Neigbourhoods in Large Neighbourhood Search (LNS) algorithms

I have been trying to implement a variant of LNS on a graph for TSP. One of the ways that I can define a neighborhood for TSP is to find $$k$$-shortest path between two nodes. But the choice of these nodes are random. I have two questions:

1. Are there better ways to define neighborhood?
2. Is there a way to find a promising neighborhood?
• This paper is particularly useful when working on (A)LNS, and provides great guidance and an overview of operators/neighborhoods. sciencedirect.com/science/article/pii/S0305054805003023 May 31 '19 at 7:11
• @AlbertSchrotenboer that seems like it deserves to be an answer, not a comment. May 31 '19 at 12:01