Using A* to solve Travelling Salesman
I've been tasked to write an implementation of the A* algorithm (heuristics provided) that will solve the travelling salesman problem. I understand the algorithm, it's simple enough, but I just can't see the code that implements it. I mean, I get it. Priority queue for the nodes, sorted by distance + heuristic(node), add the closest node on to the path. The question is, like, what happens if the closest node can't be reached from the previous closest node? How does one actually take a "graph" as a function argument? I just can't see how the algorithm actually functions, as code.
I read the Wikipedia page before posting the question. Repeatedly. It doesn't really answer the question- searching the graph is way, way different to solving the TSP. For example, you could construct a graph where the shortest node at any given time always results in a backtrack, since two paths of the same length aren't equal, whereas if you're just trying to go from A to B then two paths of the same length are equal.
You could derive a graph by which some nodes are never reached by always going closest first.
I don't really see how A* applies to the TSP. I mean, finding a route from A to B, sure, I get that. But the TSP? I don't see the connection.
Answer
I found a solution here
Use minimum spanning tree as a heuristic.
Set Initial State: Agent in the start city and has not visited any other city
Goal State: Agent has visited all the cities and reached the start city again
Successor Function: Generates all cities that have not yet visited
Edge-cost: distance between the cities represented by the nodes, use this cost to calculate g(n).
h(n): distance to the nearest unvisited city from the current city + estimated distance to travel all the unvisited cities (MST heuristic used here) + nearest distance from an unvisited city to the start city. Note that this is an admissible heuristic function. You may consider maintaining a list of visited cities and a list of unvisited cities to facilitate computations.