Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming

2025-03-03

AI Summary

Machine learning–based initial solution prediction for mixed-integer linear programming (MILP) often yields infeasible solutions or degrades solution quality. Method: This paper proposes an alternating prediction-correction neural solving framework. It introduces a trust-region search to generate reference solutions and pioneers an uncertainty-driven error-bound optimization (UEBO) mechanism that dynamically quantifies prediction confidence and adaptively fixes high-confidence variables—enabling safe dimensionality reduction. Departing from the “predict-and-fix” paradigm, the framework ensures feasibility and near-optimality while accelerating convergence. It integrates deep neural networks, trust-region optimization, and state-of-the-art MILP solvers (e.g., Gurobi, SCIP). Contribution/Results: On standard benchmarks, the method reduces optimality gap by over 50% compared to existing ML-based approaches, significantly improving solution quality, feasibility rate, and solving speed.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap.

Problem

• Improves solution quality in mixed-integer linear programming using ML.
• Reduces problem dimension by fixing high-confidence predicted variables.
• Introduces UEBO to evaluate and fix reliable predicted values.

Innovation

• Alternating prediction-correction neural framework
• Uncertainty-based Error upper Bound (UEBO)
• Trust-region search for improved solutions