Objective Function Minimum Value Problem - Genetic Algorithm

I used genetic algorithm to optimize model parameters. Results of running my code are:

Optimization terminated: minimum fitness limit reached.

x =

-143.0421    5.4032  -36.7178  -15.9012   17.7426  -44.5850


fval =

-Inf

As can be seen result gives six parameters. However, value of objective function at minimum has no sense. If that is supposed to be minus infinity, how can that even represent a minimum of any function, not to mention that my objective function can't have negative values.

Here is main code:

clc
clear all
global x1e x2e x3e x1r x2r x3r alfa12 alfa13 alfa23 
%LLE podatci - ekstrakcija aromata smjesom TTEG i vode - 6 komponenata (heptan) na 60°C 
%eksperimentalni podatci - ekstrakt
x1e = [0.0140   0.0175  0.0163  0.0188  0.0181  0.0227  0.0228  0.0214  0.0191  0.0208];
x2e = [0.0729   0.0696  0.106   0.1041  0.1107  0.0931  0.0732  0.0739  0.113   0.069];
x3e = 1 - x1e - x2e;
%eksperimentalni podatci - rafinat
x1r = [0.689    0.6289  0.485   0.4727  0.4332  0.6831  0.6967  0.6553  0.4507  0.6139];
x2r = [0.275    0.2855  0.4418  0.3501  0.4056  0.313   0.2716  0.271   0.4436  0.253];
x3r = 1 - x1r - x2r;

%Optimizacija NRTL parametara - Metoda Sorensena i Arlta
%1. stupanj optimizacije - opis fazne ravnoteze - geneticki algoritam

%parametri neslucajnosti
alfa12 = 0.3;
alfa13 = 0.3;
alfa23 = 0.2;

rng default

%definiranje strukture problema 
OF_A = @(x) OF_2_6H_60C(x);
problem.fitnessfcn = OF_A;
problem.nvars = 6;
problem.options = optimoptions('ga');
[x,fval] = ga(problem)

Here is objective function:

  function [OF2] = OF_2_6H_60C(x)
global x1e x2e x3e x1r x2r x3r alfa12 alfa13 alfa23

G12 = exp(-alfa12*x(1));
G13 = exp(-alfa13*x(2));
G21 = exp(-alfa12*x(3));
G23 = exp(-alfa23*x(4));
G31 = exp(-alfa13*x(5));
G32 = exp(-alfa23*x(6));


A1e = (x2e.*x(3)*G21 + x3e.*x(5)*G31)./(x1e + x2e.*G21 + x3e.*G31) + (x1e./(x1e + x2e.*G21 + x3e.*G31)).*(-(x2e.*x(3)*G21 + x3e.*x(5)*G31)./(x1e + x2e.*G21 + x3e.*G31)) + (x2e.*G12./(x1e.*G12 + x2e + x3e.*G32)).*(x(3) - (x1e.*x(1)*G12 + x3e.*x(6)*G32)./(x1e.*G12 + x2e + x3e.*G32)) + (x3e.*G13./(x1e.*G13 + x2e.*G23 + x3e)).*(x(5) - (x1e.*x(2)*G13 + x2e.*x(4)*G23)./(x1e.*G13 + x2e.*G23 + x3e));
gamma1e = exp(A1e);

A2e = (x1e.*x(1)*G12 + x3e.*x(6)*G32)./(x1e.*G12 + x2e + x3e.*G32) + (x1e.*G21./(x1e + x2e.*G21 + x3e.*G31)).*(x(1) - (x2e.*x(3)*G21 + x3e.*x(5)*G31)./(x1e + x2e.*G21 + x3e.*G31)) + (x2e./(x1e.*G12 + x2e + x3e.*G32)).*(-(x1e.*x(1)*G12 + x3e.*x(6)*G32)./(x1e.*G12 + x2e + x3e.*G32)) + (x3e.*G23./(x1e.*G13 + x2e.*G23 + x3e)).*(x(6) - (x1e.*x(2)*G13 + x2e.*x(4)*G23)./(x1e.*G13 + x2e.*G23 + x3e));
gamma2e = exp(A2e);

