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Mixed Integer Programming (MIP) is one of the most widely used modelingtechniques for combinatorial optimization problems. In many applications, asimilar MIP model is solved on a regular basis, maintaining remarkablesimilarities in model structures and solution appearances but differing informulation coefficients. This offers the opportunity for machine learningmethods to explore the correlations between model structures and the resultingsolution values. To address this issue, we propose to represent an MIP instanceusing a tripartite graph, based on which a Graph Convolutional Network (GCN) isconstructed to predict solution values for binary variables. The predictedsolutions are used to generate a local branching type cut which can be eithertreated as a global (invalid) inequality in the formulation resulting in aheuristic approach to solve the MIP, or as a root branching rule resulting inan exact approach. Computational evaluations on 8 distinct types of MIPproblems show that the proposed framework improves the primal solution findingperformance significantly on a state-of-the-art open-source MIP solver.

Accelerating Primal Solution Findings for Mixed Integer Programs Based on Solution Prediction