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We present a synergistic hybrid framework for the Multi-Objective Vehicle Routing Problem with Time Windows (MOVRPTW), integrating Weight-Aware Deep Reinforcement Learning (WADRL) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) to jointly minimize total travel distance and fleet size. While traditional methods falter under scalability and dynamic constraints, standalone DRL suffers from poor sample efficiency, and NSGA-II lacks adaptive learning capabilities. To bridge this gap, we embed objective weights (w1, w2) directly into the agent’s state representation and reward function, enabling the DRL agent to generate an initial, preference-aware policy population. NSGA-II then evolves this population into a diverse, high-quality Pareto front. Elite policies from this front populate a dynamic replay buffer; once sufficient coverage is achieved, they trigger targeted DRL retraining. The refined policy subsequently generates improved candidate solutions, closing a self-reinforcing optimization loop. Convergence is determined by policy stability or Pareto front saturation. This closed-loop synergy not only enhances exploration and adaptively balances competing objectives but also significantly boosts sample efficiency. Extensive experiments demonstrate that our framework consistently outperforms both pure DRL and standalone evolutionary approaches, delivering scalable, high-quality, and practically viable solutions for real-world logistics operations.

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Weight-Aware Synergy of Deep Reinforcement Learning and Evolutionary Algorithms for Multi-Objective VRPTW

  • 会议论文

  • 发表日期：

    2026年

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  • Le Fang,
  • Yanyan Guo

摘要

We present a synergistic hybrid framework for the Multi-Objective Vehicle Routing Problem with Time Windows (MOVRPTW), integrating Weight-Aware Deep Reinforcement Learning (WADRL) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) to jointly minimize total travel distance and fleet size. While traditional methods falter under scalability and dynamic constraints, standalone DRL suffers from poor sample efficiency, and NSGA-II lacks adaptive learning capabilities. To bridge this gap, we embed objective weights (w1, w2) directly into the agent’s state representation and reward function, enabling the DRL agent to generate an initial, preference-aware policy population. NSGA-II then evolves this population into a diverse, high-quality Pareto front. Elite policies from this front populate a dynamic replay buffer; once sufficient coverage is achieved, they trigger targeted DRL retraining. The refined policy subsequently generates improved candidate solutions, closing a self-reinforcing optimization loop. Convergence is determined by policy stability or Pareto front saturation. This closed-loop synergy not only enhances exploration and adaptively balances competing objectives but also significantly boosts sample efficiency. Extensive experiments demonstrate that our framework consistently outperforms both pure DRL and standalone evolutionary approaches, delivering scalable, high-quality, and practically viable solutions for real-world logistics operations.