Revisiting local branching with a machine learning lens

TL;DR

This paper introduces a machine learning framework to optimize local branching parameters in MILP solvers, improving solution quality and generalization across instances by predicting neighborhood size and adapting time limits.

Contribution

It proposes a novel learning-based approach to predict optimal neighborhood size and time limits for local branching in MILP, enhancing performance and generalization.

Findings

Learning-based parameter prediction improves solution quality.

Adaptive strategies outperform fixed parameter settings.

Method generalizes well across different instances.

Abstract

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.