Decision-focused Graph Neural Networks for Combinatorial Optimization

TL;DR

This paper introduces a decision-focused graph neural network framework that enhances combinatorial optimization by integrating GNNs with solvers in an end-to-end system, outperforming traditional and standalone GNN methods.

Contribution

It presents a novel end-to-end decision-focused framework combining GNNs and optimization solvers for combinatorial problems, with empirical validation on classical tasks.

Findings

Outperforms standalone GNN and classical methods on MaxCut, MIS, MVC

Demonstrates improved accuracy and efficiency in combinatorial optimization

Validates effectiveness across multiple classical problems

Abstract

In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks (GNNs) as an alternative to traditional algorithms, a subject that has attracted considerable attention. Despite the growing popularity of GNNs and traditional algorithm solvers in the realm of CO, there is limited research on their integrated use and the correlation between them within an end-to-end framework. The primary focus of our work is to formulate a more efficient and precise framework for CO by employing decision-focused learning on graphs. Additionally, we introduce a decision-focused framework that utilizes GNNs to address CO problems with auxiliary support. To realize an end-to-end approach, we have designed two cascaded modules: (a) an unsupervised trained graph predictive model, and (b) a solver for quadratic binary unconstrained optimization. Empirical evaluations are conducted on various classical tasks, including maximum cut, maximum independent set, and minimum vertex cover. The experimental results on classical CO problems (i.e. MaxCut, MIS, and MVC) demonstrate the superiority of our method over both the standalone GNN approach and classical methods.