Annealing Machine-assisted Learning of Graph Neural Network for Combinatorial Optimization

TL;DR

This paper introduces a hybrid approach combining Annealing Machines and Graph Neural Networks to improve scalability and accuracy in solving complex combinatorial optimization problems.

Contribution

It presents a novel merging method where AMs guide GNNs, enabling the solution of larger problems beyond AMs' original limitations.

Findings

The hybrid model effectively scales to larger problem sizes.

AM-guided GNNs achieve competitive solution quality.

The approach demonstrates feasibility on canonical problems.

Abstract

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still scaling limitations. In parallel, Graph Neural Networks (GNN) have been recently adapted to solve combinatorial problems, showing competitive results and potentially high scalability due to their distributed nature. We propose a merging approach that aims at retaining both the accuracy exhibited by AMs and the representational flexibility and scalability of GNNs. Our model considers a compression step, followed by a supervised interaction where partial solutions obtained from the AM are used to guide local GNNs from where node feature representations are obtained and combined to initialize an additional GNN-based solver that handles the original graph's target problem. Intuitively, the AM can solve the combinatorial problem indirectly by infusing its knowledge into the GNN. Experiments on canonical optimization problems show that the idea is feasible, effectively allowing the AM to solve size problems beyond its original limits.