TL;DR
This paper introduces FMIP, a novel generative framework that models the joint distribution of integer and continuous variables in MILP, significantly improving solution quality and compatibility with existing solvers.
Contribution
FMIP is the first model to jointly generate integer and continuous variables for MILP, enhancing solution accuracy and solver integration.
Findings
Reduces primal gap by 41.34% on average
Outperforms existing baselines on eight benchmarks
Compatible with various backbone networks and solvers
Abstract
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based heuristic solutions to accelerate downstream solvers. While recent generative models have shown promise in learning powerful heuristics, they suffer from a critical limitation. That is, 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. To this end, we propose Joint Continuous-Integer Flow for Mixed-Integer Linear Programming (FMIP), which is the first generative framework that models the joint distribution of both integer and continuous variables for MILP solutions. Built upon the…
Peer Reviews
Decision·ICLR 2026 Poster
The claimed empirical performance is good, achieving decent relative improvement in primal gap over state-of-the-art baselines on some benchmarks. The framework's compatibility with multiple GNN architectures and solvers, as shown in ablation studies and compatibility analyses, highlights its flexibility and generalizability. Additionally, the holistic guidance, supported by gradient-based updates for continuous variables and sampling-reweighting for integers, effectively leverages complete solu
FMIP's focus on bounded integer variables limits its applicability to general MILP problems with unbounded or non-binary integers. The reliance on flow matching introduces higher inference times compared to discriminative baselines like supervised learning. While ablations confirm the value of joint modeling and guidance, the paper could benefit from deeper analysis on failure cases or scalability to very large-scale instances beyond the tested benchmarks.
1. The paper is well-organized with a clear logical flow. 2. Extending the application of generative methods from ILP to MILP is a natural progression. 3. Empirical experiments are comprehensive, and the results show improvements over the selected baselines.
I have reviewed this paper at NeurIPS 2025, and I am satisfied with the revisions made by the authors. I do not have any major concerns, but I have a minor suggestion: The paper states that "existing generative methods for MILP suffer from a critical limitation: they model the distribution of only the integer variables." However, the transition from ILP to MILP seems relatively straightforward, and this limitation may not constitute a major challenge. I recommend that the authors emphasize the
This paper identifies and highlights one of the blind posts from previous generative models for MILPs: the lack of a proper treatment of continuous variables. I believe this is the main contribution of the paper
- The model is straightforward and amounts to the concatenation of a continuous flow and a discrete flows that can both be conditioned on predicted assignments. - The tri-partite representation is surprising and questionable (see question below)
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