Learning to Search in Local Branching

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 produce improving and highly influential development search methods in MILP. The algorithm iteratively explores a sequence solution neighborhoods defined by so-called constraint, namely, inequality limiting distance from reference solution. For LB algorithm, choice neighborhood size critical performance. Although it was initialized conservative value original scheme, our new observation that "best" strongly dependent on particular MILP instance. work, we investigate relation between behavior underlying devise leaning-based framework guiding heuristic. consists two-phase strategy. first phase, scaled regression model trained predict at iteration through task. second leverage reinforcement learning reinforced strategy dynamically adapt subsequent iterations. We computationally show can indeed be learned, leading improved performances overall generalizes well both with respect instance and, remarkably, across instances.