Multi-task Representation Learning for Mixed Integer Linear Programming

TL;DR

This paper presents a multi-task learning framework for machine learning-guided MILP solving, enabling better generalization across solvers, tasks, and problem sizes, thus improving scalability and adaptability.

Contribution

It introduces the first multi-task learning approach for MILP solving, unifying embeddings across solvers and tasks to enhance generalization and efficiency.

Findings

Performs comparably to specialized models within the same distribution.

Significantly outperforms specialized models in generalization across sizes and tasks.

Demonstrates effectiveness on three widely used MILP benchmarks.

Abstract

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILP-solving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks.