Problem Description
I have many examples (say $N$) to choose from to train my machine learning model. However, I could only select $n \ll N$ based on a set of $K$ attributes $\{a_1, a_2, \cdots, a_k\}$ already measured for the dataset.
Now I would like to find these $n$ samples so that some measure (for example, sum) of the each of the $K$ columns are maximized.
What I Tried
This looks like a knapsack problem but with multiple attributes. However, direct Google search does not seem to give me a lot of relevant results as I am looking for an existing software package that could solve this problem (or perhaps its relaxed version).
Note
Cross-posted at Math.SE with 200 bounty points.