A GREAT Architecture for Edge-Based Graph Problems Like TSP

TL;DR

This paper introduces GREAT, a graph neural network architecture designed for edge-based routing problems, capable of handling both Euclidean and non-Euclidean costs, and demonstrates its effectiveness on various vehicle routing problems.

Contribution

The paper presents a novel GNN model called GREAT that effectively addresses non-Euclidean routing problems, expanding the applicability of learning-based approaches.

Findings

GREAT achieves competitive results on non-Euclidean routing problems.

The framework successfully handles both Euclidean and non-Euclidean variants.

It is among the first to address non-Euclidean vehicle routing problems with learning-based methods.

Abstract

In the last years, an increasing number of learning-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related transformers, operating on the Euclidean coordinates representing the routing problems. However, such models are ill-suited for a wide range of real-world problems that feature non-Euclidean and asymmetric edge costs. To overcome this limitation, we propose a novel GNN-based and edge-focused neural model called Graph Edge Attention Network (GREAT). Using GREAT as an encoder to capture the properties of a routing problem instance, we build a reinforcement learning framework which we apply to both Euclidean and non-Euclidean variants of vehicle routing problems such as Traveling Salesman Problem, Capacitated Vehicle Routing Problem and Orienteering Problem. Our framework is among the first to tackle non-Euclidean variants of these problems and achieves competitive results among learning-based benchmarks.