    elseif D==10,load hybrid_func2_M_D10,
    elseif D==30,load hybrid_func2_M_D30,
    elseif D==50,load hybrid_func2_M_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%----------------------------------------------------------------
%   19.  Rotated Hybrid Composition Function 2 with a Narrow Basin for the Global Optimum
function fit=hybrid_rot_func2_narrow(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func2_data % saved the predefined optima
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    o(10,:)=0;
    func.f1=str2func('fackley');
    func.f2=str2func('fackley');
    func.f3=str2func('frastrigin');
    func.f4=str2func('frastrigin');
    func.f5=str2func('fsphere');
    func.f6=str2func('fsphere');
    func.f7=str2func('fweierstrass');
    func.f8=str2func('fweierstrass');
    func.f9=str2func('fgriewank');
    func.f10=str2func('fgriewank');
    bias=((1:fun_num)-1).*100;
    sigma=[0.1 2 1.5 1.5 1 1 1.5 1.5 2 2];
    lamda=[0.1*5/32; 5/32; 2*1; 1; 2*5/100; 5/100; 2*10; 10; 2*5/60; 5/60];
    lamda=repmat(lamda,1,D);
    c=[2 3 2 3 2 3 20 30 200 300];
    if D==2,load hybrid_func2_M_D2,
    elseif D==10,load hybrid_func2_M_D10,
    elseif D==30,load hybrid_func2_M_D30,
    elseif D==50,load hybrid_func2_M_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%----------------------------------------------------------------
%   20.  Rotated Hybrid Composition Function 2 with the Global Optimum on the Bounds  
function fit=hybrid_rot_func2_onbound(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func2_data % saved the predefined optima,
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    o(10,:)=0;
    o(1,2.*[1:floor(D/2)])=5;
    func.f1=str2func('fackley');
    func.f2=str2func('fackley');
    func.f3=str2func('frastrigin');
    func.f4=str2func('frastrigin');
    func.f5=str2func('fsphere');
    func.f6=str2func('fsphere');
    func.f7=str2func('fweierstrass');
    func.f8=str2func('fweierstrass');
    func.f9=str2func('fgriewank');
    func.f10=str2func('fgriewank');
    bias=((1:fun_num)-1).*100;
    sigma=[1 2 1.5 1.5 1 1 1.5 1.5 2 2];
    lamda=[2*5/32; 5/32; 2*1; 1; 2*5/100; 5/100; 2*10; 10; 2*5/60; 5/60];
    lamda=repmat(lamda,1,D);
    c=[2 3 2 3 2 3 20 30 200 300];
    if D==2,load hybrid_func2_M_D2,
    elseif D==10,load hybrid_func2_M_D10,
    elseif D==30,load hybrid_func2_M_D30,
    elseif D==50,load hybrid_func2_M_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%-------------------------------------------------
%    21.Rotated Hybrid Composition Function 3    
function fit=hybrid_rot_func3(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func3_data % saved the predefined optima, a 10*1000 matrix;
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    func.f1=str2func('fE_ScafferF6');
    func.f2=str2func('fE_ScafferF6');
    func.f3=str2func('frastrigin');
    func.f4=str2func('frastrigin');
    func.f5=str2func('fEF8F2');
    func.f6=str2func('fEF8F2');
    func.f7=str2func('fweierstrass');
    func.f8=str2func('fweierstrass');
    func.f9=str2func('fgriewank');
    func.f10=str2func('fgriewank');
    bias=((1:fun_num)-1).*100;
    sigma=[1,1,1,1,1,2,2,2,2,2];
    lamda=[5*5/100; 5/100; 5*1; 1; 5*1; 1; 5*10; 10; 5*5/200; 5/200];
    lamda=repmat(lamda,1,D);
    c=ones(1,D);
    if D==2,load hybrid_func3_M_D2,
    elseif D==10,load hybrid_func3_M_D10,
