Solving an ordered knapsack problem exactly with a non linear (blackbox) evaluation function
If your function (or your surrogate function) has no structure, then there's nothing to say: you can't do any better than exhaustive search.  In particular, you must examine every possible combination of the items that has the right weight.  If your function has no structure, then you must evaluate it on each possible combination of items whose total weight matches the desired value: you can't rule out any of the possible combinations.  There are exponentially such combinations, so your problem requires evaluating the function (or surrogate function) on exponentially many possible inputs.

Also, if your function has no structure, there are no heuristics or approximation algorithms that will do better than brute force (try some randomly chosen set of combinations and see which does best).

No, this case probably hasn't been studied, because it isn't interesting: there's nothing interesting or useful you can say about it, beyond what I've listed above.