How can I optimize data with no equations

Hi I have 4 different variables vectors (a,b,c and d), and I need to obtain the minimum (e) parameter which is affected by all the 4 variables. Can Anyone help me to know how can I do this kind of data optimization in Matlab without equations to obtain (e). I need to run a design software and by input these 4 variables I can then find (e).

Best regards Omar

[Adam]

If you have no equations to define e then how is it determined that it is affected by a, b, c and d at all?

[Omar Sily]

Thanks for your comment! These variables are design geometry inputs. When I input them to the design software, I can find the geometry error (e) which is affected by these input variables, but I have no equations to relate these variables with (e).

Answer 1

[John D'Errico]

Sorry, but you cannot just optimize data. There is no magic that you can apply. You need to spend the time to develop a model that can be used here. That means you will need to learn about the tools to solve your problem. It may mean that you need to choose a model of some sort.

A simple model family might be polynomials. Someone out there might suggest a polynomial model. Don't follow that advice if it is offered! You will almost always need a high order polynomial model to fit your data, and that will be a terribly bad thing.

Perhaps a better choice might be neural nets. Even there of course, you can overfit the process. But if you have no intelligent choice of model available, then neural nets are where I would suggest you start.

You will need to learn about neural nets. Get the toolbox. Learn to use it first from the examples. Read the documentation. Only then, use them to fit your data.

You may find that your data is insufficient. Sadly, this seems to happen to many people, they have really bad data or not much data at all or data that lives in the wrong places, and have no clue that there is a problem But that will come out of the analysis and modeling of your data, and is part of your learning process.

[Omar Sily]

Thanks for your detailed answer.! Based on this I would say probably I can try to follow a more hard way! I wonder if it works to use the design software to obtain the design error (e)for each possible combination of input variables. Then I can choose the minimum (e). But in case I have more than one (e1 and e2) to optimize, do I need to use nueral network to optimize them for a compromise?

[John D'Errico]

If you have multiple criteria you cannot optimize them all at once. Neural nets will not help you there, as neural nets are not an optimizer! Instead you need to aggregate them all into ONE global objective. This is usually called multi-criteria optimization.

[Omar Sily]

Thanks for your answer!

Answer 2

[Greg Heath]

 Suggestions

 1. Standardize each variable to have zero mean and unit variance
 2. If the data is not naturally ordered, then order e and reorder the 
    others accordingly
 3. Modify or delete outliers
 4. Plot a, b, c and d vs e
 5. Check the plots for recognizable dependencies  ( I tend to look for 
    polynomial dependencies)
 6. If the plots don't give you any good ideas, then consider neural nets. 
    The FITNET function is the one for curvefitting and regression.

Hope this helps.

Greg

[Omar Sily]

Thanks Greg !