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.

翻译：算法选择是一个经典问题，研究者探索如何构建表示问题实例的有效特征，并基于特征驱动的机器学习模型预测适用于给定实例的最优算法。然而，即使对于欧几里得旅行商问题（TSP）这类简单优化问题，仍缺乏通用且有效的问题实例特征表示方法。文献中基于大量领域知识与解的后分析，对TSP的关键特征已有相对清晰的理解。近年来，卷积神经网络（CNN）成为TSP算法选择的主流方法。与传统基于特征的机器学习模型相比，CNN具备自动特征学习能力，降低了领域专业知识的要求，但仍需首先生成中间表示（即多幅图像）来表征TSP实例。本文重新审视TSP的算法选择问题，提出一种新型图神经网络——GINES。该模型以城市坐标及城市间距离作为输入，通过设计新的消息传递机制与局部邻域特征提取器，学习TSP实例的空间信息。我们在两个基准数据集上评估GINES，结果表明其性能优于CNN及原始GINE模型，且在一个数据集上超越传统人工特征方法。本文最终版本将开源代码与数据集。