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

CodePudding user response：

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.