I have algorithms that get me a tight upper (UB) and lower (LB) bound to a maximization binary integer program (a routing problem). My formulation is non-compact and requires the addition of sub-tour elimination constraints (SEC) dynamically. I am using CPLEX branch-and-bound and add these constraints via the callback mechanism. The LB solution is provided as incumbent (warm start) and that works fine but as soon as I add the constraint: objective function value <= UB, the CPLEX branch-and-bound seems to add a huge number of SECs and takes much longer time to improve the given UB further and finally to converge.
I thought with a tight UB and LB, the optimal solution could be found faster than usual but it is behaving the other way round. I have no idea what actually is going on. How can I effectively use the bound information to get to the optimal solution using CPLEX branch-and-bound/branch-and-cut? Please help!
