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.
The solver generates a relaxed lower bound that indicates how far they could be from the global optimal solution. The moment that the lower bound improves enough to match a path they can guarantee that it's the global optimum
If you can prove, as they claim, that you have an algorithm that gives you the optimal solution (aside from the obvious, brute-forced one), you might be one stone throw away to make an argument for some P == NP, that would be HUGE.
But it seems that some people get offended when you tell them their perpetual motion machines are not real.
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?
The solver generates a relaxed lower bound that indicates how far they could be from the global optimal solution. The moment that the lower bound improves enough to match a path they can guarantee that it's the global optimum
(I don't know)
But I would guess the answer is "no".
If you can prove, as they claim, that you have an algorithm that gives you the optimal solution (aside from the obvious, brute-forced one), you might be one stone throw away to make an argument for some P == NP, that would be HUGE.
But it seems that some people get offended when you tell them their perpetual motion machines are not real.
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