Combinatorial optimization problem - What would you call this? 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 :

Apples
Oranges
Pears
Lemons

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).
It's called four-dimensional matching and it's NP-complete.