MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers

TL;DR

MIP-GNN introduces a data-driven, graph neural network-based approach to improve mixed-integer programming solvers by predicting variable biases, leading to enhanced decision-making and performance on challenging binary MILPs.

Contribution

The paper presents a novel framework that integrates graph neural networks into MIP solvers to predict variable biases, replacing heuristic decisions with learned insights.

Findings

Significant performance improvements on binary MILPs.

Effective integration of GNN predictions into solver components.

Demonstrated advantages over default solver configurations.

Abstract

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics, largely ignoring common patterns within a given instance distribution of the problem of interest. Here, we propose MIP-GNN, a general framework for enhancing such solvers with data-driven insights. By encoding the variable-constraint interactions of a given mixed-integer linear program (MILP) as a bipartite graph, we leverage state-of-the-art graph neural network architectures to predict variable biases, i.e., component-wise averages of (near) optimal solutions, indicating how likely a variable will be set to 0 or 1 in (near) optimal solutions of binary MILPs. In turn, the predicted biases stemming from a single, once-trained model are used to guide the solver, replacing heuristic components. We integrate MIP-GNN into a state-of-the-art MIP solver, applying it to tasks such as node selection and warm-starting, showing significant improvements compared to the default setting of the solver on two classes of challenging binary MILPs.