
September 7th, 2012, 09:55 PM
#1
Algorithm  Minimizing Equation  Dynamic Programming/Greedy
Hi,
If we are given an equation say 3x + 2y <= 10, we want to find the value of x and y such that
x + y = maximum and 10  3x  2y is minimized. How can this be done? I am thinking of it as a dynamic programming problem ! but not sure if I am right.
In the above x = 0 and y = 5 will be the answer.
Thanks.

September 8th, 2012, 12:38 PM
#2
Re: Algorithm  Minimizing Equation  Dynamic Programming/Greedy
Originally Posted by vsha041
x + y = maximum and 10  3x  2y is minimized. How can this be done?
I don't know that much about multiple objective optimization but here's a link.
http://en.wikipedia.org/wiki/Multio...e_optimization
In your particular example though the two objective functions aren't conflicting really so I guess it's a special case. You have this objective,
Min F2 = 10  (3x + 2y)
with the constraint that
3x + 2y <= 10
It's easy to see that F2 becomes smaller when (3x + 2y) grows bigger. But (3x + 2y) is limited by 10 so F2 is at minimum when
3x + 2y = 10
Then you have this objective
Max F1 = x + y
and it's in fact unlimited on
3x + 2y = 10
F1 gets forever bigger when x gets smaller.
If you set say x=10 then the corresponding y=20. If you enter this into F1 you get F1 = 10 + 20 = 10. Note that this is better than you got with x=0 and y=5 so that really wasn't the optimum.
All objectives could be met in this case but normally that wouldn't be possible. Then you'd need some way to mathematically express how to weight together all objective functions into one unified objective. According to the link I supplied one answer is "pareto optimization".
Last edited by nuzzle; September 10th, 2012 at 02:27 AM.

September 11th, 2012, 10:28 PM
#3
Re: Algorithm  Minimizing Equation  Dynamic Programming/Greedy
Thanks nuzzle for thorough explanation. I actually implemented a greedy algorithm and it worked perfectly. Thanks for your time.
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