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.

本文提出了一种基于图分类的方法，用于自动确定是使用整体式还是分解式的解决方案方法；通过适当的特征集，将优化问题表示为捕捉问题的变量和约束之间的结构和功能耦合的图；构建图分类器以确定给定问题的最佳解决方法；以解决分析凸混合整数非线性规划问题时使用分支定界法还是外逼近算法为例展示了所提出方法的应用；最后，展示了学习到的分类器如何并入现有的混合整数优化求解器中。