How to optimize this equation using GA tool?

2013 7 25
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Hi all, I have polynomial equation: y =89.81+1.96*x(1)-3.02*x(2)-1.46*x(1)^2-1*x(2)^2-4.45*x(3)^2-1.57*x(1)*x(3)-2.74*x(2)*x(3) and I am looking for optimization of the above equation with Lower bounds [-1.68 -1.68 -1.68] and Upper bounds [1.68 1.68 1.68]. When I feed this equation in GA tool and run....I get an output of
"Objective function value: 56.37940293199839 Optimization terminated: average change in the fitness value less than options.TolFun."
But for the same equation, by polynomial regression I get an output of 94.73! can anybody help?

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Alan Weiss
Alan Weiss 2013-7-25

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I don't understand what you think the problem is. The objective function that ga found is better than the one you get by "polynomial regression." So is your problem that ga got a better answer? Or that you think the answer is wrong?
I just ran your problem, and here is what I got:
fun = @(x)89.81+1.96*x(1)-3.02*x(2)-1.46*x(1)^2-1*x(2)^2-4.45*x(3)^2-1.57*x(1)*x(3)-2.74*x(2)*x(3);
lb = -1.68*ones(3,1);
ub = -lb;
[x,fval] = ga(fun, 3,[],[],[],[],lb,ub)
Optimization terminated: average change in the fitness value less than options.TolFun.
x =
1.6789 1.6800 1.6800
fval =
56.3686
Checking with fmincon shows that this is a good answer.
Alan Weiss
MATLAB mathematical toolbox documentation

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