FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming

• URL: http://arxiv.org/abs/2507.23390v2
• Date: Mon, 29 Sep 2025 07:41:12 GMT
• Title: FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming
• Authors: Hongpei Li, Hui Yuan, Han Zhang, Jianghao Lin, Dongdong Ge, Mengdi Wang, Yinyu Ye,
• Abstract summary: Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems.<n>We propose Joint Continuous-Integer Flow for Mixed-Integer Linear Programming (FMIP), which is the first generative framework that models joint distribution of both integer and continuous variables for MILP solutions.<n>FMIP is fully compatible with arbitrary backbone networks and various downstream solvers, making it well-suited for a broad range of real-world MILP applications.
• Score: 52.52020895303244
• License: http://creativecommons.org/licenses/by/4.0/
• 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 joint modeling paradigm, a holistic guidance mechanism is designed to steer the generative trajectory, actively refining solutions toward optimality and feasibility during the inference process. Extensive experiments on eight standard MILP benchmarks demonstrate the superior performance of FMIP against existing baselines, reducing the primal gap by 41.34% on average. Moreover, we show that FMIP is fully compatible with arbitrary backbone networks and various downstream solvers, making it well-suited for a broad range of real-world MILP applications.

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