  In this paper, we propose a graph classification approach for automatically
determining whether to use a monolithic or a decomposition-based solution
method. In this approach, an optimization problem is represented as a graph
that captures the structural and functional coupling among the variables and
constraints of the problem via an appropriate set of features. Given this
representation, a graph classifier is built to determine the best solution
method for a given problem. The proposed approach is used to develop a
classifier that determines whether a convex Mixed Integer Nonlinear Programming
problem should be solved using branch and bound or the outer approximation
algorithm. Finally, it is shown how the learned classifier can be incorporated
into existing mixed integer optimization solvers.
