I think I solved the subset sum problem, a NP-Complete problem. I compared the output of smaller sets to existing algorithms and the results match. Obviously, I cant compare larger sets due to the time complexity of existing algorithms.

So my question is, what is the best path forward?

I'll solve a few more of your sets below for more proof, although some sets/goals require more memory than my computer has.

For now I wont share the details of the algorithm for obvious reasons.

Some other interesting notes: - Goal=150: Set=(1...100), there are 19,378,091 subsets that sum to 150 (94 seconds to compute)