I am looking for a paper/study in which a Logic-based Benders decomposition (LLBD) framework is used when the master problem is associated with integer variables (not specifically binary).
In general LBBD, we often send fixed binary solutions to the subproblem and the Benders cuts aim to alternate the previous solutions as "combinatorial cuts". I am just curious if LLBD could be utilized in the case of having integer master variables. I have gone through a lot of recent LBBD papers, but it seems like the master problem is always associated with binary variables.
In a previous post, it is discussed that there exist no-good cut strategies, but in general, no-good cuts are not really effective to converge the optimal solution. That is why I am curious if there exists a study where authors design effective LBBD cuts when the master variables are integer.