Finding minimum value using parfor

I am trying to find the minimum value of function I have made. The function has 12 parameters.

I have used fminsearch and globalsearch but it does not seem to find the best result, so the full-search running multiple for-loops is being tried.

The form was simple but takes extremely long time that I had to try using parfor.

The problem is that I have trouble in using parallel computng with variables.

This is the basic form of my code

%Assuming that I am trying to find the minimum value for functionA(x1,x2,x3,x4,....,x12)
min_error=10000;
parfor x1=lb_x1:ub_x1
    for x2=lb_x2:ub_x2
        for x3=lb_x3:ub_x3
            ...
            for x12=lb_x12:ub_x12
               temp=functionA(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12);
               if min_error > temp
                   min_error=temp;
                   minX=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12];
               end
            end
            ...
        end
    end
end

The error comes out that it cannot access to the outer variable.

So I tried other approaches like initializing the variable inside when it does not exist, but then the parallel loop cause error in exist function.

if exist('min_error','var')
     if min_error > temp
        min_error=temp;
        minX=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12];
    end
else
   min_error=10000;
end

Do you how to search for minimum value inside the parfor loop?

Thank you

Answer 1

[Walter Roberson]

%Assuming that I am trying to find the minimum value for functionA(x1,x2,x3,x4,....,x12)
x1_vals = lb_x1 : ub_x1;
num_x1 = length(x1_vals);
min_error = zeros(num_x, 1);
minX = nan(num_x1, 12);
parfor x1idx = 1 : num_x1;
    x1 = x1_vals(x1idx);
    local_min_error = 10000;
    local_minX = nan(1,12);
    for x2=lb_x2:ub_x2
        for x3=lb_x3:ub_x3
            ...
            for x12=lb_x12:ub_x12
               temp=functionA(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12);
               if temp < local_min_error
                   local_min_error=temp;
                   local_minX=[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12];
               end
            end
            ...
        end
    end
    min_error(x1idx) = local_min_error;
    minX(x1idx, :) = local_minX;
end
bestmin = min(min_error);
minX = minX(min_error == bestmin, :);
min_error = bestmin;

However really this should be further improved to take into account that multiple configurations might result in the same min.