  Finding high-quality solutions to mixed-integer linear programming problems
(MILPs) is of great importance for many practical applications. In this
respect, the refinement heuristic local branching (LB) has been proposed to
produce improving solutions and has been highly influential for the development
of local search methods in MILP. The algorithm iteratively explores a sequence
of solution neighborhoods defined by the so-called local branching constraint,
namely, a linear inequality limiting the distance from a reference solution.
For a LB algorithm, the choice of the neighborhood size is critical to
performance. In this work, we study the relation between the size of the search
neighborhood and the behavior of the underlying LB algorithm, and we devise a
leaning based framework for predicting the best size for the specific instance
to be solved. Furthermore, we have also investigated the relation between the
time limit for exploring the LB neighborhood and the actual performance of LB
scheme, and devised a strategy for adapting the time limit. We computationally
show that the neighborhood size and time limit can indeed be learned, leading
to improved performances and that the overall algorithm generalizes well both
with respect to the instance size and, remarkably, across instances.
