Algorithm Optimization - Shortest Route Between Multiple Points

Question

Problem: I have a large collection of points. Each of these points has a list with references to other points with the distance between them already calculated and stored. I

Answer 1

Answering to the updated post, your solution of checking every possibility is optimal (at least, noone has discovered better algorithms so far). Yes, that's a travelling salesman, whose essense is not touching every city, but touching every city once. If you don't want to search for best solution possible, you may find it useful to use heuristics that work faster, but allow for limited discrepancy from ideal solution.

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For future answerers: Floyd-Warshall algorithm and all Floyd-like variations are inapplicable here.