A GREAT Architecture for Edge-Based Graph Problems Like TSP

2024-08-29

arXiv.org

AI Summary

Existing GNN- or Transformer-based combinatorial optimization methods predominantly rely on Euclidean coordinates, limiting their modeling capability on dense-edge graph problems such as non-Euclidean and asymmetric TSP. This paper introduces GREAT, the first graph neural architecture explicitly designed for edge prediction. Methodologically, GREAT features: (1) a novel edge-wise attention mechanism that overcomes classical GNN bottlenecks in dense graphs and non-Euclidean spaces; (2) unified support for both Euclidean and non-Euclidean, symmetric and asymmetric TSP formulations; and (3) interpretable graph sparsification via supervised edge classification—retaining fewer than 5% of original edges while covering a high proportion of optimal edges. Integrated with reinforcement learning for policy optimization, GREAT achieves state-of-the-art performance across multiple TSP benchmarks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In the last years, many neural network-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, GNNs are inherently not well suited to operate on dense graphs, such as in routing problems. Furthermore, models operating on Euclidean coordinates cannot be applied to non-Euclidean versions of routing problems that are often found in real-world settings. To overcome these limitations, we propose a novel GNN-related edge-based neural model called Graph Edge Attention Network (GREAT). We evaluate the performance of GREAT in the edge-classification task to predict optimal edges in the Traveling Salesman Problem (TSP). We can use such a trained GREAT model to produce sparse TSP graph instances, keeping only the edges GREAT finds promising. Compared to other, non-learning-based methods to sparsify TSP graphs, GREAT can produce very sparse graphs while keeping most of the optimal edges. Furthermore, we build a reinforcement learning-based GREAT framework which we apply to Euclidean and non-Euclidean asymmetric TSP. This framework achieves state-of-the-art results.

Problem

• Solving non-Euclidean asymmetric graph routing problems
• Proposing edge-focused GNN model for combinatorial optimization
• Handling real-world variants like TSP and CVRP

Innovation

• Edge-focused GNN model for routing problems
• Reinforcement learning with GREAT encoder
• Handles non-Euclidean asymmetric instances