Comment by moralestapia a day ago
>Our computation produced a tour together with a proof that it is a shortest-possible route [...]
Proof nowhere to be found.
Waterloo-ers are nice people but I see an increasing trend of them just lying to get some cred. Come on guys, you don't have to follow the valley model that much.
Proof in this case is that the upper bound and the lower bound of the solver converged. This is not like a SAT solver where the solution itself can be trivially evaluated to verify the solution, it requires trusting that the solver does what it's supposed to be doing, similar to what happens when you solve a MILP with Gurobi or CPLEX.
You could still save the branch-and-bound tree, the LP problems solved at the tree nodes, the derivations of the LP cutting planes, and the LP solutions that together constitute the proof. Then you could in principle create an independent verifier for the branch-and-bound tree and cutting plane derivations, which could potentially be much more straightforward and simple code than the entire Concorde TSP solver, and wouldn't have so high performance requirements.
Is the solver guaranteed not to land in a local minima/maxima?
People really really really need to take some time to understand the concept of "burden of proof", so they can't stop making fools of themselves in public.
What are you actually expecting here?
The solution was found in a few days by the LKH TSP heuristic solver. They spent months (and decades of CPU time) using well-known techniques to bound the specific problem and prove that this was an optimal solution. It’s not something that you can synthesize to a page. They are literally announcing that they verified the heuristic-derived solution.
Consider it like any science, where folks can make shit up. But you can just run the bounding algorithms yourself, or prove they are incorrect.
>What are you actually expecting here?
Didn't you read my comment?
A proof.
Why?
Because they claim to have one.
How?
A link to a paper or something.
Come in, this stuff is very low level.
>But you can just run the bounding algorithms yourself, or prove they are incorrect.
People really really really need to take some time to understand the concept of "burden of proof", so they can't stop making fools of themselves in public x2.
The proof here is essentially the execution log of the bounding program. I imagine that this would be TB, PB or beyond. Not every proof is some clever paper, some are just brute force. Like proving a number is prime, or calculating the Nth digit of Pi. A paper doesn’t always make sense, but you can still announce what you’ve done (and maybe you get a paper with algorithmic details, but it’s not a proof for specific the instance).
The code is here I think: http://webhotel4.ruc.dk/~keld/research/LKH/ although on another page they mention LKH-Merge and I'm not sure what merge is.
>Our computation produced a tour together with a proof that it is a shortest-possible route [...]
>These claims are provisional. Until someone produces a better tour or a valid counter-proof, this stands as the best-known solution.
Are we looking at the same website? Because those two are quite different things.
Not sure what you expected to get. The Concorde TSP solver is an exact solver that uses branch and bound search, it will return either a solution with a specified bound or the optimal bound. They provide the dataset and the solution they found (and I believe their solver is open source), if you don't believe them you can go ahead and find a better tour.