Publication Type

Conference Proceeding Article

Version

acceptedVersion

Publication Date

1-2026

Abstract

We propose a hybrid quantum–classical framework for the Capacitated Vehicle Routing Problem (CVRP) that integrates the Augmented Lagrangian Method (ALM) with deep reinforcement learning (RL). Directly solving CVRP via Variational Quantum Eigensolver (VQE) requires a slack-based QUBO formulation, where converting inequalities to equalities greatly increases the qubit count. To circumvent this, we employ an ALM-based reformulation that enforces constraints through Lagrange terms instead of slack variables, drastically reducing quantum resource demands. An RL agent, trained with Soft Actor–Critic, adaptively tunes the Lagrange penalties to improve convergence and feasibility. Experiments show that RL-Q-ALM outperforms static-penalty and plain VQE baselines in both solution quality and convergence stability, demonstrating RL’s potential for scalable, adaptive quantum optimization (Code available at: https://github.com/SMU-Quantum/adaptive_quantum_cvrp).

Keywords

Augmented Lagrangian Method; Capacitated Vehicle Routing Problem; Hybrid Quantum-Classical Computing; Quantum Optimization; QUBO; Reinforcement Learning; Soft Actor-Critic; Variational Quantum Eigensolver

Discipline

Numerical Analysis and Scientific Computing | Operations Research, Systems Engineering and Industrial Engineering

Research Areas

Intelligent Systems and Optimization

Publication

Quantum Computing and Artificial Intelligence: 2nd International Workshop, QC+AI 2026, Singapore, January 27: Proceedings

First Page

13

Last Page

33

ISBN

9783032176240

Identifier

10.1007/978-3-032-17625-7_2

Publisher

Springer

City or Country

Cham

Additional URL

https://doi.org/10.1007/978-3-032-17625-7_2

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