EGAM: Extended Graph Attention Model for Solving Routing Problems

TL;DR

EGAM tackles NP-hard routing problems by extending graph attention to jointly update node and edge embeddings through Edge-Node and Node-Edge attention within an autoregressive encoder-decoder framework. Trained with REINFORCE and a symmetry-based baseline, EGAM achieves near-optimal solutions without labeled data, excelling particularly on highly constrained problems such as TSPTW, TSPDL, and VRPTW. Key contributions include a generalized attention mechanism over graphs, a scalable encoder-decoder architecture with integrated attention layers, and a baseline that leverages problem symmetries to improve sample efficiency. The results demonstrate that edge-aware EGAM matches or surpasses state-of-the-art RL-based NCO solvers across diverse routing problems and scales favorably to more complex graph structures, offering a versatile framework for broader graph-structured combinatorial optimization.

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.

Figures (10)

• Figure 1: Illustration of the proposed egam structure. The rounded rectangles represent trainable network layers, while the ellipses denote the output variables. For simplicity, the residual connections of the MHA and feed-forward layers are omitted. Arrows indicate the data flow from the problem input to the sequence generation. In a single decision process, the encoder runs only once, while the decoder operates repeatedly until the full route is generated.
• Figure 2: Evolution of the training loss and cost for TSP
• Figure 3: Evolution of the validation cost for TSP
• Figure 4: Evolution of the training cost and feasible rate for TSPDL
• Figure 5: Evolution of the validation cost and feasible rate for TSPDL