I am interested in solving the TSP for (small) grid graphs. Any sort of library will do for me, but this seems to be harder than expected. I tried a couple of solvers I found out there (including concorde), but they all seem to have problems when the triangle inequality does not hold.
For instance, I would like the solver to output the tour (0, 1, 2, 1, 4, 3) for the graph (with unit edge weights) below:
0-1-2
| |
3-4
In this particular case, I told concorde that the edge (2, 4) had weight 1000 and concorde promptly produced the tour (0, 1, 2, 4, 3) of cost 1004. This is clearly not what I am looking for.
Ideally, there would be some simple (possibly brute force) implementation in Java, but anything which works will actually do. Can anyone point me to some code or do I really have to go an implement this myself?
Edit: also, it is important that I get an exact solution, not some approximation.
Edit2: indeed, this does not seem to be TSP. What I am trying to find is a shortest closed walk which visits all vertices.
Your difficulty is not the triangle inequality. The difficulty has to do with the fact that the solution you’re expecting is not a valid TSP tour.
The TSP seeks a Hamiltonian cycle; that is, a cycle that visits each vertex exactly once. Your solution,
(0, 1, 2, 1, 4, 3), visits vertex 1 twice.If that’s the solution you’re seeking, then the the problem you’re trying to solve is not the Travelling Salesman Problem.