EGAM: Extended Graph Attention Model for Solving Routing Problems

2026-01-29

AI Summary

This work addresses the limitation of conventional graph attention models in path planning, which rely solely on node features and neglect edge information, thereby constraining their representational capacity. To overcome this, the authors propose the Extended Graph Attention Model (EGAM), which, for the first time, jointly models dynamic embeddings of both nodes and edges within the graph attention mechanism. EGAM synchronously updates these representations using a multi-head dot-product attention mechanism and is trained end-to-end via an autoregressive encoder–decoder architecture combined with a policy gradient reinforcement learning algorithm enhanced by a tailored baseline. Experimental results demonstrate that EGAM achieves competitive or superior performance compared to existing methods across multiple routing problems, with particularly significant improvements in highly constrained scenarios, confirming its effectiveness in modeling complex graph structures.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Machine Learning: Graph-based Machine Learning
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Neural combinatorial optimization (NCO) solvers, implemented with graph neural networks (GNNs), have introduced new approaches for solving routing problems. Trained with reinforcement learning (RL), the state-of-the-art graph attention model (GAM) achieves near-optimal solutions without requiring expert knowledge or labeled data. In this work, we generalize the existing graph attention mechanism and propose the extended graph attention model (EGAM). Our model utilizes multi-head dot-product attention to update both node and edge embeddings, addressing the limitations of the conventional GAM, which considers only node features. We employ an autoregressive encoder-decoder architecture and train it with policy gradient algorithms that incorporate a specially designed baseline. Experiments show that EGAM matches or outperforms existing methods across various routing problems. Notably, the proposed model demonstrates exceptional performance on highly constrained problems, highlighting its efficiency in handling complex graph structures.

Problem

• routing problems
• graph attention
• neural combinatorial optimization
• edge embeddings
• constrained optimization

Innovation

• Extended Graph Attention Model
• Multi-head Dot-product Attention
• Edge Embedding
• Neural Combinatorial Optimization
• Autoregressive Encoder-Decoder