arXiv 2602.236852026-02math.OC

具有资源受限取货和送货的车辆路径问题

Vehicle Routing Problem with Resource-Constrained Pickup and Delivery

University of Rhode Island（罗德岛大学）

Manbir Sodhi, Romesh Prasad, Harishjitu Saseendran

备注：: 23 pages, 1 figure

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AI总结：

研究提出VRP-RPD问题，通过不同车辆处理同一地点的装卸任务，减少计算复杂度，采用GPU加速的ALNS和BRKGA算法在多个基准测试中实现最优解，使makespan减少达74%。

摘要：

我们引入了具有资源受限取货和送货的车辆路径问题（VRP-RPD），其中车辆将有限的相同资源运输到客户地点，以便在自主处理后进行检索和再部署。与经典取货和送货问题不同，VRP-RPD允许不同车辆处理同一地点的送货和取货，产生不存在于标准公式中的跨路线依赖性。这种解耦反映了自动驾驶机器人部署、便携式医疗设备分发、灾难救援操作、建筑工具租赁和农业传感器网络等实际场景，其中运输车辆是稀缺资源，且在处理过程中不需要等待。目标是最小化makespan，定义为最后一辆车在所有资源部署、处理和检索后返回的时间。尽管makespan目标在调度问题中很常见，但相对于处理持续时间的显著运输时间和资源容量限制从根本上改变了优化考虑。我们证明，对于超过16个客户的问题实例，精确方法在计算上是不可行的。我们开发了一个分阶段的元启发式管道：首先运行GPU加速的自适应大邻域搜索（ALNS）以获得高质量的当前解，然后将其编码为Biased Random-Key Genetic Algorithm（BRKGA）的预热起始种子，通过进化搜索优化解。在TSPlib衍生的基准测试（17-1000个节点）上评估，该管道在多个处理时间变体（基础、2x、5x、1R10、1R20）中始终实现最优解，所有实例大小上都优于基线启发式方法，使makespan减少高达74%。

英文摘要：

We introduce the Vehicle Routing Problem with Resource-Constrained Pickup and Delivery (VRP-RPD), where vehicles transport finite identical resources to customer locations for autonomous processing before retrieval and redeployment. Unlike classical pickup-and-delivery problems where the same vehicle must perform both operations for each customer, VRP-RPD permits different vehicles to handle dropoff and pickup at the same location, creating inter-route dependencies absent from standard formulations. This decoupling reflects practical scenarios in autonomous robotics deployment, portable medical equipment distribution, disaster relief operations, construction tool rental, and agricultural sensor networks, where transport vehicles are the scarce resource and need not wait during processing. The objective is to minimize makespan, defined as the time when the last vehicle returns after all resources are deployed, processed, and retrieved. Although makespan objectives are typical in scheduling problems, the significant transportation times relative to processing durations and the resource capacity constraints fundamentally alter optimization considerations. We demonstrate that exact methods are computationally intractable for instances beyond 16 customers. We develop a sequential two-stage metaheuristic pipeline: a GPU-accelerated Adaptive Large Neighborhood Search (ALNS) is run first to obtain a high-quality incumbent, which is then encoded as a warm-start seed for a Biased Random-Key Genetic Algorithm (BRKGA) that refines the solution through evolutionary search. Evaluated on TSPlib-derived benchmarks (17-1000 nodes) across multiple processing time variants (base, 2x, 5x, 1R10, 1R20), the pipeline consistently achieves the best solutions across all instance sizes, reducing makespan by up to 74% over baseline heuristics.

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