    elseif D==30,load hybrid_func3_M_D30,
    elseif D==50,load hybrid_func3_M_D50,
    else 
        for i=1:fun_num
            A=normrnd(0,1,D,D);
            eval(['M.M' int2str(i) '=cGram_Schmidt(A));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%-----------------------------------------
%   22.  Rotated Hybrid Composition Function 3 with High Condition Number Matrix
function fit=hybrid_rot_func3_highcond(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func3_data % saved the predefined optima, a 10*1000 matrix;
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    func.f1=str2func('fE_ScafferF6');
    func.f2=str2func('fE_ScafferF6');
    func.f3=str2func('frastrigin');
    func.f4=str2func('frastrigin');
    func.f5=str2func('fEF8F2');
    func.f6=str2func('fEF8F2');
    func.f7=str2func('fweierstrass');
    func.f8=str2func('fweierstrass');
    func.f9=str2func('fgriewank');
    func.f10=str2func('fgriewank');
    bias=((1:fun_num)-1).*100;
    sigma=[1,1,1,1,1,2,2,2,2,2];
    lamda=[5*5/100; 5/100; 5*1; 1; 5*1; 1; 5*10; 10; 5*5/200; 5/200];
    lamda=repmat(lamda,1,D);
    c=[10 20 50 100 200 1000 2000 3000 4000 5000];
    if D==2,load hybrid_func3_HM_D2,
    elseif D==10,load hybrid_func3_HM_D10,
    elseif D==30,load hybrid_func3_HM_D30,
    elseif D==50,load hybrid_func3_HM_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%-----------------------------------------
%   23.  Non-Continuous Rotated Hybrid Composition Function 3
function fit=hybrid_rot_func3_noncont(x)
global initial_flag
persistent  o 
[ps,D]=size(x);
if initial_flag==0
    load hybrid_func3_data % saved the predefined optima, a 10*1000 matrix;
    o=o(1,1:D);
end
o=repmat(o,ps,1);
x=(abs(x-o)<0.5).*x+(abs(x-o)>=0.5).*(round(x.*2)./2);
fit=hybrid_rot_func3(x);
%-----------------------------------------
%   24.  Rotated Hybrid Composition Function 4  
function fit=hybrid_rot_func4(x)
global initial_flag
persistent  fun_num func o sigma lamda bias M
if initial_flag==0
    [ps,D]=size(x);
    initial_flag=1;
    fun_num=10;
    load hybrid_func4_data % saved the predefined optima, a 10*1000 matrix;
    if length(o(1,:))>=D
         o=o(:,1:D);
    else
         o=-5+10*rand(fun_num,D);
    end
    func.f1=str2func('fweierstrass');
    func.f2=str2func('fE_ScafferF6');
    func.f3=str2func('fEF8F2');
    func.f4=str2func('fackley');
    func.f5=str2func('frastrigin');
    func.f6=str2func('fgriewank');
    func.f7=str2func('fE_ScafferF6_noncont');
    func.f8=str2func('frastrigin_noncont');
    func.f9=str2func('felliptic');
    func.f10=str2func('fsphere_noise');
    bias=((1:fun_num)-1).*100;
    sigma=[2,2,2,2,2,2,2,2,2,2];
    lamda=[10; 5/20; 1; 5/32; 1; 5/100 ; 5/50; 1; 5/100; 5/100; ];
    lamda=repmat(lamda,1,D);
    c=[100 50 30 10 5 5 4 3 2 2];
    if D==2,load hybrid_func4_M_D2,
    elseif D==10,load hybrid_func4_M_D10,
    elseif D==30,load hybrid_func4_M_D30,
    elseif D==50,load hybrid_func4_M_D50,
    else 
        for i=1:fun_num
            eval(['M.M' int2str(i) '=rot_matrix(D,c(i));']);
        end
    end
end
fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M);
%----------------------------------
function fit=hybrid_composition_func(x,fun_num,func,o,sigma,lamda,bias,M)
[ps,D]=size(x);
for i=1:fun_num
    oo=repmat(o(i,:),ps,1);
    weight(:,i)=exp(-sum((x-oo).^2,2)./2./(D*sigma(i)^2));
end

