A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming

Abstract

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are capable of capturing common patterns across these MILP instances. In this work, we combine ML with optimization and propose a novel predict-and-search framework for efficiently identifying high-quality feasible solutions. Specifically, we first utilize graph neural networks to predict the marginal probability of each variable, and then search for the best feasible solution within a properly defined ball around the predicted solution. We conduct extensive experiments on public datasets, and computational results demonstrate that our proposed framework achieves 51.1% and 9.9% performance improvements to MILP solvers SCIP and Gurobi on primal gaps, respectively.

G2MILP: Learning to Generate Mixed-Integer Linear Programming Instances for MILP Solvers

“…Machine learning (ML) techniques, due to its capability of capturing rich features from data, has shown impressive potential in addressing combinatorial optimization (CO) problems [26], [27], [28], especially MILP problems [8]. Some works apply ML models to directly solve MILPs [29], [30], [31]. Others attempt to incorporate ML models into heuristic components in modern solvers [10], [12], [32], [33].…”

“…We employ G2MILP to generate new instances and augment the original datasets, and then evaluate whether the enriched datasets can improve the performance of the downstream tasks. The considered tasks include predicting the optimal values of the MILP problem, as discussed in Chen et al [19], and applying a predictand-search framework for solving MILPs, as proposed by Han et al [31].…”

“…Predict-and-Search. We conduct experiments on a neural solver, i.e., the predict-and-search framework proposed by Han et al [31]. Specifically, they propose a framework that first predicts a solution and then uses solvers to search for the optimal solutions in a trust region.…”