  Mixed Integer Programming (MIP) is one of the most widely used modeling
techniques for combinatorial optimization problems. In many applications, a
similar MIP model is solved on a regular basis, maintaining remarkable
similarities in model structures and solution appearances but differing in
formulation coefficients. This offers the opportunity for machine learning
methods to explore the correlations between model structures and the resulting
solution values. To address this issue, we propose to represent an MIP instance
using a tripartite graph, based on which a Graph Convolutional Network (GCN) is
constructed to predict solution values for binary variables. The predicted
solutions are used to generate a local branching type cut which can be either
treated as a global (invalid) inequality in the formulation resulting in a
heuristic approach to solve the MIP, or as a root branching rule resulting in
an exact approach. Computational evaluations on 8 distinct types of MIP
problems show that the proposed framework improves the primal solution finding
performance significantly on a state-of-the-art open-source MIP solver.
