Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using convolutional neural networks (CNNs) on graph images to predict the cardinality of combinatorial properties of random graphs and networks. Specifically, we use image representations of modified adjacency matrices of random graphs as training samples for a CNN model to predict the stability number of random graphs; where the stability number is the cardinality of a maximum set of vertices containing no pairwise adjacency. Our approach demonstrates the potential for applying deep learning in combinatorial optimization problems.

翻译：图组合优化问题具有广泛适用性且计算难度极高，例如旅行商问题或设施选址问题。本文探讨了在图图像上应用卷积神经网络（CNNs）预测随机图与网络组合性质基数的可行性。具体而言，我们将随机图修正邻接矩阵的图像表示作为CNN模型的训练样本，以预测随机图的稳定数；其中稳定数是指不含成对邻接关系的最大顶点集的基数。我们的方法展示了深度学习在组合优化问题中的应用潜力。