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

2025-12-10

AI Summary

Existing Predict-and-Search (PaS) methods are restricted to purely binary parametric mixed-integer programs (MIPs) and cannot handle practical instances featuring fixed variables or hybrid variable types (continuous, integer, and binary). Method: We propose a generalized framework for parametric MIPs, introducing—first in this domain—an identity-aware learning mechanism that encodes variable types to jointly model heterogeneous variables; we further design a parametric feature extraction module and an end-to-end joint training strategy that tightly integrates machine learning–based prediction with exact search-based solvers. Contribution/Results: Evaluated on multiple large-scale real-world MIP benchmarks, our method significantly outperforms both Gurobi and the original PaS in solution quality and solving speed. It demonstrates strong adaptability to fixed variables and mixed-variable structures, confirming its robustness and practical deployability for industrial-scale parametric optimization.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Neuro-Symbolic Learning

Application Category

• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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 problems and overlooks the presence of fixed variables that commonly arise in practical settings. This work extends the Predict-and-Search (PaS) framework to parametric MIPs and introduces ID-PaS, an identity-aware learning framework that enables the ML model to handle heterogeneous variables 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.

Problem

• Extends Predict-and-Search to parametric mixed-integer linear programs
• Introduces identity-aware learning to handle heterogeneous variables effectively
• Improves performance over state-of-the-art solvers on real-world problems

Innovation

• Extends Predict-and-Search to parametric mixed-integer linear programs
• Introduces identity-aware learning to handle heterogeneous variables effectively
• Demonstrates superior performance over state-of-the-art solvers in experiments