Solving distance-d independent set in a simple way
I'm sorry although I prefer to think of simple answers, ur Q triggers in my mind addressing other problems (a level of a research topic not an under graduate task)

Anyways, here is what popped up in my mind just incase u find something inspiring in them

-About the Kth Largest Subset problem http://dx.doi.org/10.1016/j.ipl.2015.09.015

-About Goemetric Set Packing problem 
(I myself didn't study it a lot, but read some papers about it when someone suggested it to me. I did not use it in my work, but the way u r trying to describe ur problem tells it has a Goemetric landscape nature so maybe it will be useful for u) 

https://www.sciencedirect.com/science/article/pii/S0925772112000740

https://slideplayer.com/slide/4514539/

I have more resources if u need so

. 

Finally, u may search for exact MWIS algorithms and u'll find a lot. Here is one paper
"Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs", Sebastian Lamm
, Christian Schulz, Darren Strash, Robert Williger, Huashuo Zhangk. 
arXiv:1810.10834v1 [cs.DS] 25 Oct 2018