Specifically, my curiosity is in relation to the traveling salesman problem. I know that if you're on a 2D graph, you can represent the distance between cities using linear distance; I'm asking whether there are any established methods for representing the solution space.
For example, if one has five cities to create a path between, is there a way to represent the solution space such that every point represents a possible solution, and the graph has a clear structure used to get from a starting solution to an ending solution, where each point has a clear transition criteria to its neighbors? One possible criteria being, for instance, only being allowed to swap two cities at a time.
I've tried to search for various keywords, but so far haven't come up with anything solid - apologies if it's a well-known problem under a different name or set of search terms.