How do I run the Initial value x0 also in parallel - matlab

Question

This code works fine but the plot is not correct because the optimization function fmincon will depend on the initial condition x0 and the number of iterations. For each value of alpha (a) and beta (b), I should run the optimization many times with different initial conditions x0 to verify that I am getting the right answer. More iterations might be required to get an accurate answer.
I want to be able to run the optimization with different initial conditions for x0, a and b.
Function file
function f = threestate2(x,a,b)
c1 = cos(x(1))*(cos(x(5))*(cos(x(9))+cos(x(11)))+cos(x(7))*(cos(x(9))-cos(x(11))))...
+cos(x(3))*(cos(x(5))*(cos(x(9))-cos(x(11)))-cos(x(7))*(cos(x(9))+cos(x(11))));
c2=sin(x(1))*(sin(x(5))*(sin(x(9))*cos(x(2)+x(6)+x(10))+sin(x(11))*cos(x(2)+x(6)+x(12)))...
+sin(x(7))*(sin(x(9))*cos(x(2)+x(8)+x(10))-sin(x(11))*cos(x(2)+x(8)+x(12))))...
+sin(x(3))*(sin(x(5))*(sin(x(9))*cos(x(4)+x(6)+x(10))-sin(x(11))*cos(x(4)+x(6)+x(12)))...
-sin(x(7))*(sin(x(9))*cos(x(4)+x(8)+x(10))+sin(x(11))*cos(x(4)+x(8)+x(12))));
f=(a*a-b*b)*c1+2*a*b*c2;
Main file
%x=[x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10),x(11),x(12)]; % angles;
lb=[0,0,0,0,0,0,0,0,0,0,0,0];
ub=[pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi,pi,2*pi];
x0=[pi/8;0;pi/3;0;0.7*pi;.6;0;pi/2;.5;0;pi/4;0];
xout=[];
fout=[];
options = optimoptions(#fmincon,'Algorithm','interior-point','TolX',10^-10,'MaxIter',1500);
a=0:0.01:1;
w=NaN(length(a));
for i=1:length(a)
bhelp=(1-a(i)*a(i));
if bhelp>0
b=sqrt(bhelp);
[x,fval]=fmincon(#(x)threestate2(x,a(i),b),x0,[],[],[],[],lb,ub,[],options);
w(i)=fval;
w(i)=-w(i);
B(i)=b;
else
w(i)=NaN;
B(i)=b;
end
end
%surface(b,a,w)
%view(3)
%meshc(b,a,w)
x=a.^2;
plot(x,w)
grid on
ylabel('\fontname{Times New Roman} S_{max}(\Psi_{gs})')
xlabel('\fontname{Times New Roman}\alpha^2')
%ylabel('\fontname{Times New Roman}\beta')
title('\fontname{Times New Roman} Maximum of the Svetlichny operator(\alpha|000>+\beta|111>)')

Answer 1

If you have the Matlab Parallel Toolbox, you can use the parfor which is like a regular loop but runs in parallel.
To use it you should make your all big messy script in a function. Assuming you store your initial conditions in A(i) and you store the results in B(i) you can use something like that:
parfor i=1:length(B)
B(i)=optimise(A(i));
end
If you don't have the toolbox there are some other ways (for example MEX files) but you basically have to manage the threads yourself so I wouldn't recommend it.