How optimize multiple responses of dataset ?

Hi.

I have an application which I have a dataset (> 1,000) with the following variables: velocity(m/min), production(kg), scrap(kg) and consumption(kWh).

I'd like to use Matlab to optimize multiple responses. The independent variable is velocity (X1) and the others are response variables. I need to know which velocity delivers: max production (Y1), min scrap (Y2) and min consumption (Y3).

In the table below some data to exemplify the database:

Velocity Production Scrap Consumption
X1       Y1      Y2  Y3
1760	1934	237	1960
1760	1934	0	1728
1760	1944	0	1739
1760	1932	0	1732
1760	1951	0	1734
1760	1928	287	2024
1760	1967	128	1876
1760	1949	0	1730
1760	1938	0	1727
1761	1938	0	1877
1761	1925	155	1877
1760	1923	0	1751
1760	1900	0	1723
1765	1922	0	1723
1765	1910	219	1963
1765	1954	162	1899
1770	1944	0	1728
1770	1942	0	1727
1770	1931	33	1749
1770	1922	0	1707
1770	1923	0	1698
1770	1906	0	1697
1770	1918	0	1715
1770	1920	0	1709
1769	1920	0	1710
1770	1926	0	1702
...

I would like to know how I can implement this in Matlab if anyone can help me I appreciate it.

Regards,

A.Berg

Answer 1

[Alan Weiss]

I think that you probably want to fit a function to the data, where the function represents the response. Obviously your data does not have a simple representation because the same value of velocity appears many times, and there are multiple different responses for the same input value.

So I think that you need to come up with a functional form of the response variables, and then fit that functional form to the data. For an example of fitting, see Nonlinear Data-Fitting.

Once you have done that, you can minimize a scalar function of the response variables. For example, you might want to minimize 5*scrap + 10*consumption - production. You can minimize this function using, say, fminbnd. Or if you simply want to optimize the responses separately, make multiple minimization prooblems.

Good luck,

Alan Weiss

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