From Comparison to Selection: Enhancing Cross-Scale Generalization of Pointer Networks Trained with Reinforcement Learning for for Capacitated Vehicle Routing Problem

The task of constructing vehicles optimal routes for pickup and delivery of goods is one of most promising tasks in the context of global urban population growth. Although this kind of problems with small size can be solved by various classical approaches, a fast (or realtime) route optimizer under the constraints of the real world (such as capacity and time windows constraints) for medium-large size problems still remains a highly challenging task. In this work we, for the first time, successfully applied a deep Reinforcing Learning approach (modified JAMPR model) to solve Pickup and Delivery problem with Capacity and Time Window constraints (CPDPTW). We obtained a robust model that gives a fast optimal solution for problems of small and medium size, and gives fast suboptimal solution for problems of larger (> 200) size.

We study an integrated pickup-and-delivery problem on sparse, non-Euclidean networks that jointly optimizes cyclic routing, cargo flow allocation, and cross-cycle service. The tight coupling of these operational constraints creates a complex discrete-continuous decision space with highly restricted feasible regions. To overcome these computational challenges, we propose Double-Channel Graph Attention (DCGA), an end-to-end reinforcement learning framework. DCGA isolates network reachability and demand-service logic into separate graph channels and constructs valid routes using a simulator-coupled, constraint-informed decoder. Experiments on LinerLib benchmarks demonstrate that DCGA achieves seconds-level inference and delivers state-of-the-art solution quality on instances beyond a specific scale, with its advantage over existing baselines widening significantly as problem size increases. Supported by extensive stability and ablation analyses, our results demonstrate that this structure-aware learning approach provides an effective, low-latency engine for realistic routing-and-flow optimization.

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 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.