Learning to Optimize: Joint Routing and Flow Allocation on Sparse Non-Euclidean Networks

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.

A Policy-Improved Deep Deterministic Policy Gradient Framework for the Discount Order Acceptance Strategy of Ride-hailing Drivers

The rapid expansion of platform integration has emerged as an effective solution to mitigate market fragmentation by consolidating multiple ride-hailing platforms into a single application. To address heterogeneous passenger preferences, third-party integrators provide Discount Express service delivered by express drivers at lower trip fares. For the individual platform, encouraging broader participation of drivers in Discount Express services has the potential to expand the accessible demand pool and improve matching efficiency, but often at the cost of reduced profit margins. This study aims to dynamically manage drivers' acceptance of Discount Express from the perspective of individual platforms. The lack of historical data under the new business model necessitates online learning. However, early-stage exploration through trial and error can be costly in practice, highlighting the need for reliable early-stage performance in real-world deployment. To address these challenges, this study formulates the decision regarding the proportion of drivers' acceptance behavior as a continuous control task. In response to the high stochasticity, the opaque matching mechanisms employed by third-party integrator, and the limited availability of historical data, we propose a policy-improved deep deterministic policy gradient (pi-DDPG) framework. The proposed framework incorporates a refiner module to boost policy performance during the early training phase, leverages a convolutional long short-term memory network to effectively capture complex spatiotemporal patterns, and adopts a prioritized experience replay mechanism to enhance learning efficiency. A simulator based on a real-world dataset is developed to validate the effectiveness of the proposed pi-DDPG. Numerical experiments demonstrate that pi-DDPG achieves superior learning efficiency and significantly reduces early-stage training losses.