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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 ).

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Hybrid Learning and Optimization Methods for Solving Capacitated Vehicle Routing Problem

  • 会议论文

  • 发表日期：

    2026年

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  • Monit Sharma,
  • Hoong Chuin Lau

摘要

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 ).