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I have an combinational optimization problem and I do not know its name in literature.

My problem is the following: I have n sets containing exclusive elements, so each element is present only in a set. An element is characterized by 2 constraints values, and one profit.

I have to choose an element from each set in order to maximize the sum of the profits, while keeping the sum of each constraint below a a specified limit.

Is this an already studied problem? WHich is its name?
Can I assimilate it to an already studied problem?

Thanks to @Berthur & @mrBen replies, I discovered that this is a multiple-constrained knapsack problem where you have to create an indicator variable to force that only one element will be chosen by each set

Max
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    Sounds like a variation of the Knapsack problem: https://en.wikipedia.org/wiki/Knapsack_problem – Berthur Jul 20 '22 at 14:27
  • @Berthur In the knapsack problem I do not have the constraint of N different sets of elements from wich I have to choose the elements. Or do you see a way that I can reduce my problem into knapsack problem ? – Max Jul 20 '22 at 14:30
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    Hence a variation. Knapsack has 1 constraint, also summation based. So would this be a generalisation, with N constraints? – Berthur Jul 20 '22 at 14:42
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    @Berthur you are right. It is a multiple-constrained knapsack problem. – Max Jul 20 '22 at 14:59
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    Not sure, but [or.se] might be more adapted to that question. – mrBen Jul 20 '22 at 15:02

1 Answers1

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The problem you're describing is know as the multiple-choice knapsack problem. In your case, as you have 2 constraints, it's actually a 2-dimentional multiple-choice knapsack problem.

With the keywords multi-dimentional multiple-choice knapsack problem (sometime abbreviated as MMKP) you should be able to find the corresponding literature.

mrBen
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