Number partitioning targeting ratio of subset sums and equal size I've seen a number of questions and answers related to the partitioning problem of dividing a set into 2 subsets of equal size and sum that use greedy or dynamic programming solutions to get approximate answers. However, I am looking to split a set into 2 subsets of minimum difference in size but with a target ratio of sums.

I have tried variations of greedy algorithms that will work to minimize the largest difference of the two metrics at any point in the calculation, but this just results in a result that splits the difference between the two. I'm happy with an approximate solution since it needs to run in a reasonable amount of time.
The problem is NP-hard (assuming the numbers are represented in binary).  If you could solve your problem efficiently, you could solve the Partition problem: Partition is the special case where the minimum difference is zero (and the target ratio is 1:1).  Therefore, you should not expect any simple algorithm to be both efficient and always correct.

If you want a heuristic that gives an approximation, greedy algorithms are reasonable.  I suggest you try adapting the standard algorithms for the Partition problem.  Another approach is to use an integer linear programming solver.