Can anybody help me to find the global minima?

I am struggling with finding the global minimum of a function with 12 variables and two objectives. I have used fminmax and gamultiobj, the latest gives better results. When I optimize the function manually I get better numbers than when using gamultiobj. Thus I would like to find a way to improve the code. See below: the options and function I am using. When I do the optimization manually, the best results are obtained with this vector. X0=[0 0 0 0.1 .65 .7 .5 .7 .7 0 .4 0];

Can anybody help me in improving my algorithm and find a global minima?

Thanks,

Vittorio

options = optimoptions('ga',...
,'MaxStallGenerations',15000,'MaxGenerations',15000,'HybridFcn','fminunc');
cash_opt_mtx=gamultiobj(@NEXT_alpha,length(cash_mtx),[],[],[],[],zeros(length(cash_mtx),1),ones(length(cash_mtx),1),options);

function objective_next_alpha=NEXT_alpha(X_variables)

load original_mtx.mat
coeff=[];
for i0=1:length(X_variables)
    coeff=[coeff X_variables(i0).*ones(length(dY0_MTX),1)];
end
dY00_MTX=prod((1-coeff).*dY0_MTX+coeff,2);
Y00_MTX=cumprod(dY00_MTX);

%X_variables
objective_next_alpha(1)=1/Y00_MTX(end);
%Y00_MTX(end)
objective_next_alpha(2)=maxdrawdown(Y00_MTX);
if objective_next_alpha(2)>0.15
    objective_next_alpha(1)=inf;
end

end

[Walter Roberson]

I am not sure what it means to find the global minimum of a function with two objectives? If it is expected that the exact same point will be the global minimum for both objectives, then just minimize one of them.

[Vittorio]

@WalterRoberson

I meant, I have a Matlab function that returns two values given 12 independent variables. These two outputs are a function of these variables. These two outputs are not minimized for the same X. I would like to find the X that provides the lowest value for the two output. See it as best trade-off.

[Walter Roberson]

You need to define the tradeoff equation. For example is it better for one of the two to be its minimum and the other to be 3 above its minimum (total error 3, sum of squares 9) or for both to be 2 above their minimum (total error 4, sum of squares 4)?

[Vittorio]

It is better now, thank you. I have tried most of the algos available (particleswarm being the best) but still the manual optimization gives better results than the one does using all these optimizers.

Puzzling...