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

Mixed-Integer Linear Programming (MILP) is an optimization technique widely used in various fields. Existing 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 does not guarantee solution feasibility (i.e., satisfying all constraints) due to inaccurate predictions and primarily focuses on prediction for binary decision variables. When addressing MILP involving non-binary integer variables using machine learning (ML), feasibility issues can become even more pronounced. Since finding an optimal solution requires satisfying all constraints, addressing feasibility is critical. To overcome these limitations, we propose a novel reinforcement learning (RL)-based solver that interacts with MILP to incrementally discover better feasible solutions without relying on traditional solvers. We design reward functions tailored for MILP, which enable the RL agent to learn relationships between decision variables and constraints. Furthermore, we leverage a Transformer encoder-based graph neural network (GNN) to effectively model complex relationships among decision variables. Our experimental results demonstrate that the proposed method can solve MILP problems and find near-optimal solutions without delegating the remainder to traditional solvers. The proposed method provides a meaningful step forward as an initial study in solving MILP problems entirely with ML in an end-to-end manner.