This part is unclear; what exactly did you change? Are you saying that the LP relaxation has value 271.666, but, when you enforce integrality, Gurobi can actually find and prove optimality of a solution with value 218?
Were you really just solving LPs up to this point in the article? How can these intermediate LPs be so slow to solve (6+ years) and yet Gurobi is able to solve the integer-restricted problem?
I've always been solving the integer problem of course. But throughout the article, I improve the model formulation again and again through insights, which makes the LP relaxation tighter. Initially, it gave 305.0 as upper bound, but after tightening the model (addind constraints that cut off that 305 solution and others) it gives 271.666...
- which leads to insanely faster search. It's like brute-forcing through all passwords of length 20 and a wizard telling you that you're wrong when you reach character 7 instead of 13.
Were you really just solving LPs up to this point in the article? How can these intermediate LPs be so slow to solve (6+ years) and yet Gurobi is able to solve the integer-restricted problem?