Rethinking the Capacity of Graph Neural Networks for Branching Strategy

Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching (SB) scores that provide an efficient strategy in the branch-and-bound algorithm.
Although message-passing GNN (MP-GNN), as the simplest GNN structure, is frequently employed in the existing literature to learn SB scores, we prove a fundamental limitation in its expressive power -- there exist two MILP instances …

algorithm capacity cs.lg gnn gnns graph graph neural networks heuristics linear math.oc mixed networks neural networks paper strategy