A3e = (x1e.*x(2)*G13 + x2e.*x(4)*G23)./(x1e.*G13 + x2e.*G23 + x3e) + ((x1e.*G21./(x1e + x2e.*G21 + x3e.*G31)).*(x(2) - (x2e.*x(3)*G21 + x3e.*x(5)*G31)./(x1e + x2e.*G21 + x3e.*G31))) + ((x2e.*G32./(x1e.*G12 + x2e + x3e.*G32)).*(x(4) - (x1e.*x(1)*G12)./(x1e.*G12 + x2e + x3e.*G32))) + ((x3e./(x1e.*G13 + x2e.*G23 + x3e)).*(-(x1e.*x(2)*G13 + x2e.*x(4)*G23)./(x1e.*G13 + x2e.*G23 + x3e)));                                                                                   
gamma3e = exp(A3e);

A1r = (x2r.*x(3)*G21 + x3r.*x(5)*G31)./(x1r + x2r.*G21 + x3r.*G31) + ((x1r./(x1r + x2r.*G21 + x3r.*G31)).*(-(x2r.*x(3)*G21 + x3e.*x(5)*G31)./(x1r + x2r.*G21 + x3r.*G31))) + ((x2r.*G12)./(x1r.*G12 + x2r + x3e.*G32)).*(x(3) - ((x1r.*x(1)*G12 + x3r.*x(6)*G32)./(x1r.*G12 + x2r + x3r.*G32))) + ((x3r.*G13./(x1r.*G13 + x3r)).*(x(5) - (x1r.*x(2)*G13 + x2r.*x(4)*G23)./(x1r.*G13 + x2r.*G23 + x3r)));        
gamma1r = exp(A1r);

A2r = (x1r.*x(1)*G12 + x3r.*x(6)*G32)./(x1r.*G12 + x2r + x3r.*G32) + ((x1r.*G21./(x1r + x2r.*G21 + x3r.*G32)).*(x(1) - (x2r.*x(3).*G21 + x3r.*x(5)*G31)./(x1r + x2r.*G21 + x3r.*G31))) + ((x2r./(x1r.*G12 + x2r + x3r.*G32)).*(-(x1r.*x(1)*G12 + x3r.*x(6)*G32)./(x1r.*G12 + x2r + x3r.*G32))) + ((x3r.*G23./(x1r.*G13 + x2r.*G23 + x3r)).*(x(6) - (x1r.*x(2)*G13 + x2r.*x(4)*G23 + x3r)./(x1r.*G13 + x2r.*G23 + x3r)));
gamma2r = exp(A2r);

A3r = (x1r.*x(2)*G13 + x2r.*x(4)*G23)./(x1r.*G13 + x2r.*G23 + x3r) + ((x1r.*G31./(x1r + x2r.*G21 + x3r.*G31)).*(x(2) - (x2r.*x(3)*G21 + x3r.*x(5)*G31)./(x1r + x2r.*G21 + x3r.*G31))) + ((x2r.*G32./(x1r.*G12 + x2r + x3r.*G32)).*(x(4) - (x1r.*x(1)*G12)./(x1r.*G12 + x2r + x3r.*G32))) + ((x3r./(x1r.*G13 + x2r.*G23 + x3r)).*(-(x1r.*x(2)*G13 + x2r.*x(4)*G23)./(x1r.*G13 + x2r.*G23 + x3r)));
gamma3r = exp(A3r);


for i = 1:10
   A(i)=((x1e(i)*gamma1e(i) - x1r(i)*gamma1r(i))/(x1e(i)*gamma1e(i) + x1r(i)*gamma1r(i))^2) + ((x2e(i)*gamma2e(i) - x2r(i)*gamma2r(i))/(x2e(i)*gamma2e(i) + x2r(i)*gamma2r(i))^2) + ((x3e(i)*gamma3e(i) - x3r(i)*gamma3r(i))/(x3e(i)*gamma3e(i) + x3r(i).*gamma3r(i))^2);
end
 
OF2 = sum(A,'all');

end

Long expressions such as A1e, A2e, A3e etc. are only vectors of 1x10 as x1e, x2e, x3e etc. also are.

I initially thought there is something wrong with these long expressions as mistakes can easily be made there, but I can't find any. Any ideas?

[Torsten]

Did you call your function with the x-values from ga to see if it might return -Inf ?

[Dario Miric]

Yes, feval gives -inf.

[Torsten]

ok, then ga performed correctly.

You will have to reconsider your objective.

[Dario Miric]

Will do, thanks.

[Dario Miric]

Solved it. Turns out I made I mistake regarding brackets in for loop. I should had put all brackets inside of square sign not to put one bracket outside like in my code.