  Graph-structured data is ubiquitous throughout natural and social sciences,
and Graph Neural Networks (GNNs) have recently been shown to be effective at
solving prediction and inference problems on graph data. In this paper, we
propose and demonstrate that GNNs can be applied to solve Combinatorial
Optimization (CO) problems. CO concerns optimizing a function over a discrete
solution space that is often intractably large. To learn to solve CO problems,
we formulate the optimization process as a sequential decision making problem,
where the return is related to how close the candidate solution is to
optimality. We use a GNN to learn a policy to iteratively build increasingly
promising candidate solutions. We present preliminary evidence that GNNs
trained through Q-Learning can solve CO problems with performance approaching
state-of-the-art heuristic-based solvers, using only a fraction of the
parameters and training time.
