FOG: A Unified Framework for Federated Combinatorial Optimization on Graphs

With the revolutionary advancements in deep learning technologies, neural combinatorial optimization (NCO) emerges as a promising field for solving complex combinatorial optimization problems (COPs) in real-world scenarios. By lever-aging the learning ability of deep neural networks, NCO trains network models to learn the mapping from problem instances to optimal solutions, offering advantages in terms of scalability and generalization to unseen instances. However, in spite of the effectiveness, existing NCO approaches have been developed under the assumption of a centralized setting, which requires all historical data to be stored and accessed centrally on a single device. In practical applications, a more common scenario is the distributed storage of data across multiple devices. Therefore, the centralized assumption in NCO is difficult to meet due to the necessity of privacy protection and data security. To tackle this problem, in this paper, we propose a privacy-preserving framework of federated combinatorial optimization on graphs, named FOG. We formulate COPs as graph optimization tasks and propose to train a graph neural network (GNN) model via data-driven federated learning approaches. We further introduce the edge-aware message passing mechanism in the GNN model, which enhances the model capability by integrating both the edge and node information during the inference process. The proposed framework is evaluated on the well-known TSP benchmarks with various scales, and the experimental results show that FOG achieves highly competitive performance while being able to protect data privacy.