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Cluster-Aware Attention-Based Deep Reinforcement Learning for Pickup and Delivery Problems

arXiv:2603.10053v1 Announce Type: new Abstract: The Pickup and Delivery Problem (PDP) is a fundamental and challenging variant of the Vehicle Routing Problem, characterized by tightly coupled pickup--delivery pairs, precedence constraints, and spatial layouts that often exhibit clustering. Existing deep reinforcement learning (DRL) approaches either model all nodes on a flat graph, relying on implicit learning to enforce constraints, or achieve strong performance through inference-time collaborative search at the cost of substantial latency. In this paper, we propose \emph{CAADRL} (Cluster-Aware Attention-based Deep Reinforcement Learning), a DRL framework that explicitly exploits the multi-scale structure of PDP instances via cluster-aware encoding and hierarchical decoding. The encoder builds on a Transformer and combines global self-attention with intra-cluster attention over depot, pickup, and delivery nodes, producing embeddings that are both globally informative and locally role

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Wentao Wang, Lifeng Han, Guangyu Zou · · 1 min read · 7 views
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arXiv:2603.10053v1 Announce Type: new Abstract: The Pickup and Delivery Problem (PDP) is a fundamental and challenging variant of the Vehicle Routing Problem, characterized by tightly coupled pickup--delivery pairs, precedence constraints, and spatial layouts that often exhibit clustering. Existing deep reinforcement learning (DRL) approaches either model all nodes on a flat graph, relying on implicit learning to enforce constraints, or achieve strong performance through inference-time collaborative search at the cost of substantial latency. In this paper, we propose \emph{CAADRL} (Cluster-Aware Attention-based Deep Reinforcement Learning), a DRL framework that explicitly exploits the multi-scale structure of PDP instances via cluster-aware encoding and hierarchical decoding. The encoder builds on a Transformer and combines global self-attention with intra-cluster attention over depot, pickup, and delivery nodes, producing embeddings that are both globally informative and locally role-aware. Based on these embeddings, we introduce a Dynamic Dual-Decoder with a learnable gate that balances intra-cluster routing and inter-cluster transitions at each step. The policy is trained end-to-end with a POMO-style policy gradient scheme using multiple symmetric rollouts per instance. Experiments on synthetic clustered and uniform PDP benchmarks show that CAADRL matches or improves upon strong state-of-the-art baselines on clustered instances and remains highly competitive on uniform instances, particularly as problem size increases. Crucially, our method achieves these results with substantially lower inference time than neural collaborative-search baselines, suggesting that explicitly modeling cluster structure provides an effective and efficient inductive bias for neural PDP solvers.

Executive Summary

The article proposes a novel deep reinforcement learning framework, Cluster-Aware Attention-based Deep Reinforcement Learning (CAADRL), to tackle the Pickup and Delivery Problem (PDP). CAADRL leverages a Transformer-based encoder to model the multi-scale structure of PDP instances, incorporating global self-attention and intra-cluster attention. The framework's Dynamic Dual-Decoder balances intra-cluster routing and inter-cluster transitions, achieving strong performance on clustered and uniform PDP benchmarks. Importantly, CAADRL significantly reduces inference time compared to neural collaborative-search baselines. The results demonstrate the effectiveness and efficiency of explicitly modeling cluster structure in PDP solvers.

Key Points

  • ▸ CAADRL employs a Transformer-based encoder with global self-attention and intra-cluster attention for modeling PDP instances.
  • ▸ The Dynamic Dual-Decoder balances intra-cluster routing and inter-cluster transitions for improved performance.
  • ▸ CAADRL achieves strong performance on both clustered and uniform PDP benchmarks.

Merits

Strength in Modeling Cluster Structure

CAADRL's explicit modeling of cluster structure provides an effective inductive bias for neural PDP solvers, leading to improved performance and reduced inference time.

Improved Performance on Clustering Instances

CAADRL matches or improves upon state-of-the-art baselines on clustered instances, demonstrating its effectiveness in tackling complex PDP scenarios.

Demerits

Limited Generalizability to Non-Clustered Instances

While CAADRL performs well on clustered instances, its performance on uniform instances may not be as strong, highlighting the need for further research on non-clustered scenarios.

Computational Complexity of Dynamic Dual-Decoder

The Dynamic Dual-Decoder's learnable gate may introduce computational complexity, which could impact the method's scalability for large problem sizes.

Expert Commentary

The article presents a significant advancement in the field of PDP solvers, leveraging the power of Transformer-based encoding and dynamic decoders to tackle the complexities of clustering instances. While the method's performance on uniform instances may not be as strong, the results demonstrate the effectiveness of explicitly modeling cluster structure in PDP solvers. Furthermore, the article's focus on reducing inference time highlights the importance of computational efficiency in real-world applications. As the field continues to evolve, it will be essential to explore the potential of CAADRL in tackling more complex PDP scenarios and adapting the framework to other variants of the Vehicle Routing Problem.

Recommendations

  • ✓ Future research should focus on adapting CAADRL to tackle non-clustered instances and exploring the potential of the Dynamic Dual-Decoder for other variants of the Vehicle Routing Problem.
  • ✓ Practitioners and policymakers should consider the benefits of explicitly modeling cluster structure in PDP solvers to improve the efficiency and effectiveness of logistics operations.

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