Vehicle Routing Problems via Quantum Graph Attention Network Deep Reinforcement Learning

TL;DR

This paper introduces a quantum-enhanced graph attention network within a deep reinforcement learning framework to improve vehicle routing solutions, achieving faster convergence and lower costs compared to classical methods.

Contribution

It presents a novel Quantum Graph Attention Network (Q-GAT) that replaces MLPs with parameterized quantum circuits, reducing parameters and enhancing efficiency in vehicle routing problems.

Findings

Q-GAT reduces trainable parameters by over 50%.

Q-GAT achieves about 5% lower routing costs.

Q-GAT converges faster than classical GAT models.

Abstract

The vehicle routing problem (VRP) is a fundamental NP-hard task in intelligent transportation systems with broad applications in logistics and distribution. Deep reinforcement learning (DRL) with Graph Neural Networks (GNNs) has shown promise, yet classical models rely on large multi-layer perceptrons (MLPs) that are parameter-heavy and memory-bound. We propose a Quantum Graph Attention Network (Q-GAT) within a DRL framework, where parameterized quantum circuits (PQCs) replace conventional MLPs at critical readout stages. The hybrid model maintains the expressive capacity of graph attention encoders while reducing trainable parameters by more than 50%. Using proximal policy optimization (PPO) with greedy and stochastic decoding, experiments on VRP benchmarks show that Q-GAT achieves faster convergence and reduces routing cost by about 5% compared with classical GAT baselines. These results demonstrate the potential of PQC-enhanced GNNs as compact and effective solvers for large-scale routing and logistics optimization.