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 and should be applied to solve Combinatorial Optimization (CO) problems. Combinatorial Optimization (CO) concerns optimizing a function over a discrete solution space that is often intractably large. To learn to solve CO problems, we…