空间信息增强型图神经网络TSP算法选择问题的再探讨
Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networks
摘要：
算法选择是一个众所周知的问题，研究人员研究如何构建代表问题实例的有用特征，然后应用基于特征的机器学习模型来预测哪种算法最适合给定实例。然而，即使是简单的优化问题，如欧几里德旅行商问题（TSP），缺乏一个通用的和有效的特征表示的问题实例。基于广泛的领域知识和对解决方案的后分析，TSP的重要特征在文献中得到了相对较好的理解。近年来，卷积神经网络（CNN）已成为一种流行的TSP算法选择方法。与传统的基于特征的机器学习模型相比，CNN具有自动特征学习能力，并且需要较少的领域专业知识。然而，仍然需要生成中间表示，即，多个图像首先表示TSP实例。在本文中，我们重新审视TSP的算法选择问题，并提出了一种新的图神经网络（GNN），称为GINES。GINES将城市的坐标和城市之间的距离作为输入。它由一种新的消息传递机制和一个局部邻域特征提取器组成，用于学习TSP实例的空间信息。我们在两个基准数据集上评估GINES。实验结果表明，GINES模型的性能优于CNN和原始GINE模型。它比传统的手工制作的基于特征的方法在一个数据集上更好。代码和数据集将在本文的最终版本中发布。
英文摘要：
Algorithm selection is a well-known problem where researchers investigate how to construct useful features representing the problem instances and then apply feature-based machine learning models to predict which algorithm works best with the given instance. However, even for simple optimization problems such as Euclidean Traveling Salesman Problem (TSP), there lacks a general and effective feature representation for problem instances. The important features of TSP are relatively well understood in the literature, based on extensive domain knowledge and post-analysis of the solutions. In recent years, Convolutional Neural Network (CNN) has become a popular approach to select algorithms for TSP. Compared to traditional feature-based machine learning models, CNN has an automatic feature-learning ability and demands less domain expertise. However, it is still required to generate intermediate representations, i.e., multiple images to represent TSP instances first. In this paper, we revisit the algorithm selection problem for TSP, and propose a novel Graph Neural Network (GNN), called GINES. GINES takes the coordinates of cities and distances between cities as input. It is composed of a new message-passing mechanism and a local neighborhood feature extractor to learn spatial information of TSP instances. We evaluate GINES on two benchmark datasets. The results show that GINES outperforms CNN and the original GINE models. It is better than the traditional handcrafted feature-based approach on one dataset. The code and dataset will be released in the final version of this paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
