Learning to Schedule Heuristics in Branch-and-Bound

TL;DR

This paper introduces a data-driven approach to dynamically schedule heuristics in MIP solvers, significantly improving early solution quality by tailoring heuristic sequences to specific problem instances.

Contribution

It presents the first formal framework and algorithm for learning instance-specific heuristic schedules in exact MIP solvers, outperforming default heuristic management rules.

Findings

Reduced primal integral by up to 49% on challenging instances.

Demonstrated effectiveness of data-driven heuristic scheduling.

Improved early solution finding in MIP solving.

Abstract

Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.