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Mixed-integer programming (MIP) technology offers a generic way offormulating and solving combinatorial optimization problems. While generallyreliable, state-of-the-art MIP solvers base many crucial decisions onhand-crafted heuristics, largely ignoring common patterns within a giveninstance distribution of the problem of interest. Here, we propose MIP-GNN, ageneral framework for enhancing such solvers with data-driven insights. Byencoding the variable-constraint interactions of a given mixed-integer linearprogram (MILP) as a bipartite graph, we leverage state-of-the-art graph neuralnetwork architectures to predict variable biases, i.e., component-wise averagesof (near) optimal solutions, indicating how likely a variable will be set to 0or 1 in (near) optimal solutions of binary MILPs. In turn, the predicted biasesstemming from a single, once-trained model are used to guide the solver,replacing heuristic components. We integrate MIP-GNN into a state-of-the-artMIP solver, applying it to tasks such as node selection and warm-starting,showing significant improvements compared to the default setting of the solveron two classes of challenging binary MILPs.

MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers