The first generative framework that models the joint distribution of both integer and continuous variables for Mixed-Integer Linear Programming solutions.
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents significant computational challenges.
While recent generative models have shown promise, they suffer from a critical limitation: they model the distribution of only the integer variables and fail to capture the intricate coupling between integer and continuous variables, creating an information bottleneck and ultimately leading to suboptimal solutions.
We propose FMIP, the first generative framework that models the joint distribution of both integer and continuous variables for MILP solutions. Built upon the joint modeling paradigm, a holistic guidance mechanism steers the generative trajectory toward optimality and feasibility during inference.
41.34%
Average relative improvement over existing baselines across 8 standard MILP benchmarks.
Compared to existing methods that only model integer variables
FMIP jointly models both variable types with holistic guidance, while existing methods only handle integer variables.
First framework to model complete distribution of both integer and continuous variables
01Steers sampling toward optimality and feasibility using complete solution feedback
02Works with arbitrary backbone networks and various downstream solvers
03Superior results on 8 benchmarks with 41.34% average improvement
04FMIP achieves 41.34% average improvement across 8 benchmarks and 4 downstream solvers
| Dataset | ND (400s) |
PS (600s) |
PMVB (600s) |
Apollo (800s) |
|---|---|---|---|---|
| CA Auctions | 50.6% | 0.0% | 0.0% | 0.0% |
| GIS Independent Set | 4.1% | 14.3% | 0.0% | 0.0% |
| MIS Max Independent Set | 95.9% | 0.0% | 100% | 100% |
| FCMNF Network Flow | 3.5% | 0.0% | 0.0% | 0.0% |
| SC Set Covering | 60.0% | 100% | 97.9% | 100% |
| LB Load Balancing | 93.8% | 100% | 0.0% | 100% |
| IP Item Placement | 71.6% | 74.9% | 48.1% | 100% |
| MIPLIB Standard | 0.4% | 0.5% | 0.6% | 0.3% |
| Average | 47.2% | 23.7% | 30.8% | 37.5% |
FMIP is freely available on GitHub. Try it on your MILP problems today!
View on GitHub@misc{li2025fmipjointcontinuousintegerflow,
title={FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming},
author={Hongpei Li and Hui Yuan and Han Zhang and Jianghao Lin and Dongdong Ge and Mengdi Wang and Yinyu Ye},
year={2025},
eprint={2507.23390},
archivePrefix={arXiv},
primaryClass={math.OC},
url={https://arxiv.org/abs/2507.23390},
}