Why would an (the excel) evolutionary algorithm be better at, or simply be able to, solve what seems to be a linear problem, when the LP (and also NLP) algorithm struggle to, or simply fail to.
The problem is of the form:
Max X; X = x1 + x2 + x3...
x1 = (k1 × z1) + (k2 x z2) + (k3 x z3)...
x2 = (k1 x y1) + (k2 x y2) + (k3 x y3)...
x3 = (k1 x q1) + (k2 x q2) + (k3 x q3)...
k are the coefficients of the problem to optimize; z, y, q are factors and are given/ constants.
The evolutionary algorithm can find a (better) solution (to the initial solution). The LP algorithm occasionally finds a solution, and not better (mostly worse) than the evolutionary algorithm. The NLP algorithm does not really find a solution at all.
I teach Mgt Sci and use Excel with my students for a lot of the material. Quite often, I have to go in and reform my problems so that Excel will get the correct answer.
Excel uses a an approximation method to decide when to stop searching for an answer. You might need to change the precision level or increase the number of iterations among the other options within Excel.
There might be a few issues with how the different methods start searching for the optimal solution. Starting points and precision can doom an optimization.
I see no reason why an LP would fail to solve this, can you inbox me the full problem?
You problem is equivalent to (if I understand your notation):
X=k1(z1+y1+q1)+k2(z2+y2+q2)+k3(z3+y3+q3)->max
If z, y, q are given constants, then their sums are also given constants, say K1, K2, K3
X=k1*K1 + k2*K2 +k3*K3 ->max
There are no constraints for the decision variables k1, k2, k3.
This is a linear form that is maximized as these variables take unlimited max values......, hence there is no unique solution. Something is missing in your problem statement.
Alexander Kolker ,
you are right,
Max X; X = x1 + x2 + x3...
x1 = (k1 × z1) + (k2 x z2) + (k3 x z3)...
x2 = (k1 x y1) + (k2 x y2) + (k3 x y3)...
x3 = (k1 x q1) + (k2 x q2) + (k3 x q3)...
can be:
Max X; X = x1 + x2 + x3...
X = (k1 × (z1 + y1 + q1)) + (k2 x (z2 + y2 + q2)) + (k3 x (z3 + y3 + q3)...
as long as there are no constraints on x1, x2, x3...
i did not mention this, but there are constraints on the coefficients: k:
x
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