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

arXiv: https://arxiv.org/abs/2512.10211 · HTML: https://mlsanity.com/paper/2512.10211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Dual Lagrangian Learning for Conic Optimization](https://mlsanity.com/paper/2402.03086/) (2024)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2401.10467/) (2024)
- [Balans: Multi-Armed Bandits-based Adaptive Large Neighborhood Search for Mixed-Integer Programming Problem](https://mlsanity.com/paper/2412.14382/) (2024)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [A General Large Neighborhood Search Framework for Solving Integer Linear Programs](https://mlsanity.com/paper/2004.00422/) (2020)
- [Learning for Online Mixed-Integer Model Predictive Control with Parametric Optimality Certificates](https://mlsanity.com/paper/2303.12152/) (2023)
- [Verification of First-Order Methods for Parametric Quadratic Optimization](https://mlsanity.com/paper/2403.03331/) (2024)
- [Practice-Based Optimization for the Strategic Locomotive Assignment Problem](https://mlsanity.com/paper/2507.22235/) (2025)
- [A Fair OR-ML Framework for Resource Substitution in Large-Scale Networks](https://mlsanity.com/paper/2511.18269/) (2025)
- [Domain-Aware Machine Learning for Accelerating MILP-Based Motion Planning with Temporal Logic and Chance Constraints](https://mlsanity.com/paper/2508.07515/) (2025)

## Built on by (most cited first, 1 of 1)

- [Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs](https://mlsanity.com/paper/2606.21440/) (2026)

## Abstract (arXiv)

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.