EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems

TL;DR

EFormer introduces an edge-based Transformer model for vehicle routing problems that effectively utilizes edge information, employing a novel encoding and decoding strategy, and demonstrates superior performance and generalization on synthetic and real-world datasets.

Contribution

The paper presents EFormer, a novel edge-based Transformer architecture with a dual-encoder design and reinforcement learning training, improving VRP solutions over existing methods.

Findings

Outperforms baseline models on synthetic datasets.

Shows strong generalization to real-world instances.

Effective in large-scale and diverse VRP scenarios.

Abstract

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer's core design in solving VRPs.