[tmp,tmpid]=sort(weight,2);
for i=1:ps
    weight(i,:)=(weight(i,:)==tmp(i,fun_num)).*weight(i,:)+(weight(i,:)~=tmp(i,fun_num)).*(weight(i,:).*(1-tmp(i,fun_num).^10));
end
weight=weight./repmat(sum(weight,2),1,fun_num);

fit=0;
for i=1:fun_num
    oo=repmat(o(i,:),ps,1);
    eval(['f=feval(func.f' int2str(i) ',((x-oo)./repmat(lamda(i,:),ps,1))*M.M' int2str(i) ');']);
    x1=5*ones(1,D);
    eval(['f1=feval(func.f' int2str(i) ',(x1./lamda(i,:))*M.M' int2str(i) ');']);
    fit1=2000.*f./f1;
    fit=fit+weight(:,i).*(fit1+bias(i));
end
%-------------------------------------------------
%basic functions

function f=fsphere(x)
%Please notice there is no use to rotate a sphere function, with rotation
%here just for a similar structure as other functions and easy programming
[ps,D]=size(x);
f=sum(x.^2,2);
%--------------------------------
function f=fsphere_noise(x)
[ps,D]=size(x);
f=sum(x.^2,2).*(1+0.1.*normrnd(0,1,ps,1));
%--------------------------------
function f=fgriewank(x)
[ps,D]=size(x);
f=1;
for i=1:D
    f=f.*cos(x(:,i)./sqrt(i));
end
f=sum(x.^2,2)./4000-f+1;
%--------------------------------
function f=fackley(x)
[ps,D]=size(x);
f=sum(x.^2,2);
f=20-20.*exp(-0.2.*sqrt(f./D))-exp(sum(cos(2.*pi.*x),2)./D)+exp(1);
%--------------------------------
function f=frastrigin(x)
[ps,D]=size(x);
f=sum(x.^2-10.*cos(2.*pi.*x)+10,2);
%--------------------------------
function f=frastrigin_noncont(x)
[ps,D]=size(x);
x=(abs(x)<0.5).*x+(abs(x)>=0.5).*(round(x.*2)./2);
f=sum(x.^2-10.*cos(2.*pi.*x)+10,2);
%--------------------------------
function [f]=fweierstrass(x)
[ps,D]=size(x);
x=x+0.5;
a = 0.5;
b = 3;
kmax = 20;
c1(1:kmax+1) = a.^(0:kmax);
c2(1:kmax+1) = 2*pi*b.^(0:kmax);
f=0;
c=-w(0.5,c1,c2);
for i=1:D
f=f+w(x(:,i)',c1,c2);
end
f=f+c*D;

function y = w(x,c1,c2)
y = zeros(length(x),1);
for k = 1:length(x)
  y(k) = sum(c1 .* cos(c2.*x(:,k)));
end
%--------------------------------
function f=fE_ScafferF6(x)
fhd=str2func('ScafferF6');
[ps,D]=size(x);

f=0;
for i=1:(D-1)
    f=f+feval(fhd,(x(:,i:i+1)));
end
    f=f+feval(fhd,x(:,[D,1]));
%--------------------------------    
function f=fE_ScafferF6_noncont(x)
fhd=str2func('ScafferF6');
[ps,D]=size(x);
x=(abs(x)<0.5).*x+(abs(x)>=0.5).*(round(x.*2)./2);
f=0;
for i=1:(D-1)
    f=f+feval(fhd,(x(:,i:i+1)));
end
    f=f+feval(fhd,x(:,[D,1]));
%------------------------------
function f=fEF8F2(x)
[ps,D]=size(x);
f=0;
for i=1:(D-1)
    f=f+F8F2(x(:,[i,i+1]));
end
    f=f+F8F2(x(:,[D,1]));

%--------------------------------
function f=fschwefel_102(x)
[ps,D]=size(x);
f=0;
for i=1:D
    f=f+sum(x(:,1:i),2).^2;
end
%--------------------------------
function f=felliptic(x)
[ps,D]=size(x);
a=1e+6;
f=0;
for i=1:D
f=f+a.^((i-1)/(D-1)).*x(:,i).^2;
end
%--------------------------------
% classical Gram Schmid 
 function [q,r] = cGram_Schmidt (A)
% computes the QR factorization of $A$ via
% classical Gram Schmid 
% 
 [n,m] = size(A); 
 q = A;    
 for j=1:m
     for i=1:j-1 
         r(i,j) = q(:,j)'*q(:,i);
     end
     for i=1:j-1   
       q(:,j) = q(:,j) -  r(i,j)*q(:,i);
     end
     t =  norm(q(:,j),2 ) ;
     q(:,j) = q(:,j) / t ;
     r(j,j) = t  ;
 end 

function M=rot_matrix(D,c)
A=normrnd(0,1,D,D);
P=cGram_Schmidt(A);
A=normrnd(0,1,D,D);
Q=cGram_Schmidt(A);
u=rand(1,D);
D=c.^((u-min(u))./(max(u)-min(u)));
D=diag(D);
M=P*D*Q;

Answer 1

[Walter Roberson]

Once you have completed the program the first time, the global initial_flag is set to 1. When you run the program again, initial_flag is still 1, and in that case fhd (which is not global or persistent) is not assigned a value. The program will always fail after that until you assign 0 to the global outside of the program (remembering to tell the command line that you are dealing with a global.)

Code cleanup suggestion: transform

    if func_num==1 fhd=str2func('sphere_func'); %[-100,100]
    elseif func_num==2 fhd=str2func('schwefel_102'); %[-100,100]
    elseif func_num==3 fhd=str2func('high_cond_elliptic_rot_func'); %[-100,100]
    elseif func_num==4 fhd=str2func('schwefel_102_noise_func'); %[-100,100]

into

persistent fhandles

if isempty(fhandles)
  fhandles = { @sphere_func, %[-100,100]
               @schwefel_102, %[-100,100]
               @high_cond_elliptic_rot_func', %[-100,100]
               @schwefel_102_noise_func, %[-100,100]
               ...
              };
end

if numel(func_num) ~= 1 | func_num < 1 | func_num > length(fhandles)
  error('invalid function number');
end

fhnd = fhandles{func_num};