Genuinely interested in being educated here: If Gurobi's integer programming solver didn't find a solution better than 218, is that a guarantee that there exists no solution better than 218? Is it equivalent to a mathematical proof?
(Let's assume, for the sake of argument, that there's no bugs in Gurobi's solver and no bugs in the author's implementation of the problem for Gurobi to solve.)
I guess I'm basically asking whether it's possible that Gurobi got trapped in a local maximum, or whether this can be considered a definitive universal solution.
(Let's assume, for the sake of argument, that there's no bugs in Gurobi's solver and no bugs in the author's implementation of the problem for Gurobi to solve.)
I guess I'm basically asking whether it's possible that Gurobi got trapped in a local maximum, or whether this can be considered a definitive universal solution.