Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose

TL;DR

This paper introduces a machine learning-based method to automatically decide between monolithic and decomposition-based optimization techniques by classifying problem graphs, improving solver efficiency.

Contribution

It presents a novel graph classification approach to predict the most suitable optimization method, integrating machine learning into mixed integer nonlinear programming solvers.

Findings

The classifier accurately predicts when to use branch and bound or outer approximation.

The approach improves solver decision-making efficiency.

The method can be integrated into existing optimization software.

Abstract

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.