A self-supervised learning model for graph clustering optimization problems

Abstract

The graph clustering optimization problems are ubiquitous in both scientific and engineering fields, for example the graph partitioning problem and facility location problem. Since most of these problems are NP-hard, it is challenging to design effective algorithms for them. Recently, deep learning has achieved promising performances in solving combinatorial optimization problems. However, existing supervised learning-based methods are limited by the absence of labeled instances, while reinforcement learning-based methods tend to be hard to train and converge slowly for large instances. In this paper, we propose a self-supervised model named GCOM to address NP-hard graph clustering optimization problems. It adopts a pre-training and fine-tuning framework. In the pre-training process, we utilize graph contrastive learning to mine the latent clustering relations and useful optimization strategies, which can be generalized to the downstream tasks. Additionally, two effective graph encodings are introduced to enhance the expressive power of our model. We evaluate our model on facility location problem (FLP) and balanced graph partitioning (BGP). Extensive experiments conducted on both synthetic and real-world datasets validate superior performance, strong generalization ability and high sample-efficiency of our model.