RL-MILP Solver: A Reinforcement Learning Approach for Solving Mixed-Integer Linear Programs with Graph Neural Networks

Mixed-integer linear programming (MILP) is a widely used optimization technique across various fields. Existing $\textit{end-to-end learning}$ methods for MILP generate values for a subset of decision variables and delegate the remaining problem to traditional MILP solvers. However, this approach often fails to guarantee solution feasibility (i.e., satisfying all constraints) due to inaccurate predictions and primarily focuses on binary decision variables. Satisfying all constraints is a prerequisite for obtaining the optimal solution, and the feasibility issue becomes even more critical with non-binary integer (integer, for short) variables. Thus, addressing the feasibility of MILP involving integer variables is crucial. To address these challenges, we propose a novel reinforcement learning (RL)-based solver that not only finds the first feasible solution but also incrementally discovers better feasible solutions without delegating the remainder to off-the-shelf solvers. Our experimental results demonstrate that the proposed method achieves (near-)optimal solutions.

@article{lee2025_2411.19517,
  title={ RL-MILP Solver: A Reinforcement Learning Approach for Solving Mixed-Integer Linear Programs with Graph Neural Networks },
  author={ Tae-Hoon Lee and Min-Soo Kim },
  journal={arXiv preprint arXiv:2411.19517},
  year={ 2025 }
}