ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs

TL;DR

This paper introduces ID-PAS+, an advanced machine learning framework that improves predict-and-search methods for solving complex mixed-integer linear programs with diverse variable types, outperforming existing solvers.

Contribution

It extends the Predict-and-Search framework to handle heterogeneous variables and fixed structures, enhancing performance on real-world large-scale MIPs.

Findings

ID-PAS+ outperforms Gurobi and PAS on several real-world problems.

The framework effectively manages heterogeneous variable types.

Experiments demonstrate consistent superior performance.

Abstract

Mixed-Integer Linear Programs (MIPs) are powerful and flexible tools for modeling a wide range of real-world combinatorial optimization problems. Predict-and-Search methods operate by using a predictive model to estimate promising variable assignments and then guiding a search procedure toward high-quality solutions. Recent research has demonstrated that incorporating machine learning (ML) into the Predict-and-Search framework significantly enhances its performance. Still, it is restricted to binary-only problems and overlooks the presence of fixed variable structures that commonly arise in real-world settings. This work extends the current Predict-and-Search (PAS) framework to parametric general parametric MIPs and introduces ID-PAS+, an identity-aware learning framework that enables the ML model to handle heterogeneous variable types more effectively. Experiments on several real-world large-scale problems demonstrate that ID-PAS+ consistently achieves superior performance compared to the state-of-the-art solver Gurobi and PAS.