Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networks

TL;DR

This paper introduces GINES, a novel graph neural network that directly utilizes spatial information of TSP instances, outperforming CNN and traditional methods in algorithm selection tasks.

Contribution

The paper proposes GINES, a new GNN model with a specialized message-passing mechanism for better TSP instance representation, advancing algorithm selection accuracy.

Findings

GINES outperforms CNN and original GINE models on benchmark datasets.

GINES surpasses traditional handcrafted feature-based approaches on at least one dataset.

The model effectively captures spatial information for improved TSP algorithm prediction.

Abstract

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.