Math Is Fun Forum

karenkeight

Member

Registered: 2011-03-26

Posts: 2

optimization problem?

Good morning! I don't know how to approach this problem:

I have one machine and I need to obtain the best input parameters for it. To find that parameters I run the machine and get for each run a performance vector. The performance vector is composed of n attributes all of them ranging from 0 to 1, closer values to 1 indicate better performance.

If for example n=3 and I run the machine twice I get this two performance vectors:

A = (0.977 , 0.998, 0.911)
B = (0.981 , 0.621, 0.934)

How could I find which execution is better ?
In this case B seems better because gets better results in first and third attributes but the difference in second attribute is quite high. Maybe if second attribute is more important the A run is better.

Should I rank the attributes according to their importance? What could I do if it is not possible for me to rank the attributes, or if all of them are equally important?

Is it a good solution to simply count the number of attributes that one run outperforms the other and return as solution the run with higher number of 'winning' attributes?

Thanks in advance
Karen

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: optimization problem?

Hi karenkeight,

May be more importance should be given to the standard deviation.
The vector A has lower s.d., so I guess that's a better execution.
*edit: I thought n=3 trials and A,B as two machines. Sorry!

Last edited by gAr (2011-03-26 03:02:16)

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: optimization problem?

Hi Karen;

Welcome to the forum!

Everything you asked would depend on the importance of each parameter. You could weight them according to your estimate of their worth. If they were all of the same value then again there would be lots of ways to rate which one was better. It would depend a lot on your best guess and your understanding of the problem.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

karenkeight

Member

Registered: 2011-03-26

Posts: 2

Re: optimization problem?

Thanks so much gAr and bobbym,

If I don't  know which weight to give each attribute but I know that the best value for each attribute is 1, I could calculate a total value of A based on the deviation from 1 like this:

total value of A = sqr(1-0.977)+sqr(1-0.998)+sqr(1-0.911)

Would that be a correct method? Which other method could I use?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: optimization problem?

Hi Karen;

There is no right and wrong here. You could use the mean, you could use the fact that 2 are closer to 1 in B. Supposing you could not afford even 1 entry like that .62 then you would have to choose A. Why do you choose A = sqr(1-0.977)+sqr(1-0.998)+sqr(1-0.911)?

gAr's idea of sd is perfectly okay also. We need more side info. Perhaps a little more info about the problem.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.