Optimizing Nursing Care Taxi Dispatch Leveraging Integer Linear Programming Solvers and Machine Learning

In recent years, the growing complexity of last-mile pickup operations has increased the need for fast and accurate decision-making on logistics platforms. This challenge is fundamentally driven by two key and tightly coupled decision-making processes: order dispatching and routing. Solving them separately overlooks their interdependence, while fully end-to-end learning can be unstable and costly on large, variable-scale instances due to sparse rewards. To solve this problem, we propose an integrated optimization framework which couples a learned routing oracle with real-time dispatching heuristics. For the routing subproblem, we develop a Dynamic-Residual Graph Attention Network encoder with a Look-Ahead Courier-Personalized decoder. For the dispatching subproblem, we develop a routing-oracle-guided dispatching heuristic with local search, where the oracle provides near-optimal solutions to select candidate couriers while retaining real-time scalability. Extensive experiments on real-world datasets from Cainiao Logistics are used to test the performance of our approach, including an offline evaluation and an online rolling-horizon simulation. The experimental results show that our approach outperforms other benchmarks regarding solution quality and solving time, indicating it can effectively support logistics companies in solving real-time and large-scale last-mile pickup problems.

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity to spatial symmetries, and brittle out-of-distribution behavior. We revisit the classical Cluster-First-Route-Second (CFRS) paradigm -- long known to be asymptotically optimal but largely overlooked by NCO -- and argue that it is structurally aligned with the core strengths of deep learning: similarity and assignment over global context, rather than the construction of long sequential tours. We introduce Neural CFRS, the first purely non-autoregressive one-shot neural CFRS framework for the CVRP. It enforces global fleet-capacity constraints end-to-end via a differentiable entropic Optimal Transport layer, producing a continuous transport plan to sparsify an exact capacitated assignment solver. We provide formal theoretical guarantees that our architecture intrinsically abstracts away $E(2)$ spatial, inter-route permutation, and intra-route traversal symmetries. By equipping the framework with a pre-trained spatial vocabulary, we unlock extreme parameter efficiency and zero-shot scaling. Designed primarily for real-world spatial distributions under a constant capacity setting, Neural CFRS scales robustly to out-of-distribution $N=1000$ instances with a < 4% gap -- retaining an approximate 5% gap at this scale even as an ultra-lightweight, single-layer architecture. Furthermore, when deployed out-of-the-box on standard benchmarks, we achieve a highly competitive 2.73% optimality gap on size-100 problems.

Solving practical multi-depot vehicle routing problems (MDVRP) is a challenging optimization task central to modern logistics, increasingly driven by e-commerce. To address the MDVRP's computational complexity, neural-based combinatorial optimization methods offer a promising scalable alternative to traditional approaches. However, neural-based methods typically rely on rigid architectures and input encodings tailored to specific problem formulations. In real-world settings, heterogeneous constraints create multiple MDVRP variants, limiting the applicability of such models. While multi-task learning (MTL) has begun to accelerate the development of unified neural-based solvers, prior works focus almost exclusively on single-depot VRPs, leaving the MDVRP unaddressed. To bridge this gap, we propose Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing (FiLMMeD), a novel unified neural-based model for 24 different MDVRP variants. We introduce three main contributions: (1) to improve the model's generalization, we augment the standard Transformer encoder with Feature-wise Linear Modulation (FiLM), which dynamically conditions learned internal representations based on the active set of constraints; (2) we provide an initial demonstration of Preference Optimization in the MTL setting, establishing it as a superior alternative to Reinforcement Learning for future MTL works; (3) to mitigate the generalization gap caused by the introduction of multi-depot constraints, we introduce a targeted curriculum learning strategy that progressively exposes the model to increasingly more complex constraint interactions. Extensive experiments on 24 MDVRP variants (including 8 novel formulations) and 16 single-depot VRPs confirm the effectiveness of FiLMMeD, which consistently outperforms state-of-the-art baselines. Our code is available at: https://github.com/AJ-Correa/FiLMMeD/tree/main