New Method Accelerates MILP Solving with Early Solution Consistency.

Mixed-Integer Linear Programming (MILP) is critical for industrial decision-making but can be computationally intensive for complex instances. While some learning-based methods predict solutions from static features, they often overlook valuable information generated during the solver's search process. This research observes that early-stage solutions, which are cheap to obtain, often share structural similarities with the final, high-quality solutions. Motivated by this, the paper proposes a new paradigm that shifts the learning target from direct variable assignment to predicting "early-to-final consistency." For each variable, the model predicts whether its early assignment will persist in the full-budget solution. These consistency predictions then guide the downstream search, for example, by fixing consistent assignments. Experiments across four MILP benchmarks show that this method reduces the primal gap by 56.9% on average and completely closes it for combinatorial auction instances, even transferring zero-shot to different solvers.