Enhancing Machine Learning Approaches for Graph Optimization Problems with Diversifying Graph Augmentation

Recently, many machine learning-based approaches that effectively solve graph optimization problems have been proposed. These approaches are usually trained on graphs randomly generated with graph generators or sampled from existing datasets. However, we observe that such training graphs lead to poor testing performance if the testing graphs are not generated analogously, i.e., the generalibility of the models trained on those randomly generated training graphs are very limited. To address this critical issue, in this paper, we propose a new framework, named Learning with Iterative Graph Diversification (LIGD), and formulate a new research problem, named Diverse Graph Modification Problem (DGMP), that iteratively generate diversified training graphs and train the models that solve graph optimization problems to significantly improve their performance. We propose three approaches to solve DGMP by considering both the performance of the machine-learning approaches and the structural properties of the training graphs. Experimental results on well-known problems show that our proposed approaches significantly boost the performance of both supervised and reinforcement learning approaches and produce near-optimal results, significantly outperforming the baseline approaches, such as graph augmentation and deep learning-based graph generation approaches.