I'm trying to solve an optimization problem which can be described as follows.
- There are four sets objects. For simplicity, let's call them :
- The sets can contain unequal numbers of their respective objects
- These objects must be organized into groups containing exactly one of each object
- Each possible group can be evaluated by some merit function (ie: function of the difference between the masses of the constituent objects of the group, say)
- The maximum number of groups with a merit function below some threshold must be formed with the objects in the input sets.
- In the above set of groups, no object can be duplicated - it must belong uniquely to one group.
My question is not necessarily how to solve this problem - this is no doubt an extremely broad question. What I would like to know is whether or not this problem has, or is of a class of problem, with some formal name.
Primarily, I'm looking for search terms to help research similar problems (and the types of solutions that are known for it).