# How optimize multiple responses of dataset ?

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A. Berg on 9 Jul 2021
Answered: Alan Weiss on 9 Jul 2021
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
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### Answers (1)

Alan Weiss on 9 Jul 2021
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
MATLAB mathematical toolbox documentation
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