I want to minimize the value of one variable which depends directly on four variables and indirectly on three variables.
I need to adjust the parameters from a machine (establised manually) to reduce the efect in "response" variable. Also, I have other variables which I can't choose their values.
I have at least 5000 observations which given some independent variables and the machine parameters established I have the response variable value.
I think in linear programming but I don't have an objective function and constraints but I want to minimize efects. Also I think in DOA and Taguchi but I dont have to do and experiment, I have 5000 experimients really done.
I will appreciate your responses! Thanks
Linear Programming can be applied, if you have establish an algebraic relationship between the eight variables involved (1 output, 4 direct, 3 indirect), and these relations are all linear! In mechanical engineering applications, this linearity assumption most likely does not hold. So in case you can give algebraic but nonlinear relations between the variables (involving functions like exp, sin, cos, tan, or higher-order polynomials), then you are in the world of nonlinear programming, where still mathematical solvers exist (but in general you only get local instead of global optima).
If you do not have algebraic relations yet established, just 5000 measurements (observations), you cannot apply these methods. You might try to get them by checking for correlations or fitting linear or nonlinear functions to the data, or using the measurements as test bed for an ANN (artificial neuronal network).
Thank you for your tips. That's my problem. I have something like this: X1+X2+X3+X4+Z1+...+Z3 = Y
I don't have any algebraic relationship, so I tried to ANN but my problem is that I need the optimal values for X1+...+X4 that minimize Y and if I do ANN I can "predict" Y for given values of X1+...+X4 (and Z1+...+Z3). For this reason I'm a little confuse.
Edurne Alonso-Morán: You are indeed right, the ANN is for the prediction of Y for new parameters X1,...,X4 (and Z1,Z2,Z3). To do so, it must have learnt (trained) from the 5000 experiments you did before. When you present a new, previously unseen input, the ANN will surrogate its answer (Y) from the experiments closest by. As a matter of fact, you will not get a "better" optimum than what you have so far. In other words: it would be best to take the smallest Y among your 5000 results as best guest for the minimum.
There are, however, techniques to (maybe) find an even smaller Y, but to use them, you must be willing to do further experiments (5001, 5002, ...), and I understand that you do not want to do it. In case you change your mind, check out for Nelder-Mead-Simplex, for example: https://en.wikipedia.org/wiki/Nelder–Mead_method
Thank you again. I don't have problems to doing more experimients. I am going to read about Nelder-Mead method that I have never heard before.
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